eval_decls_feb04.json

[{"decl_name": "Prime.exists_mem_multiset_dvd", "module": "Mathlib.Algebra.BigOperators.Associated", "idx_in_module": 0, "gt_premises": ["Prime.dvd_or_dvd", "Multiset.induction_on", "Multiset.mem_cons_of_mem", "Multiset.prod_cons", "Multiset.mem_cons_self", "Prime.not_dvd_one"], "gt_hints": {"Prime.dvd_or_dvd": "notInSimpAll", "Multiset.induction_on": "notInSimpAll", "Multiset.mem_cons_of_mem": "notInSimpAll", "Multiset.prod_cons": "notInSimpAll", "Multiset.mem_cons_self": "notInSimpAll", "Prime.not_dvd_one": "notInSimpAll"}}, {"decl_name": "Fin.sum_pow_mul_eq_add_pow", "module": "Mathlib.Algebra.BigOperators.Fin", "idx_in_module": 63, "gt_premises": ["Finset.sum_congr", "Fintype.card_fin", "Fintype.sum_pow_mul_eq_add_pow"], "gt_hints": {"Finset.sum_congr": "notInSimpAll", "Fintype.card_fin": "notInSimpAll", "Fintype.sum_pow_mul_eq_add_pow": "notInSimpAll"}}, {"decl_name": "Fin.prod_congr'", "module": "Mathlib.Algebra.BigOperators.Fin", "idx_in_module": 76, "gt_premises": [], "gt_hints": {}}, {"decl_name": "Finset.sum_apply_ite", "module": "Mathlib.Algebra.BigOperators.Group.Finset", "idx_in_module": 388, "gt_premises": ["Finset.sum_apply_dite", "congr_arg\u2082", "Finset.sum_attach"], "gt_hints": {"Finset.sum_apply_dite": "notInSimpAll", "congr_arg\u2082": "notInSimpAll", "Finset.sum_attach": "notInSimpAll"}}, {"decl_name": "Fintype.prod_of_injective", "module": "Mathlib.Algebra.BigOperators.Group.Finset", "idx_in_module": 933, "gt_premises": ["Set.image_univ", "Finset.coe_univ", "Function.Injective.injOn", "Set.mapsTo_univ_iff", "Finset.mem_univ", "Finset.prod_of_injOn", "Set.mem_range", "Set.mem_univ"], "gt_hints": {"Set.image_univ": "notInSimpAll", "Finset.coe_univ": "notInSimpAll", "Function.Injective.injOn": "notInSimpAll", "Set.mapsTo_univ_iff": "notInSimpAll", "Finset.mem_univ": "notInSimpAll", "Finset.prod_of_injOn": "notInSimpAll", "Set.mem_range": "notInSimpAll", "Set.mem_univ": "notInSimpAll"}}, {"decl_name": "FGModuleCat.ihom_obj", "module": "Mathlib.Algebra.Category.FGModuleCat.Basic", "idx_in_module": 12, "gt_premises": [], "gt_hints": {}}, {"decl_name": "AddMagmaCat.addEquiv_coe_eq", "module": "Mathlib.Algebra.Category.Semigrp.Basic", "idx_in_module": 24, "gt_premises": [], "gt_hints": {}}, {"decl_name": "add_pow_prime_eq", "module": "Mathlib.Algebra.CharP.Lemmas", "idx_in_module": 13, "gt_premises": ["Commute.all", "Commute.add_pow_prime_eq"], "gt_hints": {"Commute.all": "notInSimpAll", "Commute.add_pow_prime_eq": "notInSimpAll"}}, {"decl_name": "iterateFrobenius_inj", "module": "Mathlib.Algebra.CharP.Reduced", "idx_in_module": 0, "gt_premises": ["sub_eq_zero", "IsReduced.eq_zero"], "gt_hints": {"sub_eq_zero": "notInSimpAll", "IsReduced.eq_zero": "notInSimpAll"}}, {"decl_name": "GenContFract.of_convs_eq_convs'", "module": "Mathlib.Algebra.ContinuedFractions.Computation.ApproximationCorollaries", "idx_in_module": 0, "gt_premises": ["ContFract.convs_eq_convs'"], "gt_hints": {"ContFract.convs_eq_convs'": "notInSimpAll"}}, {"decl_name": "DirectSum.support_of_subset", "module": "Mathlib.Algebra.DirectSum.Basic", "idx_in_module": 16, "gt_premises": ["DFinsupp.support_single_subset"], "gt_hints": {"DFinsupp.support_single_subset": "notInSimpAll"}}, {"decl_name": "one_div_add_one_div", "module": "Mathlib.Algebra.Field.Basic", "idx_in_module": 71, "gt_premises": ["Commute.all", "Commute.one_div_add_one_div"], "gt_hints": {"Commute.all": "notInSimpAll", "Commute.one_div_add_one_div": "notInSimpAll"}}, {"decl_name": "AddChar.map_nsmul_pow", "module": "Mathlib.Algebra.Group.AddChar", "idx_in_module": 16, "gt_premises": ["AddChar.map_nsmul_eq_pow"], "gt_hints": {"AddChar.map_nsmul_eq_pow": "notInSimpAll"}}, {"decl_name": "div_ne_one", "module": "Mathlib.Algebra.Group.Basic", "idx_in_module": 476, "gt_premises": ["div_eq_one"], "gt_hints": {"div_eq_one": "notInSimpAll"}}, {"decl_name": "AddSemigroup.ext", "module": "Mathlib.Algebra.Group.Defs", "idx_in_module": 25, "gt_premises": [], "gt_hints": {}}, {"decl_name": "RightCancelMonoid.toMonoid_injective", "module": "Mathlib.Algebra.Group.Ext", "idx_in_module": 33, "gt_premises": [], "gt_hints": {}}, {"decl_name": "MonoidHom.one_comp", "module": "Mathlib.Algebra.Group.Hom.Defs", "idx_in_module": 372, "gt_premises": [], "gt_hints": {}}, {"decl_name": "Set.mem_range_mulIndicator", "module": "Mathlib.Algebra.Group.Indicator", "idx_in_module": 140, "gt_premises": ["Set.mulIndicator", "Set.eq_univ_iff_forall", "funext", "Set.mem_image", "Set.mem_range", "ite_eq_iff"], "gt_hints": {"Set.mulIndicator": "unmodified", "Set.eq_univ_iff_forall": "unmodified", "funext": "notInSimpAll", "Set.mem_image": "notInSimpAll", "Set.mem_range": "notInSimpAll", "ite_eq_iff": "unmodified"}}, {"decl_name": "Sigma.curry_inv", "module": "Mathlib.Algebra.Group.Pi.Lemmas", "idx_in_module": 203, "gt_premises": [], "gt_hints": {}}, {"decl_name": "Finset.vsub_subset_vsub_left", "module": "Mathlib.Algebra.Group.Pointwise.Finset.Basic", "idx_in_module": 686, "gt_premises": ["Finset.image\u2082_subset_left"], "gt_hints": {"Finset.image\u2082_subset_left": "notInSimpAll"}}, {"decl_name": "Set.list_sum_singleton", "module": "Mathlib.Algebra.Group.Pointwise.Set.BigOperators", "idx_in_module": 45, "gt_premises": ["map_list_sum"], "gt_hints": {"map_list_sum": "notInSimpAll"}}, {"decl_name": "MonoidHom.restrict_range", "module": "Mathlib.Algebra.Group.Subgroup.Ker", "idx_in_module": 13, "gt_premises": ["funext", "SubgroupClass.toSubmonoidClass", "exists_prop_congr"], "gt_hints": {"funext": "notInSimpAll", "SubgroupClass.toSubmonoidClass": "notInSimpAll", "exists_prop_congr": "notInSimpAll"}}, {"decl_name": "AddSubgroup.closure_iUnion", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "idx_in_module": 195, "gt_premises": ["GaloisConnection.l_iSup", "GaloisInsertion.gc"], "gt_hints": {"GaloisConnection.l_iSup": "notInSimpAll", "GaloisInsertion.gc": "notInSimpAll"}}, {"decl_name": "Subgroup.closure_singleton_one", "module": "Mathlib.Algebra.Group.Subgroup.Lattice", "idx_in_module": 213, "gt_premises": ["Subgroup.eq_bot_iff_forall", "one_zpow", "Subgroup.mem_closure_singleton", "funext"], "gt_hints": {"Subgroup.eq_bot_iff_forall": "unmodified", "one_zpow": "notInSimpAll", "Subgroup.mem_closure_singleton": "unmodified", "funext": "notInSimpAll"}}, {"decl_name": "AddSubgroup.op_top", "module": "Mathlib.Algebra.Group.Subgroup.MulOppositeLemmas", "idx_in_module": 11, "gt_premises": [], "gt_hints": {}}, {"decl_name": "Subgroup.closure_induction_left", "module": "Mathlib.Algebra.Group.Subgroup.Pointwise", "idx_in_module": 