name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.shiftNegShift | Mathlib.CategoryTheory.Shift.Basic | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"CategoryTheory.Functor.comp",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Functor.id",
"CategoryTheory.Iso",
"CategoryTheory.Equivalence.functor",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"CategoryTheory.sh... | true |
Std.Do.SPred.pure_congr | Std.Do.SPred.DerivedLaws | [
"Iff.mpr",
"Std.Do.SPred.entails",
"Std.Do.SPred.pure",
"Std.Do.SPred.bientails",
"Std.Do.SPred.pure_mono",
"List",
"And",
"Iff",
"And.intro",
"Iff.mp",
"Std.Do.SPred.bientails.iff"
] | true |
instInvolutiveInvColex.eq_1 | Mathlib.Algebra.Order.Group.Synonym | [
"Colex",
"InvolutiveInv",
"instInvolutiveInvColex",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.Probability.Moments.Variance.0.ProbabilityTheory.meas_ge_le_evariance_div_sq._simp_1_1 | Mathlib.Probability.Moments.Variance | [
"ENNReal.rpow_mul",
"Real",
"HMul.hMul",
"ENNReal.instPowReal",
"HPow.hPow",
"Real.instMul",
"ENNReal",
"instHPow",
"Eq.symm",
"Eq",
"instHMul"
] | false |
CategoryTheory.GrothendieckTopology.HasSheafCompose.mk | Mathlib.CategoryTheory.Sites.Whiskering | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.comp",
"CategoryTheory.GrothendieckTopology.HasSheafCompose.mk",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.GrothendieckTopology.HasSheafCompose",
"CategoryTheory.Category.opposite",
"CategoryTheory.Presheaf.IsSheaf",
"Categor... | true |
OpenPartialHomeomorph.eventually_right_inverse' | Mathlib.Topology.OpenPartialHomeomorph.Continuity | [
"Filter.Eventually",
"Membership.mem",
"nhds",
"OpenPartialHomeomorph.eventually_right_inverse",
"OpenPartialHomeomorph.toFun'",
"TopologicalSpace",
"OpenPartialHomeomorph.map_source",
"PartialEquiv.source",
"OpenPartialHomeomorph.toPartialEquiv",
"Eq",
"Set.instMembership",
"OpenPartialHomeom... | true |
SSet.modelCategoryQuillen.instCategoryWithCofibrations | Mathlib.AlgebraicTopology.SimplicialSet.CategoryWithFibrations | [
"HomotopicalAlgebra.CategoryWithCofibrations.mk",
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.MorphismProperty.monomorphisms",
"SSet",
"CategoryTheory.types",
"SimplexCategory",
"CategoryTheory.Category.opposite",
"SimplexCategory.smallCategory",
"HomotopicalAlgebra.CategoryWith... | true |
_private.Mathlib.Data.Nat.Factorization.Basic.0.Nat.dvd_iff_prime_pow_dvd_dvd._simp_1_2 | Mathlib.Data.Nat.Factorization.Basic | [
"Exists",
"propext",
"Classical.not_forall",
"Eq",
"Not"
] | false |
_private.Mathlib.Logic.ExistsUnique.0.List.decidableBExistsUnique._proof_10 | Mathlib.Logic.ExistsUnique | [
"Lean.Grind.of_eq_eq_true",
"Lean.Grind.eq_false_of_not_eq_true",
"False",
"Lean.Grind.not_not",
"Lean.Grind.not_and",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Lean.Grind.not_or",
"HEq.refl",
"False.elim",
"Classical.byContradiction",
"Lean.Grind._simp_1",
"Lean.Grind.and_eq_of_eq_tru... | false |
Aesop.instInhabitedUnsafeRuleInfo | Aesop.Rule | [
"Aesop.UnsafeRuleInfo",
"Aesop.instInhabitedUnsafeRuleInfo.default",
"Inhabited",
"Inhabited.mk"
] | true |
SModEq | Mathlib.LinearAlgebra.SModEq.Basic | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"Submodule.Quotient.mk",
"Submodule.hasQuotient",
"AddCommGroup",
"HasQuotient.Quotient",
"Module",
"Ring.toSemiring",
"Eq",
"Ring"