44, "gt_premises": ["Submonoid.closure_induction_left", "OneMemClass.one_mem", "inv_inv", "Subgroup.closure_toSubmonoid", "MulMemClass.mul_mem", "Submonoid.subset_closure", "SubgroupClass.toSubmonoidClass", "SubmonoidClass.toOneMemClass", "InvMemClass.inv_mem", "Subgroup.subset_closure", "SubgroupClass.toInvMemClass", "SubmonoidClass.toMulMemClass"], "gt_hints": {"Submonoid.closure_induction_left": "notInSimpAll", "OneMemClass.one_mem": "notInSimpAll", "inv_inv": "notInSimpAll", "Subgroup.closure_toSubmonoid": "notInSimpAll", "MulMemClass.mul_mem": "notInSimpAll", "Submonoid.subset_closure": "notInSimpAll", "SubgroupClass.toSubmonoidClass": "notInSimpAll", "SubmonoidClass.toOneMemClass": "notInSimpAll", "InvMemClass.inv_mem": "notInSimpAll", "Subgroup.subset_closure": "notInSimpAll", "SubgroupClass.toInvMemClass": "notInSimpAll", "SubmonoidClass.toMulMemClass": "notInSimpAll"}}, {"decl_name": "Submonoid.pow_coe", "module": "Mathlib.Algebra.Group.Submonoid.Membership", "idx_in_module": 202, "gt_premises": [], "gt_hints": {}}, {"decl_name": "Function.support_subset_comp", "module": "Mathlib.Algebra.Group.Support", "idx_in_module": 87, "gt_premises": [], "gt_hints": {}}, {"decl_name": "Function.mulSupport_mul", "module": "Mathlib.Algebra.Group.Support", "idx_in_module": 110, "gt_premises": ["Function.mulSupport_binop_subset", "one_mul"], "gt_hints": {"Function.mulSupport_binop_subset": "notInSimpAll", "one_mul": "notInSimpAll"}}, {"decl_name": "IsUnit.mul_right_injective", "module": "Mathlib.Algebra.Group.Units.Basic", "idx_in_module": 136, "gt_premises": ["IsUnit.mul_left_cancel"], "gt_hints": {"IsUnit.mul_left_cancel": "notInSimpAll"}}, {"decl_name": "AddUnits.val_neg_eq_neg_val", "module": "Mathlib.Algebra.Group.Units.Defs", "idx_in_module": 143, "gt_premises": ["neg_eq_of_add_eq_zero_right", "AddUnits.add_neg"], "gt_hints": {"neg_eq_of_add_eq_zero_right": "notInSimpAll", "AddUnits.add_neg": "notInSimpAll"}}, {"decl_name": "IsAddUnit.add", "module": "Mathlib.Algebra.Group.Units.Defs", "idx_in_module": 200, "gt_premises": [], "gt_hints": {}}, {"decl_name": "isAddUnit_map_of_leftInverse", "module": "Mathlib.Algebra.Group.Units.Hom", "idx_in_module": 63, "gt_premises": ["IsAddUnit.of_leftInverse", "IsAddUnit.map"], "gt_hints": {"IsAddUnit.of_leftInverse": "notInSimpAll", "IsAddUnit.map": "notInSimpAll"}}, {"decl_name": "eq_div_iff", "module": "Mathlib.Algebra.GroupWithZero.Units.Basic", "idx_in_module": 107, "gt_premises": ["Ne.isUnit", "IsUnit.eq_div_iff"], "gt_hints": {"Ne.isUnit": "notInSimpAll", "IsUnit.eq_div_iff": "notInSimpAll"}}, {"decl_name": "CochainComplex.HomComplex.Cochain.shift_v'", "module": "Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift", "idx_in_module": 37, "gt_premises": ["Lean.Omega.LinearCombo.coordinate_eval_2", "HomologicalComplex.XIsoOfEq_rfl", "Lean.Omega.LinearCombo.coordinate_eval_3", "le_of_le_of_eq", "CochainComplex.HomComplex.Cochain.shift_v", "CochainComplex.shiftFunctor_obj_X", "Lean.Omega.LinearCombo.coordinate_eval_0", "Int.sub_eq_zero_of_eq", "CategoryTheory.Category.id_comp", "Lean.Omega.tidy_sat", "Lean.Omega.LinearCombo.add_eval", "CategoryTheory.Iso.refl_hom", "Int.add_one_le_of_lt", "Lean.Omega.Constraint.not_sat'_of_isImpossible", "add_comm", "of_decide_eq_true", "Int.lt_or_gt_of_ne", "Lean.Omega.combo_sat'", "Lean.Omega.Constraint.addInequality_sat", "Lean.Omega.Int.add_congr", "CategoryTheory.Category.comp_id", "CochainComplex.shiftFunctorObjXIso", "Int.sub_nonneg_of_le", "Lean.Omega.LinearCombo.coordinate_eval_1", "Decidable.byContradiction", "Lean.Omega.LinearCombo.sub_eval", "add_assoc", "Lean.Omega.Constraint.addEquality_sat", "Lean.Omega.Int.sub_congr", "CategoryTheory.Iso.refl_inv"], "gt_hints": {"Lean.Omega.LinearCombo.coordinate_eval_2": "notInSimpAll", "HomologicalComplex.XIsoOfEq_rfl": "unmodified", "Lean.Omega.LinearCombo.coordinate_eval_3": "notInSimpAll", "le_of_le_of_eq": "notInSimpAll", "CochainComplex.HomComplex.Cochain.shift_v": "notInSimpAll", "CochainComplex.shiftFunctor_obj_X": "unmodified", "Lean.Omega.LinearCombo.coordinate_eval_0": "notInSimpAll", "Int.sub_eq_zero_of_eq": "notInSimpAll", "CategoryTheory.Category.id_comp": "unmodified", "Lean.Omega.tidy_sat": "notInSimpAll", "Lean.Omega.LinearCombo.add_eval": "notInSimpAll", "CategoryTheory.Iso.refl_hom": "unmodified", "Int.add_one_le_of_lt": "notInSimpAll", "Lean.Omega.Constraint.not_sat'_of_isImpossible": "notInSimpAll", "add_comm": "notInSimpAll", "of_decide_eq_true": "notInSimpAll", "Int.lt_or_gt_of_ne": "notInSimpAll", "Lean.Omega.combo_sat'": "notInSimpAll", "Lean.Omega.Constraint.addInequality_sat": "notInSimpAll", "Lean.Omega.Int.add_congr": "notInSimpAll", "CategoryTheory.Category.comp_id": "unmodified", "CochainComplex.shiftFunctorObjXIso": "unmodified", "Int.sub_nonneg_of_le": "notInSimpAll", "Lean.Omega.LinearCombo.coordinate_eval_1": "notInSimpAll", "Decidable.byContradiction": "notInSimpAll", "Lean.Omega.LinearCombo.sub_eval": "notInSimpAll", "add_assoc": "notInSimpAll", "Lean.Omega.Constraint.addEquality_sat": "notInSimpAll", "Lean.Omega.Int.sub_congr": "notInSimpAll", "CategoryTheory.Iso.refl_inv": "unmodified"}}, {"decl_name": "CochainComplex.mappingCone.inl_v_fst_v", "module": "Mathlib.Algebra.Homology.HomotopyCategory.MappingCone", "idx_in_module": 7, "gt_premises": ["CochainComplex.mappingCone.inl.proof_1", "HomologicalComplex.homotopyCofiber.inlX_fstX", "add_neg_cancel_right", "CochainComplex.mappingCone.fst", "CochainComplex.mappingCone.inl"], "gt_hints": {"CochainComplex.mappingCone.inl.proof_1": "notInSimpAll", "HomologicalComplex.homotopyCofiber.inlX_fstX": "notInSimpAll", "add_neg_cancel_right": "notInSimpAll", "CochainComplex.mappingCone.fst": "unmodified", "CochainComplex.mappingCone.inl": "unmodified"}}, {"decl_name": "CochainComplex.mappingCone.d_fst_v", "module": "Mathlib.Algebra.Homology.HomotopyCategory.MappingCone", "idx_in_module": 134, "gt_premises": ["HomologicalComplex.homotopyCofiber.d_fstX"], "gt_hints": {"HomologicalComplex.homotopyCofiber.d_fstX": "notInSimpAll"}}, {"decl_name": "CochainComplex.mappingCone.triangle_mor\u2082", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "idx_in_module": 3, "gt_premises": ["CochainComplex.mappingCone.triangle.proof_1"], "gt_hints": {"CochainComplex.mappingCone.triangle.proof_1": "notInSimpAll"}}, {"decl_name": "CochainComplex.mappingCone.trianglehMapOfHomotopy_hom\u2082", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated", "idx_in_module": 42, "gt_premises": [], "gt_hints": {}}, {"decl_name": "CochainComplex.shiftFunctorAdd'_hom_app_f", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "idx_in_module": 16, "gt_premises": [], "gt_hints": {}}, {"decl_name": "CochainComplex.XIsoOfEq_shift", "module": "Mathlib.Algebra.Homology.HomotopyCategory.Shift", "idx_in_module": 61, "gt_premises": [], "gt_hints": {}}, {"decl_name": "HomologicalComplex.unopInverse_map", "module": "Mathlib.Algebra.Homology.Opposite", "idx_in_module": 55, "gt_premises": [], "gt_hints": {}}, {"decl_name": "CategoryTheory.ShortComplex.Exact.moduleCat_of_range_eq_ker", "module": "Mathlib.Algebra.Homology.ShortComplex.ModuleCat", "idx_in_module": 42, "gt_premises": ["le_refl"], "gt_hints": {"le_refl": "notInSimpAll"}}, {"decl_name": "CategoryTheory.ShortComplex.LeftHomologyMapData.natTransApp_\u03c6K", "module": "Mathlib.Algebra.Homology.ShortComplex.PreservesHomology", "idx_in_module": 167, "gt_premises": [], "gt_hints": {}}, {"decl_name": "CategoryTheory.ShortComplex.LeftHomologyData.unop_p", "module": "Mathlib.Algebra.Homology.ShortComplex.RightHomology", "idx_in_module": 106, "gt_premises": [], "gt_hints": {}}, {"decl_name": "HomologicalComplex\u2082.total.mapIso_inv", "module": "Mathlib.Algebra.Homology.TotalComplex", "idx_in_module": 177, "gt_premises": [], "gt_hints": {}}, {"decl_name": "commute_lmul_lmul_sq", "module": "Mathlib.Algebra.Jordan.Basic", "idx_in_module": 7, "gt_premises": ["IsJordan.lmul_lmul_comm_lmul", "AddMonoidHom.ext"], "gt_hints": {"IsJordan.lmul_lmul_comm_lmul": "notInSimpAll", "AddMonoidHom.ext": "notInSimpAll"}}, {"decl_name": "LieModuleHom.coe_linear_mk", "module": "Mathlib.Algebra.Lie.Basic", "idx_in_module": 186, "gt_premises": [], "gt_hints": {}}, {"decl_name": "LieModuleHom.smul_apply", "module": "Mathlib.Algebra.Lie.Basic", "idx_in_module": 213, "gt_premises": [], "gt_hints": {}}, {"decl_name": "LieModuleEquiv.refl_apply", "module": "Mathlib.Algebra.Lie.Basic", "idx_in_module": 243, "gt_premises": [], "gt_hints": {}}, {"decl_name": "LieDerivation.coe_neg", "module": "Mathlib.Algebra.Lie.Derivation.Basic", "idx_in_module": 43, "gt_premises": [], "gt_hints": {}}, {"decl_name": "LieSubmodule.mem_idealizer", "module": "Mathlib.Algebra.Lie.Normalizer", "idx_in_module": 29, "gt_premises": [], "gt_hints": {}}, {"decl_name": "LieIdeal.idealizer_eq_normalizer", "module": "Mathlib.Algebra.Lie.Normalizer", "idx_in_module": 30, "gt_premises": ["neg_mem_iff", "AddSubgroupClass.toNegMemClass", "LieSubmodule.ext", "lie_skew"], "gt_hints": {"neg_mem_iff": "unmodified", "AddSubgroupClass.toNegMemClass": "notInSimpAll", "LieSubmodule.ext": "notInSimpAll", "lie_skew": "notInSimpAll"}}, {"decl_name": "LieModule.genWeightSpace_zsmul_add_ne_bot", "module": "Mathlib.Algebra.Lie.Weights.Chain", "idx_in_module": 137, "gt_premises": ["smul_neg", "neg_smul", "Nat.cast_smul_eq_nsmul", "LieModule.genWeightSpace_nsmul_add_ne_bot_of_le"], "gt_hints": {"smul_neg": "notInSimpAll", "neg_smul": "notInSimpAll", "Nat.cast_smul_eq_nsmul": "notInSimpAll", "LieModule.genWeightSpace_nsmul_add_ne_bot_of_le": "notInSimpAll"}}, {"decl_name": "AddCommGroup.zsmul_modEq_zsmul", "module": "Mathlib.Algebra.ModEq", "idx_in_module": 44, "gt_premises": ["smul_sub", "smul_right_inj", "SMulCommClass.smul_comm"], "gt_hints": {"smul_sub": "notInSimpAll", "smul_right_inj": "notInSimpAll", "SMulCommClass.smul_comm": "notInSimpAll"}}, {"decl_name": "Submodule.coe_mk", "module": "Mathlib.Algebra.Module.Submodule.Defs", "idx_in_module": 43, "gt_premises": [], "gt_hints": {}}, {"decl_name": "Submodule.zero_eq_bot", "module": "Mathlib.Algebra.Module.Submodule.Pointwise", "idx_in_module": 27, "gt_premises": [], "gt_hints": {}}, {"decl_name": "Module.isTorsionBySet_quotient_iff", "module": "Mathlib.Algebra.Module.Torsion", "idx_in_module": 164, "gt_premises": ["Function.Surjective.forall", "Subtype.forall", "forall\u2082_congr", "Submodule.Quotient.mk_eq_zero", "Submodule.mkQ_surjective"], "gt_hints": {"Function.Surjective.forall": "notInSimpAll", "Subtype.forall": "notInSimpAll", "forall\u2082_congr": "notInSimpAll", "Submodule.Quotient.mk_eq_zero": "notInSimpAll", "Submodule.mkQ_surjective": "notInSimpAll"}}, {"decl_name": "AddMonoidAlgebra.single_mul_apply_of_not_exists_add", "module": "Mathlib.Algebra.MonoidAlgebra.Defs", "idx_in_module": 457, "gt_premises": ["MonoidAlgebra.single_mul_apply_of_not_exists_mul"], "gt_hints": {"MonoidAlgebra.single_mul_apply_of_not_exists_mul": "notInSimpAll"}}, {"decl_name": "AddMonoidAlgebra.Monic.leadingCoeff_mul_eq_right", "module": "Mathlib.Algebra.MonoidAlgebra.Degree", "idx_in_module": 221, "gt_premises": ["AddMonoidAlgebra.leadingCoeff.eq_1", "AddMonoidAlgebra.apply_supDegree_add_supDegree", "AddMonoidAlgebra.Monic.supDegree_mul_of_ne_zero_right", "MulZeroClass.mul_zero", "one_mul"], "gt_hints": {"AddMonoidAlgebra.leadingCoeff.eq_1": "notInSimpAll", "AddMonoidAlgebra.apply_supDegree_add_supDegree": "notInSimpAll", "AddMonoidAlgebra.Monic.supDegree_mul_of_ne_zero_right": "notInSimpAll", "MulZeroClass.mul_zero": "notInSimpAll", "one_mul": "notInSimpAll"}}, {"decl_name": "AddMonoidAlgebra.support_mul_single", "module": "Mathlib.Algebra.MonoidAlgebra.Support", "idx_in_module": 31, "gt_premises": ["MonoidAlgebra.support_mul_single"], "gt_hints": {"MonoidAlgebra.support_mul_single": "notInSimpAll"}}, {"decl_name": "MvPolynomial.hom_bind\u2081", "module": "Mathlib.Algebra.MvPolynomial.Monad", "idx_in_module": 56, "gt_premises": ["MvPolynomial.bind\u2081.eq_1", "MvPolynomial.algebraMap_eq", "MvPolynomial.map_aeval"], "gt_hints": {"MvPolynomial.bind\u2081.eq_1": "notInSimpAll", "MvPolynomial.algebraMap_eq": "notInSimpAll", "MvPolynomial.map_aeval": "notInSimpAll"}}, {"decl_name": "MvPolynomial.vars_sum_subset", "module": "Mathlib.Algebra.MvPolynomial.Variables", "idx_in_module": 56, "gt_premises": ["Finset.induction_on", "Finset.Subset.trans", "subset_refl", "MvPolynomial.vars_0", "MvPolynomial.vars_add_subset", "Finset.union_subset_union", "Finset.sum_insert", "Finset.biUnion_insert", "Finset.Subset.refl"], "gt_hints": {"Finset.induction_on": "notInSimpAll", "Finset.Subset.trans": "notInSimpAll", "subset_refl": "notInSimpAll", "MvPolynomial.vars_0": "notInSimpAll", "MvPolynomial.vars_add_subset": "notInSimpAll", "Finset.union_subset_union": "notInSimpAll", "Finset.sum_insert": "notInSimpAll", "Finset.biUnion_insert": "notInSimpAll", "Finset.Subset.refl": "notInSimpAll"}}, {"decl_name": "lt_div_iff_of_neg", "module": "Mathlib.Algebra.Order.Field.Basic", "idx_in_module": 191, "gt_premises": ["lt_iff_lt_of_le_iff_le", "div_le_iff_of_neg"], "gt_hints": {"lt_iff_lt_of_le_iff_le": "notInSimpAll", "div_le_iff_of_neg": "notInSimpAll"}}, {"decl_name": 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{"CategoryTheory.GradedObject.