] | true |
HomotopicalAlgebra.BifibrantObject.homMk_homMk | Mathlib.AlgebraicTopology.ModelCategory.Bifibrant | [
"HomotopicalAlgebra.BifibrantObject",
"CategoryTheory.CategoryStruct.toQuiver",
"HomotopicalAlgebra.IsCofibrant",
"Quiver.Hom",
"HomotopicalAlgebra.IsFibrant",
"HomotopicalAlgebra.BifibrantObject.homMk",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"HomotopicalAl... | true |
CochainComplex.mappingCone.id | Mathlib.Algebra.Homology.HomotopyCategory.MappingCone | [
"add_neg_cancel",
"HomologicalComplex.instCategory",
"CochainComplex.HomComplex.instAddCommGroupCochain",
"CochainComplex.mappingCone.inl_snd_assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"CochainComplex.HomComplex.Cochain.comp_id",
"CochainComplex.mappingCone.inr",
"Quiver.Hom",
"CochainComplex... | true |
_private.Mathlib.Algebra.Homology.SpectralObject.Page.0.CategoryTheory.Abelian.SpectralObject.shortComplexMap._proof_1 | Mathlib.Algebra.Homology.SpectralObject.Page | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
"Int.instNegInt",
"Int.sub_nonne... | false |
IsPrincipalIdealRing.mk | Mathlib.RingTheory.Ideal.Span | [
"Semiring.toModule",
"Ideal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"IsPrincipalIdealRing",
"Semiring",
"IsPrincipalIdealRing.mk",
"Semiring.toNonAssocSemiring",
"Submodule.IsPrincipal"
] | true |
Std.Time.Internal.Bounded.LE.ofNat._proof_1 | Std.Time.Internal.Bounded | [
"Iff.mpr",
"Int",
"LE.le",
"instLENat",
"Nat.cast",
"And",
"instOfNat",
"Nat",
"And.intro",
"instNatCastInt",
"Int.ofNat_le",
"OfNat.ofNat",
"Int.instLEInt",
"Int.natCast_nonneg"
] | false |
Std.Antisymm.trichotomous_of_antisymm_not | Init.Data.Order.Lemmas | [
"Std.Antisymm.antisymm",
"Std.Antisymm",
"Std.Trichotomous.mk",
"Std.Trichotomous",
"Not"
] | true |
CategoryTheory.ComonadHom.noConfusionType | Mathlib.CategoryTheory.Monad.Basic | [
"CategoryTheory.Comonad",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ComonadHom.casesOn",
"CategoryTheory.ComonadHom",
"CategoryTheory.Comonad.δ",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Functor.map",
"CategoryTheory.Comonad.toFuncto... | false |
List.prod_ne_zero | Mathlib.Algebra.BigOperators.Ring.List | [
"Nontrivial",
"MulOne.toOne",
"MulZeroClass.toMul",
"Membership.mem",
"mt",
"Ne",
"MulZeroOneClass.toMulOneClass",
"List",
"MulOneClass.toMulOne",
"MonoidWithZero",
"NoZeroDivisors",
"MonoidWithZero.toMulZeroOneClass",
"List.instMembership",
"List.prod_eq_zero_iff",
"Iff.mp",
"Zero.toO... | true |
dense_iff_exists_between | Mathlib.Topology.Order.Basic | [
"Nontrivial",
"OrderTopology",
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"Dense",
"DistribLattice.toLattice",
"OrderTopology.to_orderClosedTopology",
"Dense.exists_between",
"TopologicalSpace",
"And",
"Iff",
... | true |
CategoryTheory.Bicategory.associator_inv_naturality_right_assoc | Mathlib.CategoryTheory.Bicategory.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.associator_inv_naturality_right",
"congrArg",
"Eq.mp",
"id",
"CategoryTheory.Bicategory.toCategoryStruct",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.Bicategory",
"Categ... | true |
_private.Mathlib.Analysis.Normed.Operator.NormedSpace.0.NormedSpace.equicontinuous_TFAE.match_1_3 | Mathlib.Analysis.Normed.Operator.NormedSpace | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"Continuous",