\u03b9_mapBifunctorMapObjDesc": "notInSimpAll"}}, {"decl_name": "CategoryTheory.Groupoid.vertexGroup_mul", "module": "Mathlib.CategoryTheory.Groupoid.VertexGroup", "idx_in_module": 4, "gt_premises": [], "gt_hints": {}}, {"decl_name": "CategoryTheory.Idempotents.isIdempotentComplete_of_isIdempotentComplete_opposite", "module": "Mathlib.CategoryTheory.Idempotents.Basic", "idx_in_module": 89, "gt_premises": ["CategoryTheory.op_comp", "CategoryTheory.unop_comp", "CategoryTheory.IsIdempotentComplete.idempotents_split"], "gt_hints": {"CategoryTheory.op_comp": "notInSimpAll", "CategoryTheory.unop_comp": "backwardOnly", "CategoryTheory.IsIdempotentComplete.idempotents_split": "notInSimpAll"}}, {"decl_name": "CategoryTheory.Functor.IsEventuallyConstantFrom.cocone\u03b9App_eq_id", "module": "Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant", "idx_in_module": 44, "gt_premises": ["CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_hom_inv_id", "CategoryTheory.Functor.IsEventuallyConstantFrom.cocone\u03b9App_eq"], "gt_hints": {"CategoryTheory.Functor.IsEventuallyConstantFrom.isoMap_hom_inv_id": "notInSimpAll", "CategoryTheory.Functor.IsEventuallyConstantFrom.cocone\u03b9App_eq": "notInSimpAll"}}, {"decl_name": "CategoryTheory.Limits.colimit.homIso_hom", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "idx_in_module": 181, "gt_premises": ["CategoryTheory.Limits.IsColimit.homIso_hom"], "gt_hints": {"CategoryTheory.Limits.IsColimit.homIso_hom": "notInSimpAll"}}, {"decl_name": "CategoryTheory.Limits.colimit.pre_id", "module": "Mathlib.CategoryTheory.Limits.HasLimits", "idx_in_module": 258, "gt_premises": ["CategoryTheory.Limits.colimit.hom_ext", "CategoryTheory.Category.id_comp", "CategoryTheory.Limits.colimit.\u03b9_pre", "CategoryTheory.Limits.\u03b9_colimMap"], "gt_hints": {"CategoryTheory.Limits.colimit.hom_ext": "notInSimpAll", "CategoryTheory.Category.id_comp": "notInSimpAll", "CategoryTheory.Limits.colimit.\u03b9_pre": "notInSimpAll", "CategoryTheory.Limits.\u03b9_colimMap": "notInSimpAll"}}, {"decl_name": "CategoryTheory.Limits.MonoCoprod.mono_inl_iff", "module": "Mathlib.CategoryTheory.Limits.MonoCoprod", "idx_in_module": 8, "gt_premises": ["CategoryTheory.Iso.isIso_hom", "CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom"], "gt_hints": {"CategoryTheory.Iso.isIso_hom": "notInSimpAll", "CategoryTheory.Limits.IsColimit.comp_coconePointUniqueUpToIso_hom": "notInSimpAll"}}, {"decl_name": "CategoryTheory.Limits.hasPullback_of_preservesPullback", "module": "Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks", "idx_in_module": 16, "gt_premises": ["CategoryTheory.Limits.pullback.condition", "CategoryTheory.Functor.map_comp"], "gt_hints": {"CategoryTheory.Limits.pullback.condition": "notInSimpAll", "CategoryTheory.Functor.map_comp": "notInSimpAll"}}, {"decl_name": "CategoryTheory.Limits.\u03b9_colimitFiberwiseColimitIso_hom_assoc", "module": 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"CategoryTheory.eq_whisker'": "notInSimpAll"}}, {"decl_name": "CategoryTheory.left_comp_retraction", "module": "Mathlib.CategoryTheory.Limits.Shapes.Reflexive", "idx_in_module": 10, "gt_premises": ["Exists.choose_spec", "CategoryTheory.IsCoreflexivePair.common_retraction"], "gt_hints": {"Exists.choose_spec": "notInSimpAll", "CategoryTheory.IsCoreflexivePair.common_retraction": "notInSimpAll"}}, {"decl_name": "CategoryTheory.MorphismProperty.of_postcomp", "module": "Mathlib.CategoryTheory.MorphismProperty.Composition", "idx_in_module": 29, "gt_premises": ["CategoryTheory.MorphismProperty.HasOfPostcompProperty.of_postcomp"], "gt_hints": {"CategoryTheory.MorphismProperty.HasOfPostcompProperty.of_postcomp": "notInSimpAll"}}, {"decl_name": "CategoryTheory.Bifunctor.diagonal'", "module": "Mathlib.CategoryTheory.Products.Bifunctor", "idx_in_module": 7, "gt_premises": ["CategoryTheory.Category.id_comp", "CategoryTheory.Functor.map_comp", "CategoryTheory.Category.comp_id", "CategoryTheory.prod_comp"], "gt_hints": {"CategoryTheory.Category.id_comp": "notInSimpAll", "CategoryTheory.Functor.map_comp": "notInSimpAll", "CategoryTheory.Category.comp_id": "notInSimpAll", "CategoryTheory.prod_comp": "notInSimpAll"}}, {"decl_name": "CategoryTheory.ThinSkeleton.fromThinSkeleton_obj", "module": "Mathlib.CategoryTheory.Skeletal", "idx_in_module": 63, "gt_premises": [], "gt_hints": {}}, {"decl_name": "CategoryTheory.Subobject.underlyingIso_inv_top_arrow", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "idx_in_module": 48, "gt_premises": ["CategoryTheory.Subobject.underlyingIso_arrow"], "gt_hints": {"CategoryTheory.Subobject.underlyingIso_arrow": "notInSimpAll"}}, {"decl_name": "CategoryTheory.Subobject.inf_le_left", "module": "Mathlib.CategoryTheory.Subobject.Lattice", "idx_in_module": 80, "gt_premises": ["Quotient.inductionOn\u2082'"], "gt_hints": {"Quotient.inductionOn\u2082'": "notInSimpAll"}}, {"decl_name": "CategoryTheory.Pretriangulated.rotate_map_hom\u2083", "module": "Mathlib.CategoryTheory.Triangulated.Rotate", "idx_in_module": 18, "gt_premises": [], "gt_hints": {}}, {"decl_name": "Finset.addEnergy_mono_right", "module": "Mathlib.Combinatorics.Additive.Energy", "idx_in_module": 8, "gt_premises": ["Finset.addEnergy_mono", "Finset.Subset.rfl"], "gt_hints": {"Finset.addEnergy_mono": "notInSimpAll", "Finset.Subset.rfl": "notInSimpAll"}}, {"decl_name": "Multiset.bell_zero", "module": "Mathlib.Combinatorics.Enumerative.Bell", "idx_in_module": 0, "gt_premises": [], "gt_hints": {}}, {"decl_name": "UV.disjoint_of_mem_compression_of_not_mem", "module": "Mathlib.Combinatorics.SetFamily.Compression.UV", "idx_in_module": 78, "gt_premises": ["ne_of_mem_of_not_mem", "if_neg", "disjoint_sdiff_self_right", "UV.mem_compression", "if_pos"], "gt_hints": {"ne_of_mem_of_not_mem": "notInSimpAll", "if_neg": "notInSimpAll", "disjoint_sdiff_self_right": "notInSimpAll", "UV.mem_compression": "notInSimpAll", "if_pos": "notInSimpAll"}}, {"decl_name": "SimpleGraph.ComponentCompl.nonempty", "module": "Mathlib.Combinatorics.SimpleGraph.Ends.Defs", "idx_in_module": 21, "gt_premises": ["SimpleGraph.ComponentCompl.ind"], "gt_hints": {"SimpleGraph.ComponentCompl.ind": "notInSimpAll"}}, {"decl_name": "AkraBazziRecurrence.exists_eventually_const_mul_le_r", "module": "Mathlib.Computability.AkraBazzi.AkraBazzi", "idx_in_module": 75, "gt_premises": ["AkraBazziRecurrence.eventually_bi_mul_le_r", "AkraBazziRecurrence.bi_min_div_two_lt_one", "div_pos", "Mathlib.Meta.Positivity.pos_of_isNat", "Mathlib.Meta.NormNum.isNat_ofNat", "AkraBazziRecurrence.b_pos"], "gt_hints": {"AkraBazziRecurrence.eventually_bi_mul_le_r": "notInSimpAll", "AkraBazziRecurrence.bi_min_div_two_lt_one": "notInSimpAll", "div_pos": "notInSimpAll", "Mathlib.Meta.Positivity.pos_of_isNat": "notInSimpAll", "Mathlib.Meta.NormNum.isNat_ofNat": "notInSimpAll", "AkraBazziRecurrence.b_pos": "notInSimpAll"}}, {"decl_name": 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"Mathlib.Tactic.Ring.mul_add": "notInSimpAll", "real_inner_add_add_self": "notInSimpAll", "Mathlib.Tactic.Ring.of_eq": "notInSimpAll", "vadd_vsub_assoc": "notInSimpAll", "Mathlib.Tactic.Ring.mul_zero": "notInSimpAll", "Mathlib.Tactic.Ring.cast_pos": "notInSimpAll", "dist_eq_norm_vsub": "notInSimpAll", "Mathlib.Tactic.Ring.add_congr": "notInSimpAll", "Mathlib.Tactic.Ring.mul_pp_pf_overlap": "notInSimpAll", "Mathlib.Tactic.Ring.mul_congr": "notInSimpAll", "Mathlib.Tactic.Ring.atom_pf": "notInSimpAll", "Mathlib.Tactic.Ring.add_pf_add_zero": "notInSimpAll", "Mathlib.Tactic.Ring.mul_pf_left": "notInSimpAll", "Mathlib.Tactic.Ring.mul_pf_right": "notInSimpAll", "Mathlib.Tactic.Ring.add_pf_add_gt": "notInSimpAll", "Mathlib.Meta.NormNum.isNat_ofNat": "notInSimpAll"}}, {"decl_name": "EuclideanGeometry.inter_eq_singleton_orthogonalProjectionFn", "module": "Mathlib.Geometry.Euclidean.Basic", "idx_in_module": 96, "gt_premises": ["Classical.choose_spec", "AffineSubspace.inter_eq_singleton_of_nonempty_of_isCompl", "AffineSubspace.direction_mk'", "AffineSubspace.mk'_nonempty", "Submodule.isCompl_orthogonal_of_completeSpace", "nonempty_subtype"], "gt_hints": {"Classical.choose_spec": "notInSimpAll", "AffineSubspace.inter_eq_singleton_of_nonempty_of_isCompl": "notInSimpAll", "AffineSubspace.direction_mk'": "notInSimpAll", "AffineSubspace.mk'_nonempty": "notInSimpAll", "Submodule.isCompl_orthogonal_of_completeSpace": "notInSimpAll", "nonempty_subtype": "notInSimpAll"}}, {"decl_name": "EuclideanGeometry.Sphere.ext", "module": "Mathlib.Geometry.Euclidean.Sphere.Basic", "idx_in_module": 0, "gt_premises": [], "gt_hints": {}}, {"decl_name": "EuclideanGeometry.oangle_add_oangle_add_oangle_eq_pi", "module": "Mathlib.Geometry.Euclidean.Triangle", "idx_in_module": 129, "gt_premises": ["vsub_ne_zero", "neg_vsub_eq_vsub_rev", "Orientation.oangle_add_cyc3_neg_left"], "gt_hints": {"vsub_ne_zero": "notInSimpAll", "neg_vsub_eq_vsub_rev": "notInSimpAll", "Orientation.oangle_add_cyc3_neg_left": "notInSimpAll"}}, {"decl_name": "smooth_prod_assoc", "module": "Mathlib.Geometry.Manifold.ContMDiff.Product", "idx_in_module": 76, "gt_premises": ["contMDiff_prod_assoc"], "gt_hints": {"contMDiff_prod_assoc": "notInSimpAll"}}, {"decl_name": "ContMDiffMap.mdifferentiable'", "module": "Mathlib.Geometry.Manifold.ContMDiffMFDeriv", "idx_in_module": 147, "gt_premises": ["ContMDiff.mdifferentiable", "ContMDiffMap.contMDiff"], "gt_hints": {"ContMDiff.mdifferentiable": "notInSimpAll", "ContMDiffMap.contMDiff": "notInSimpAll"}}, {"decl_name": "Units.contMDiff_val", "module": "Mathlib.Geometry.Manifold.Instances.UnitsOfNormedAlgebra", "idx_in_module": 4, "gt_premises": ["contMDiff_isOpenEmbedding", "Units.isOpenEmbedding_val"], "gt_hints": {"contMDiff_isOpenEmbedding": "notInSimpAll", "Units.isOpenEmbedding_val": "notInSimpAll"}}, {"decl_name": "ModelWithCorners.hasMFDerivWithinAt", "module": "Mathlib.Geometry.Manifold.MFDeriv.Atlas", "idx_in_module": 1, "gt_premises": ["HasMFDerivAt.hasMFDerivWithinAt", "ModelWithCorners.hasMFDerivAt"], "gt_hints": {"HasMFDerivAt.hasMFDerivWithinAt": "notInSimpAll", "ModelWithCorners.hasMFDerivAt": "notInSimpAll"}}, {"decl_name": "MDifferentiableAt.congr_of_eventuallyEq", "module": "Mathlib.Geometry.Manifold.MFDeriv.Basic", "idx_in_module": 377, "gt_premises": ["HasMFDerivAt.congr_of_eventuallyEq", "MDifferentiableAt.hasMFDerivAt", "HasMFDerivAt.mdifferentiableAt"], "gt_hints": {"HasMFDerivAt.congr_of_eventuallyEq": "notInSimpAll", "MDifferentiableAt.hasMFDerivAt": "notInSimpAll", "HasMFDerivAt.mdifferentiableAt": "notInSimpAll"}}, {"decl_name": "MDifferentiableWithinAt.differentiableWithinAt", "module": "Mathlib.Geometry.Manifold.MFDeriv.FDeriv", "idx_in_module": 25, "gt_premises": ["PartialEquiv.trans_refl", "Set.range_id", "DifferentiableWithinAt.continuousWithinAt", "Set.inter_univ"], "gt_hints": {"PartialEquiv.trans_refl": "notInSimpAll", "Set.range_id": "notInSimpAll", "DifferentiableWithinAt.continuousWithinAt": "notInSimpAll", "Set.inter_univ": "notInSimpAll"}}, {"decl_name": "AlgebraicGeometry.LocallyRingedSpace.isLocalRingHomValStalkMap", "module": "Mathlib.Geometry.RingedSpace.LocallyRingedSpace", "idx_in_module": 18, "gt_premises": ["AlgebraicGeometry.LocallyRingedSpace.isLocalHomValStalkMap"], "gt_hints": {"AlgebraicGeometry.LocallyRingedSpace.isLocalHomValStalkMap": "notInSimpAll"}}, {"decl_name": "Abelianization.lift.of", "module": "Mathlib.GroupTheory.Abelianization", "idx_in_module": 28, "gt_premises": [], "gt_hints": {}}, {"decl_name": "Abelianization.lift.unique", "module": "Mathlib.GroupTheory.Abelianization", "idx_in_module": 29, "gt_premises": ["QuotientGroup.induction_on"], "gt_hints": {"QuotientGroup.induction_on": "notInSimpAll"}}, {"decl_name": "AddCon.refl", "module": "Mathlib.GroupTheory.Congruence.Defs", "idx_in_module": 21, "gt_premises": ["Setoid.refl'"], "gt_hints": {"Setoid.refl'": "notInSimpAll"}}, {"decl_name": "QuotientAddGroup.preimage_image_mk", "module": "Mathlib.GroupTheory.Coset.Defs", "idx_in_module": 77, "gt_premises": ["neg_add_cancel_right", "neg_mem_iff", "add_neg_cancel_left", "AddSubgroupClass.toNegMemClass", "neg_add_rev", "neg_neg", "SetLike.exists", "Set.mem_image", "exists_prop_congr", "exists_prop", "Set.mem_iUnion", "funext", "Set.ext", "Set.mem_preimage", "QuotientAddGroup.eq", "AddSubgroup.neg_mem"], "gt_hints": {"neg_add_cancel_right": "notInSimpAll", "neg_mem_iff": "notInSimpAll", "add_neg_cancel_left": "notInSimpAll", "AddSubgroupClass.toNegMemClass": "notInSimpAll", "neg_add_rev": "notInSimpAll", "neg_neg": "notInSimpAll", "SetLike.exists": "notInSimpAll", "Set.mem_image": "notInSimpAll", "exists_prop_congr": "notInSimpAll", "exists_prop": "notInSimpAll", "Set.mem_iUnion": "notInSimpAll", "funext": "notInSimpAll", "Set.ext": "notInSimpAll", "Set.mem_preimage": "notInSimpAll", "QuotientAddGroup.eq": "notInSimpAll", "AddSubgroup.neg_mem": "notInSimpAll"}}, {"decl_name": "EckmannHilton.mul_assoc", "module": "Mathlib.GroupTheory.EckmannHilton", "idx_in_module": 13, "gt_premises": ["Std.LawfulIdentity.right_id", "EckmannHilton.mul", "EckmannHilton.IsUnital.toLawfulIdentity", "Std.LawfulIdentity.left_id"], "gt_hints": {"Std.LawfulIdentity.right_id": "notInSimpAll", "EckmannHilton.mul": "notInSimpAll", "EckmannHilton.IsUnital.toLawfulIdentity": "notInSimpAll", "Std.LawfulIdentity.left_id": "notInSimpAll"}}, {"decl_name": "FixedPoints.mem_subgroup", "module": "Mathlib.GroupTheory.GroupAction.Defs", "idx_in_module": 54, "gt_premises": [], "gt_hints": {}}, {"decl_name": "DomAddAct.symm_mk_zsmul", "module": "Mathlib.GroupTheory.GroupAction.DomAct.Basic", "idx_in_module": 78, "gt_premises": [], "gt_hints": {}}, {"decl_name": "DistribMulActionHom.one_apply", "module": "Mathlib.GroupTheory.GroupAction.Hom", "idx_in_module": 138, "gt_premises": [], "gt_hints": {}}, {"decl_name": "HNNExtension.NormalWord.t_pow_smul_eq_unitsSMul", "module": "Mathlib.GroupTheory.HNNExtension", "idx_in_module": 205, "gt_premises": ["Int.units_eq_one_or", "map_inv", "zpow_neg", "HNNExtension.NormalWord.instMulAction_1.proof_1", "funext", "instHSMul", "Equiv.Perm.inv_def", "SMul.smul", "HNNExtension.lift_t", "zpow_one", "MulAction.toEndHom"], "gt_hints": {"Int.units_eq_one_or": "notInSimpAll", "map_inv": "notInSimpAll", "zpow_neg": "notInSimpAll", "HNNExtension.NormalWord.instMulAction_1.proof_1": "notInSimpAll", "funext": "notInSimpAll", "instHSMul": "unmodified", "Equiv.Perm.inv_def": "unmodified", "SMul.smul": "unmodified", "HNNExtension.lift_t": "notInSimpAll", "zpow_one": "notInSimpAll", "MulAction.toEndHom": "unmodified"}}, {"decl_name": "Equiv.Perm.mem_conj_support", "module": "Mathlib.GroupTheory.Perm.ConjAct", "idx_in_module": 