"SeminormedAddCommGroup",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"Preorder.t... | false |
Subgroup.op.eq_1 | Mathlib.Algebra.Group.Subgroup.MulOpposite | [
"Monoid.toMulOneClass",
"Subsemigroup.mk",
"MulOpposite",
"Subgroup.op._proof_1",
"Group",
"Subgroup.op._proof_2",
"Subgroup.mk",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Subgroup",
"Subgroup.one_mem",
"MulOpposite.instGroup",
"Subgroup.op",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne... | true |
_private.Mathlib.Analysis.Complex.JensenFormula.0.continuous_herglotzLogIntegrand_circle._proof_1_1 | Mathlib.Analysis.Complex.JensenFormula | [
"instLawfulOrderLT_mathlib",
"AddGroup.toSubtractionMonoid",
"Lean.Grind.Linarith.Expr.zero",
"Norm.norm",
"Lean.Grind.Linarith.Expr",
"NegZeroClass.toNeg",
"Lean.RArray.leaf",
"Complex.norm_nonneg",
"lt_of_le_of_lt",
"Lean.Grind.Field.toCommRing",
"False",
"Lean.Grind.Order.lt_unsat_k",
"Re... | false |
ULiftable.congr | Mathlib.Control.ULiftable | [
"outParam",
"Equiv",
"ULiftable"
] | true |
_private.Mathlib.Data.WSeq.Relation.0.Stream'.WSeq.liftRel_join.match_1_1 | Mathlib.Data.WSeq.Relation | [
"Stream'.WSeq.join",
"Exists",
"Stream'.WSeq.LiftRel",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"Stream'.WSeq",
"Exists.intro",
"Eq",
"Stream'.WSeq.append"
] | false |
HomologicalComplex.HasGoodTrifunctor₁₂Obj | Mathlib.Algebra.Homology.BifunctorAssociator | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"ComplexShape.ρ₁₂",
"CategoryTheory.Functor.category",
"HomologicalComplex",
"ComplexShape",
"TotalComplexShape",
"HomologicalComplex.X",
"CategoryTheory.GradedObject.HasGoodTrifunctor₁₂Obj",
"CategoryTheory.Category",
"ComplexS... | true |
Valuation.one_apply_eq_one_iff | Mathlib.RingTheory.Valuation.Basic | [
"Nontrivial",
"MulOne.toOne",
"Valuation.one",
"Ne",
"CommMonoidWithZero.toMonoidWithZero",
"MonoidWithZeroHom.one_apply_eq_one_iff",
"LinearOrderedCommMonoidWithZero.toCommMonoidWithZero",
"MulZeroOneClass.toMulOneClass",
"instDistribOfSemiring",
"instMulZeroOneClassOfSemiring",
"MulOneClass.to... | true |
CategoryTheory.Functor.CoconeTypes.descColimitType_injective_iff_of_isFiltered' | Mathlib.CategoryTheory.Limits.Types.ColimitTypeFiltered | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.IsFiltered.rightToMax",
"CategoryTheory.IsFiltered.coeqHom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"_private.Mathlib.CategoryTheory.Limits.Types.ColimitTypeFiltered.0.CategoryTheory.Functor.CoconeTypes.descColimitType_injective_iff_of... | true |
Std.ExtTreeMap.getKey_minKey? | Std.Data.ExtTreeMap.Lemmas | [
"Std.ExtDTreeMap.getKey_minKey?",
"Std.ExtTreeMap.isSome_minKey?_of_contains",
"Ordering",
"Std.TransCmp",
"Std.ExtTreeMap.getKey",
"Bool.true",
"Std.ExtTreeMap",
"Option.get",
"Std.ExtTreeMap.inner",
"Bool",
"Std.ExtTreeMap.contains",
"Std.ExtTreeMap.minKey?",
"Eq"
] | true |
Std.Internal.List.contains_of_contains_insertList_of_contains_eq_false_right | Std.Data.Internal.List.Associative | [
"False",
"Std.Internal.List.insertList",
"congrArg",
"Bool.false_eq_true",
"Std.Internal.List.contains_insertList_iff",
"Eq.mp",
"Bool.true",
"List",
"Std.Internal.List.containsKey",
"EquivBEq",
"Iff.mp",
"Bool",
"congrFun'",
"or_false",
"Or",
"Bool.false",
"BEq",
"Eq",
"Sigma",
... | true |
UInt16.ofBitVec_shiftRight | Init.Data.UInt.Bitwise | [
"instPowNat",
"UInt16.toBitVec",