0, "gt_premises": ["ConjAct.smul_def", "Equiv.Perm.coe_mul", "ConjAct.ofConjAct_inv", "Equiv.Perm.mem_support", "Function.comp_apply", "Equiv.apply_eq_iff_eq_symm_apply"], "gt_hints": {"ConjAct.smul_def": "unmodified", "Equiv.Perm.coe_mul": "unmodified", "ConjAct.ofConjAct_inv": "unmodified", "Equiv.Perm.mem_support": "unmodified", "Function.comp_apply": "unmodified", "Equiv.apply_eq_iff_eq_symm_apply": "notInSimpAll"}}, {"decl_name": "Equiv.Perm.Disjoint.cycleFactorsFinset_mul_eq_union", "module": "Mathlib.GroupTheory.Perm.Cycle.Factors", "idx_in_module": 303, "gt_premises": ["Equiv.Perm.cycleFactorsFinset_eq_finset", "Finset.mem_union", "Equiv.Perm.Disjoint.mono", "Equiv.Perm.cycleFactorsFinset_mem_commute", "Equiv.Perm.mem_support", "Set.Pairwise.mono'", "Finset.coe_subset", "Equiv.Perm.mem_cycleFactorsFinset_iff", "Finset.noncommProd_union_of_disjoint", "Equiv.Perm.Disjoint.disjoint_cycleFactorsFinset", "Equiv.Perm.mem_cycleFactorsFinset_support_le", "forall_swap", "Equiv.Perm.cycleFactorsFinset_pairwise_disjoint", "Equiv.Perm.Disjoint.commute", "Finset.subset_union_left", "Finset.subset_union_right", "Equiv.Perm.cycleFactorsFinset_noncommProd", "Finset.coe_union", "Equiv.Perm.Disjoint.symmetric", "Set.Pairwise.mono", "Set.pairwise_union_of_symmetric"], "gt_hints": {"Equiv.Perm.cycleFactorsFinset_eq_finset": "notInSimpAll", "Finset.mem_union": "notInSimpAll", "Equiv.Perm.Disjoint.mono": "notInSimpAll", "Equiv.Perm.cycleFactorsFinset_mem_commute": "notInSimpAll", "Equiv.Perm.mem_support": "notInSimpAll", "Set.Pairwise.mono'": "notInSimpAll", "Finset.coe_subset": "notInSimpAll", "Equiv.Perm.mem_cycleFactorsFinset_iff": "unmodified", "Finset.noncommProd_union_of_disjoint": "notInSimpAll", "Equiv.Perm.Disjoint.disjoint_cycleFactorsFinset": "notInSimpAll", "Equiv.Perm.mem_cycleFactorsFinset_support_le": "notInSimpAll", "forall_swap": "unmodified", "Equiv.Perm.cycleFactorsFinset_pairwise_disjoint": "notInSimpAll", "Equiv.Perm.Disjoint.commute": "notInSimpAll", "Finset.subset_union_left": "notInSimpAll", "Finset.subset_union_right": "notInSimpAll", "Equiv.Perm.cycleFactorsFinset_noncommProd": "notInSimpAll", "Finset.coe_union": "notInSimpAll", "Equiv.Perm.Disjoint.symmetric": "notInSimpAll", "Set.Pairwise.mono": "notInSimpAll", "Set.pairwise_union_of_symmetric": "notInSimpAll"}}, {"decl_name": "Equiv.Perm.IsThreeCycle.orderOf", "module": "Mathlib.GroupTheory.Perm.Cycle.Type", "idx_in_module": 322, "gt_premises": ["normalize_eq", "Equiv.Perm.IsThreeCycle.cycleType", "Equiv.Perm.lcm_cycleType", "Multiset.lcm_singleton"], "gt_hints": {"normalize_eq": "notInSimpAll", "Equiv.Perm.IsThreeCycle.cycleType": "notInSimpAll", "Equiv.Perm.lcm_cycleType": "notInSimpAll", "Multiset.lcm_singleton": "notInSimpAll"}}, {"decl_name": "Equiv.Perm.apply_pow_apply_eq_iff", "module": "Mathlib.GroupTheory.Perm.Support", "idx_in_module": 132, "gt_premises": ["Equiv.Perm.mul_apply", "Commute.self_pow", "Equiv.apply_eq_iff_eq"], "gt_hints": {"Equiv.Perm.mul_apply": "notInSimpAll", "Commute.self_pow": "notInSimpAll", "Equiv.apply_eq_iff_eq": "notInSimpAll"}}, {"decl_name": "QuotientAddGroup.map_map", "module": "Mathlib.GroupTheory.QuotientGroup.Defs", "idx_in_module": 77, "gt_premises": ["QuotientAddGroup.induction_on", "LE.le.trans_eq", "AddSubgroup.comap_comap", "AddSubgroup.comap_mono", "LE.le.trans"], "gt_hints": {"QuotientAddGroup.induction_on": "notInSimpAll", "LE.le.trans_eq": "notInSimpAll", "AddSubgroup.comap_comap": "notInSimpAll", "AddSubgroup.comap_mono": "notInSimpAll", "LE.le.trans": "notInSimpAll"}}, {"decl_name": "hammingDist_comp", "module": "Mathlib.InformationTheory.Hamming", "idx_in_module": 36, "gt_premises": ["Finset.card_mono", "Finset.monotone_filter_right", "hammingDist_comp_le_hammingDist", "le_antisymm"], "gt_hints": {"Finset.card_mono": "notInSimpAll", "Finset.monotone_filter_right": "notInSimpAll", "hammingDist_comp_le_hammingDist": "notInSimpAll", "le_antisymm": "notInSimpAll"}}, {"decl_name": "AffineSubspace.not_le_iff_exists", "module": "Mathlib.LinearAlgebra.AffineSpace.AffineSubspace", "idx_in_module": 192, "gt_premises": ["Set.not_subset"], "gt_hints": {"Set.not_subset": "notInSimpAll"}}, {"decl_name": "Finset.weightedVSubOfPoint_subtype_eq_filter", "module": "Mathlib.LinearAlgebra.AffineSpace.Combination", "idx_in_module": 91, "gt_premises": ["Finset.sum_subtype_eq_sum_filter", "Finset.weightedVSubOfPoint_apply"], "gt_hints": {"Finset.sum_subtype_eq_sum_filter": "notInSimpAll", "Finset.weightedVSubOfPoint_apply": "notInSimpAll"}}, {"decl_name": "Collinear.mem_affineSpan_of_mem_of_ne", "module": "Mathlib.LinearAlgebra.AffineSpace.FiniteDimensional", "idx_in_module": 209, "gt_premises": ["IsUnit.div_mul_cancel", "collinear_iff_of_mem", "isUnit_iff_ne_zero", "smul_smul", "vadd_left_mem_affineSpan_pair", "zero_smul", "vadd_vsub", "zero_vadd"], "gt_hints": {"IsUnit.div_mul_cancel": "notInSimpAll", "collinear_iff_of_mem": "notInSimpAll", "isUnit_iff_ne_zero": "notInSimpAll", "smul_smul": "unmodified", "vadd_left_mem_affineSpan_pair": "notInSimpAll", "zero_smul": "notInSimpAll", "vadd_vsub": "notInSimpAll", "zero_vadd": "notInSimpAll"}}, {"decl_name": "LinearMap.compAlternatingMap_codRestrict", "module": "Mathlib.LinearAlgebra.Alternating.Basic", "idx_in_module": 104, "gt_premises": ["AlternatingMap.ext"], "gt_hints": {"AlternatingMap.ext": "notInSimpAll"}}, {"decl_name": "CliffordAlgebra.forall_mul_self_eq_iff", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.Basic", "idx_in_module": 46, "gt_premises": ["map_add", "two_mul", "SMulCommClass.symm", "two_smul", "IsUnit.mul_left_cancel", "QuadraticMap.polar_self", "CliffordAlgebra.mul_add_swap_eq_polar_of_forall_mul_self_eq", "AddMonoidHomClass.toAddHomClass", "RingHomClass.toAddMonoidHomClass"], "gt_hints": {"map_add": "notInSimpAll", "two_mul": "notInSimpAll", "SMulCommClass.symm": "notInSimpAll", "two_smul": "notInSimpAll", "IsUnit.mul_left_cancel": "notInSimpAll", "QuadraticMap.polar_self": "notInSimpAll", "CliffordAlgebra.mul_add_swap_eq_polar_of_forall_mul_self_eq": "notInSimpAll", "AddMonoidHomClass.toAddHomClass": "notInSimpAll", "RingHomClass.toAddMonoidHomClass": "notInSimpAll"}}, {"decl_name": "CliffordAlgebra.reverseEquiv_apply", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.Conjugation", "idx_in_module": 33, "gt_premises": [], "gt_hints": {}}, {"decl_name": "CliffordAlgebra.changeForm.neg_proof", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.Contraction", "idx_in_module": 73, "gt_premises": ["congr_arg", "neg_sub"], "gt_hints": {"congr_arg": "notInSimpAll", "neg_sub": "notInSimpAll"}}, {"decl_name": "CliffordAlgebra.foldr_one", "module": "Mathlib.LinearAlgebra.CliffordAlgebra.Fold", "idx_in_module": 5, "gt_premises": ["MonoidHomClass.toOneHomClass", "RingHomClass.toMonoidHomClass", "AlgHomClass.toRingHomClass", "CliffordAlgebra.foldr.proof_3", "map_one", "CliffordAlgebra.foldr.proof_1", "CliffordAlgebra.foldr.proof_2", "LinearMap.congr_fun"], "gt_hints": {"MonoidHomClass.toOneHomClass": "notInSimpAll", "RingHomClass.toMonoidHomClass": "notInSimpAll", "AlgHomClass.toRingHomClass": "notInSimpAll", "CliffordAlgebra.foldr.proof_3": 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"Finsupp.mem_supported_support", "module": "Mathlib.LinearAlgebra.Finsupp.Supported", "idx_in_module": 7, "gt_premises": ["subset_refl", "Finsupp.mem_supported"], "gt_hints": {"subset_refl": "notInSimpAll", "Finsupp.mem_supported": "notInSimpAll"}}, {"decl_name": "Matrix.charmatrix_apply_eq", "module": "Mathlib.LinearAlgebra.Matrix.Charpoly.Basic", "idx_in_module": 2, "gt_premises": ["Matrix.scalar_apply", "Matrix.charmatrix", "Matrix.diagonal_apply_eq", "Matrix.map_apply", "RingHom.mapMatrix_apply", "Matrix.sub_apply"], "gt_hints": {"Matrix.scalar_apply": "unmodified", "Matrix.charmatrix": "unmodified", "Matrix.diagonal_apply_eq": "unmodified", "Matrix.map_apply": "unmodified", "RingHom.mapMatrix_apply": "unmodified", "Matrix.sub_apply": "unmodified"}}, {"decl_name": "Matrix.det_fromBlocks_one\u2081\u2081", "module": "Mathlib.LinearAlgebra.Matrix.SchurComplement", "idx_in_module": 66, "gt_premises": ["Matrix.mul_one", "Matrix.det_fromBlocks\u2081\u2081", "invOf_one", "Matrix.det_one", "one_mul"], "gt_hints": {"Matrix.mul_one": "notInSimpAll", "Matrix.det_fromBlocks\u2081\u2081": "notInSimpAll", "invOf_one": "notInSimpAll", "Matrix.det_one": "notInSimpAll", "one_mul": "notInSimpAll"}}, {"decl_name": "Matrix.SpecialLinearGroup.coe_mk", "module": "Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup", "idx_in_module": 6, "gt_premises": [], "gt_hints": {}}, {"decl_name": "MultilinearMap.compLinearMapMultilinear_apply", "module": "Mathlib.LinearAlgebra.Multilinear.Basic", "idx_in_module": 351, "gt_premises": [], "gt_hints": {}}, {"decl_name": "Basis.orientation_neg_single", "module": "Mathlib.LinearAlgebra.Orientation", "idx_in_module": 77, "gt_premises": ["Orientation.proof_1", "inv_neg'", "mul_one", "zero_lt_one", "Finset.prod_update_of_mem", "Left.neg_neg_iff", "units_smul_eq_neg_iff", "Basis.orientation_unitsSMul", "inv_one", "Finset.prod_congr", "Finset.mem_univ", "IsCancelAdd.toIsLeftCancelAdd", "Finset.prod_const_one"], "gt_hints": {"Orientation.proof_1": 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"HurwitzZeta.completedSinZeta_neg", "module": "Mathlib.NumberTheory.LSeries.HurwitzZetaOdd", "idx_in_module": 179, "gt_premises": ["HurwitzZeta.hurwitzOddFEPair.proof_1", "HurwitzZeta.hurwitzOddFEPair.proof_11", "Complex.ofReal_neg", "HurwitzZeta.sinKernel_neg", "WeakFEPair.symm", "WeakFEPair.hg_top", "HurwitzZeta.hurwitzOddFEPair.proof_2", "WeakFEPair.hf_top", "HurwitzZeta.hurwitzOddFEPair.proof_4", "funext", "HurwitzZeta.hurwitzOddFEPair.proof_3", "Function.comp_def", "mellin", "StrongFEPair.\u039b", "HurwitzZeta.hurwitzOddFEPair.proof_5", "HurwitzZeta.hurwitzOddFEPair.proof_7", "MeasureTheory.integral_neg", "StrongFEPair.hg\u2080", "HurwitzZeta.hurwitzOddFEPair.proof_10", "StrongFEPair.hf\u2080", "smul_neg", "WeakFEPair.hk", "WeakFEPair.h_feq'", "WeakFEPair.hf_int", "HurwitzZeta.hurwitzOddFEPair.proof_9", "WeakFEPair.hg_int", "neg_div", "HurwitzZeta.hurwitzOddFEPair.proof_6", "HurwitzZeta.completedSinZeta", "HurwitzZeta.hurwitzOddFEPair.proof_8", 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{"decl_name": "Finset.iInf_biUnion", "module": "Mathlib.Order.CompleteLattice.Finset", "idx_in_module": 50, "gt_premises": ["Finset.iSup_biUnion"], "gt_hints": {"Finset.iSup_biUnion": "notInSimpAll"}}, {"decl_name": "Finset.set_biUnion_finset_image", "module": "Mathlib.Order.CompleteLattice.Finset", "idx_in_module": 64, "gt_premises": ["Finset.iSup_finset_image"], "gt_hints": {"Finset.iSup_finset_image": "notInSimpAll"}}, {"decl_name": "sSup_eq_bot", "module": "Mathlib.Order.CompleteLattice", "idx_in_module": 115, "gt_premises": ["sSup_le", "le_sSup", "bot_unique", "le_bot_iff"], "gt_hints": {"sSup_le": "notInSimpAll", "le_sSup": "notInSimpAll", "bot_unique": "notInSimpAll", "le_bot_iff": "notInSimpAll"}}, {"decl_name": "iInf_eq_of_forall_ge_of_forall_gt_exists_lt", "module": "Mathlib.Order.CompleteLattice", "idx_in_module": 279, "gt_premises": ["iSup_eq_of_forall_le_of_forall_lt_exists_gt"], "gt_hints": {"iSup_eq_of_forall_le_of_forall_lt_exists_gt": "notInSimpAll"}}, {"decl_name": "sup_biSup", "module": "Mathlib.Order.CompleteLattice", "idx_in_module": 330, "gt_premises": ["biSup_sup", "funext", "sup_comm", "iSup_congr_Prop"], "gt_hints": {"biSup_sup": "notInSimpAll", "funext": "notInSimpAll", "sup_comm": "notInSimpAll", "iSup_congr_Prop": "notInSimpAll"}}, {"decl_name": "InverseSystem.PEquivOn.restrict_equiv", "module": "Mathlib.Order.DirectedInverseSystem", "idx_in_module": 71, "gt_premises": ["InverseSystem.PEquivOn.restrict.proof_1"], "gt_hints": {"InverseSystem.PEquivOn.restrict.proof_1": "notInSimpAll"}}, {"decl_name": "disjointedRec_zero", "module": "Mathlib.Order.Disjointed", "idx_in_module": 15, "gt_premises": [], "gt_hints": {}}, {"decl_name": "Filter.tendsto_Ici_atTop", "module": "Mathlib.Order.Filter.AtTopBot", "idx_in_module": 379, "gt_premises": ["Filter.tendsto_comap_iff", "Function.comp_def", "Filter.atTop_Ici_eq"], "gt_hints": {"Filter.tendsto_comap_iff": "notInSimpAll", "Function.comp_def": "notInSimpAll", "Filter.atTop_Ici_eq": "notInSimpAll"}}, {"decl_name": "Filter.HasAntitoneBasis.comp_mono", "module": "Mathlib.Order.Filter.AtTopBot", "idx_in_module": 420, "gt_premises": ["Filter.HasAntitoneBasis.toHasBasis", "Set.Subset.rfl", "Filter.Tendsto.eventually_ge_atTop", "Antitone.comp_monotone", "Filter.HasBasis.to_hasBasis", "Filter.Eventually.exists", "Filter.atTop_neBot", "trivial", "Filter.HasAntitoneBasis.antitone"], "gt_hints": {"Filter.HasAntitoneBasis.toHasBasis": "notInSimpAll", "Set.Subset.rfl": "notInSimpAll", "Filter.Tendsto.eventually_ge_atTop": "notInSimpAll", "Antitone.comp_monotone": "notInSimpAll", "Filter.HasBasis.to_hasBasis": "notInSimpAll", "Filter.Eventually.exists": "notInSimpAll", "Filter.atTop_neBot": "notInSimpAll", "trivial": "notInSimpAll", "Filter.HasAntitoneBasis.antitone": "notInSimpAll"}}, {"decl_name": "Filter.compl_mem_comap", "module": "Mathlib.Order.Filter.Basic", "idx_in_module": 418, "gt_premises": ["Filter.mem_comap_iff_compl", "compl_compl"], "gt_hints": {"Filter.mem_comap_iff_compl": "notInSimpAll", "compl_compl": "notInSimpAll"}}, {"decl_name": "Filter.mem_principal", "module": "Mathlib.Order.Filter.Defs", "idx_in_module": 24, "gt_premises": [], "gt_hints": {}}, {"decl_name": "GaloisConnection.le_u_l_trans", "module": "Mathlib.Order.GaloisConnection", "idx_in_module": 23, "gt_premises": ["GaloisConnection.l_le", "GaloisConnection.monotone_u", "LE.le.trans"], "gt_hints": {"GaloisConnection.l_le": "notInSimpAll", "GaloisConnection.monotone_u": "notInSimpAll", "LE.le.trans": "notInSimpAll"}}, {"decl_name": "grade_strictMono", "module": "Mathlib.Order.Grade", "idx_in_module": 6, "gt_premises": ["GradeOrder.grade_strictMono"], "gt_hints": {"GradeOrder.grade_strictMono": "notInSimpAll"}}, {"decl_name": "TopHom.cancel_right", "module": "Mathlib.Order.Hom.Bounded", "idx_in_module": 43, "gt_premises": ["DFunLike.ext_iff", "Function.Surjective.forall", "congr_arg", "TopHom.ext"], "gt_hints": {"DFunLike.ext_iff": "notInSimpAll", "Function.Surjective.forall": "notInSimpAll", "congr_arg": "notInSimpAll", "TopHom.ext": "notInSimpAll"}}, {"decl_name": "TopHom.symm_dual_id", "module": "Mathlib.Order.Hom.Bounded", "idx_in_module": 139, "gt_premises": [], "gt_hints": {}}, {"decl_name": "OrderHom.coe_iInf", "module": "Mathlib.Order.Hom.Order", "idx_in_module": 20, "gt_premises": ["OrderHom.iInf_apply", "funext", "iInf_apply"], "gt_hints": {"OrderHom.iInf_apply": "unmodified", "funext": "notInSimpAll", "iInf_apply": "notInSimpAll"}}, {"decl_name": "Nat.card_fintypeIoo", "module": "Mathlib.Order.Interval.Finset.Nat", "idx_in_module": 46, "gt_premises": ["Finset.mem_Ioo", "Nat.card_Ioo", "Fintype.card_ofFinset"], "gt_hints": {"Finset.mem_Ioo": "notInSimpAll", "Nat.card_Ioo": "notInSimpAll", "Fintype.card_ofFinset": "notInSimpAll"}}, {"decl_name": "Set.Iio_union_Ico_eq_Iio", "module": "Mathlib.Order.Interval.Set.Basic", "idx_in_module": 421, "gt_premises": ["Set.Iio_subset_Iio_union_Ico", "Set.Subset.antisymm", "lt_of_lt_of_le"], "gt_hints": {"Set.Iio_subset_Iio_union_Ico": "notInSimpAll", "Set.Subset.antisymm": "notInSimpAll", "lt_of_lt_of_le": "notInSimpAll"}}, {"decl_name": "Set.uIcc_subset_uIcc_union_uIcc", "module": "Mathlib.Order.Interval.Set.UnorderedInterval", "idx_in_module": 70, "gt_premises": ["Set.mem_union", "Set.mem_uIcc", "le_total"], "gt_hints": {"Set.mem_union": "unmodified", "Set.mem_uIcc": "unmodified", "le_total": "notInSimpAll"}}, {"decl_name": "Ne.lt_sup_or_lt_sup", "module": "Mathlib.Order.Lattice", "idx_in_module": 69, "gt_premises": ["left_lt_sup", "Ne.not_le_or_not_le", "right_lt_sup"], "gt_hints": {"left_lt_sup": "notInSimpAll", "Ne.not_le_or_not_le": "notInSimpAll", "right_lt_sup": "notInSimpAll"}}, {"decl_name": "inf_congr_right", "module": "Mathlib.Order.Lattice", "idx_in_module": 126, "gt_premises": ["sup_congr_right"], "gt_hints": {"sup_congr_right": "notInSimpAll"}}, {"decl_name": "not_minimal_iff_exists_lt", "module": "Mathlib.Order.Minimal", "idx_in_module": 66, "gt_premises": ["not_minimal_iff", "funext"], "gt_hints": {"not_minimal_iff": "notInSimpAll", "funext": "notInSimpAll"}}, {"decl_name": "empty_relation_apply", "module": "Mathlib.Order.RelClasses", "idx_in_module": 28, "gt_premises": [], "gt_hints": {}}, {"decl_name": "RelEmbedding.isWellOrder", "module": "Mathlib.Order.RelIso.Basic", "idx_in_module": 93, "gt_premises": ["RelEmbedding.wellFounded", "IsStrictTotalOrder.toIsStrictOrder", "IsWellFounded.wf", "IsWellOrder.toIsWellFounded", "RelEmbedding.isStrictTotalOrder", "IsStrictTotalOrder.toIsTrichotomous", "IsStrictOrder.toIsTrans"], "gt_hints": {"RelEmbedding.wellFounded": "notInSimpAll", "IsStrictTotalOrder.toIsStrictOrder": "notInSimpAll", "IsWellFounded.wf": "notInSimpAll", "IsWellOrder.toIsWellFounded": "notInSimpAll", "RelEmbedding.isStrictTotalOrder": "notInSimpAll", "IsStrictTotalOrder.toIsTrichotomous": "notInSimpAll", "IsStrictOrder.toIsTrans": "notInSimpAll"}}, {"decl_name": "RelEmbedding.sumLiftRelInr_apply", "module": "Mathlib.Order.RelIso.Basic", "idx_in_module": 129, "gt_premises": [], "gt_hints": {}}, {"decl_name": "RelSeries.append_length", "module": "Mathlib.Order.RelSeries", "idx_in_module": 80, "gt_premises": [], "gt_hints": {}}, {"decl_name": "Set.sInf_eq_sInter", "module": "Mathlib.Order.SetNotation", "idx_in_module": 5, "gt_premises": [], "gt_hints": {}}, {"decl_name": "InitialSeg.isSuccLimit_apply_iff", "module": "Mathlib.Order.SuccPred.InitialSeg", "idx_in_module": 14, "gt_premises": ["InitialSeg.isMin_apply_iff", "not_isMin_iff", "Order.IsSuccLimit"], "gt_hints": {"InitialSeg.isMin_apply_iff": "notInSimpAll", "not_isMin_iff": "notInSimpAll", "Order.IsSuccLimit": "unmodified"}}, {"decl_name": "Order.IsSuccPrelimit.succ_lt", "module": "Mathlib.Order.SuccPred.Limit", "idx_in_module": 67, "gt_premises": ["lt_iff_le_and_ne", "IsMax.succ_eq", "Order.IsSuccPrelimit.isMax", "Order.succ_le_iff_of_not_isMax"], "gt_hints": {"lt_iff_le_and_ne": "notInSimpAll", "IsMax.succ_eq": "notInSimpAll", "Order.IsSuccPrelimit.isMax": "notInSimpAll", "Order.succ_le_iff_of_not_isMax": "notInSimpAll"}}, {"decl_name": "SubRootedTree.bot_mem_iff", "module": "Mathlib.Order.SuccPred.Tree", "idx_in_module": 46, "gt_premises": ["SubRootedTree.mem_iff", "le_bot_iff"], "gt_hints": {"SubRootedTree.mem_iff": "unmodified", "le_bot_iff": "notInSimpAll"}}, {"decl_name": "Pi.bihimp_apply", "module": "Mathlib.Order.SymmDiff", "idx_in_module": 272, "gt_premises": [], "gt_hints": {}}, {"decl_name": "StrictMono.le_apply", "module": "Mathlib.Order.WellFounded", "idx_in_module": 61, "gt_premises": ["StrictMono.id_le"], "gt_hints": {"StrictMono.id_le": "notInSimpAll"}}, {"decl_name": "ProbabilityTheory.indepSets_of_indepSets_of_le_right", "module": "Mathlib.Probability.Independence.Basic", "idx_in_module": 60, "gt_premises": ["ProbabilityTheory.Kernel.indepSets_of_indepSets_of_le_right"], "gt_hints": {"ProbabilityTheory.Kernel.indepSets_of_indepSets_of_le_right": "notInSimpAll"}}, 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{"decl_name": "upperSemicontinuousWithinAt_biInf", "module": "Mathlib.Topology.Semicontinuous", "idx_in_module": 287, "gt_premises": ["upperSemicontinuousWithinAt_iInf"], "gt_hints": {"upperSemicontinuousWithinAt_iInf": "notInSimpAll"}}, {"decl_name": "HasSeparatingCover.mono", "module": "Mathlib.Topology.Separation.Basic", "idx_in_module": 29, "gt_premises": ["Set.disjoint_of_subset", "HasSubset.Subset.trans"], "gt_hints": {"Set.disjoint_of_subset": "notInSimpAll", "HasSubset.Subset.trans": "notInSimpAll"}}, {"decl_name": "t0Space_iff_nhds_injective", "module": "Mathlib.Topology.Separation.Basic", "idx_in_module": 57, "gt_premises": ["t0Space_iff_inseparable"], "gt_hints": {"t0Space_iff_inseparable": "notInSimpAll"}}, {"decl_name": "TopCat.Presheaf.app_surjective_of_stalkFunctor_map_bijective", "module": "Mathlib.Topology.Sheaves.Stalks", "idx_in_module": 187, "gt_premises": ["CategoryTheory.NatTrans.naturality", "TopCat.Presheaf.germ_exist", "TopCat.Presheaf.germ_eq", 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