"BitVec.instHShiftRight",
"BitVec.instHShiftRightNat",
"Dvd.dvd",
"UInt16.toBitVec_shiftRight",
"UInt16.ofBitVec",
"BitVec.instOfNat",
"congrArg",
"UInt16.toNat_ofNat'",
"BitVec",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"BitVec.toNat",
"BitVec.ofNat"... | true |
_private.Mathlib.Data.Set.Basic.0.Set.sep_ext_iff._simp_1_2 | Mathlib.Data.Set.Basic | [
"and_congr_right_iff",
"And",
"Iff",
"propext",
"Eq"
] | false |
Lean.Lsp.ParameterInformationLabel.name.injEq | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.ParameterInformationLabel.name",
"Lean.Lsp.ParameterInformationLabel",
"Eq.propIntro",
"String",
"Lean.Lsp.ParameterInformationLabel.name.inj",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
Option.isNone.eq_1 | Mathlib.Computability.TuringMachine.StackTuringMachine | [
"Option.isNone",
"Option.some",
"Bool",
"Eq.refl",
"Bool.false",
"Eq"
] | true |
Std.DTreeMap.Raw.Const.get_insertManyIfNewUnit_list | Std.Data.DTreeMap.Raw.Lemmas | [
"Unit.unit",
"Std.DTreeMap.Raw.instMembership",
"instForInOfForIn'",
"Membership.mem",
"Ordering",
"inferInstance",
"Std.DTreeMap.Raw.Const.insertManyIfNewUnit",
"Id",
"Membership",
"List",
"Unit",
"List.instMembership",
"Id.instMonad",
"Std.DTreeMap.Raw.Const.get",
"Eq",
"rfl",
"Lis... | true |
_private.Mathlib.Analysis.Meromorphic.TrailingCoefficient.0.MeromorphicAt.meromorphicTrailingCoeffAt_add_eq_left_of_lt._simp_1_3 | Mathlib.Analysis.Meromorphic.TrailingCoefficient | [
"instHAdd",
"HAdd.hAdd",
"IsLeftCancelAdd",
"propext",
"Eq",
"add_right_inj",
"Add"
] | false |
Bundle.ContinuousRiemannianMetric._sizeOf_1 | Mathlib.Topology.VectorBundle.Riemannian | [
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toNormedAddCommGroup",
"ContinuousLinearMap.continuousSMul",
"RingHomSurjective.ids",
"Real",
"Algebra.to_smulCommClass",
"Continuous",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule... | false |
ConditionallyCompletePartialOrderInf.mk._flat_ctor | Mathlib.Order.ConditionallyCompletePartialOrder.Defs | [
"LT.mk",
"DirectedOn",
"ConditionallyCompletePartialOrderInf.mk",
"Preorder.mk",
"InfSet.mk",
"GE.ge",
"Preorder.lt_iff_le_not_ge._autoParam",
"autoParam",
"And",
"Iff",
"Set.Nonempty",
"IsGLB",
"LE.mk",
"BddBelow",
"ConditionallyCompletePartialOrderInf",
"Eq",
"Not",
"PartialOrder... | false |
Batteries.Tactic.GeneralizeProofs.Config.mk.noConfusion | Batteries.Tactic.GeneralizeProofs | [
"Batteries.Tactic.GeneralizeProofs.Config",
"Batteries.Tactic.GeneralizeProofs.Config.noConfusion",
"id",
"Nat",
"Bool",
"Batteries.Tactic.GeneralizeProofs.Config.mk",
"Eq"
] | false |
UniqueMDiffOn | Mathlib.Geometry.Manifold.MFDeriv.Defs | [
"NormedSpace",
"Membership.mem",
"UniqueMDiffWithinAt",
"TopologicalSpace",
"ModelWithCorners",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Set.instMembership",
"NormedAddCommGroup",
"Set",
"ChartedSpace"
] | true |
isAddConj_zero_right._simp_1 | Mathlib.Algebra.Group.Conj | [
"AddMonoid.toAddZeroClass",
"IsAddConj",
"AddZeroClass.toAddZero",
"AddZero.toZero",
"AddMonoid",
"propext",
"isAddConj_zero_right",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
Array.allM_congr | Init.Data.Array.Lemmas | [
"Array",
"funext",
"Nat",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Monad",
"Eq",
"Array.allM"
] | true |
_private.Init.Data.String.Extra.0.String.findLeadingSpacesSize.consumeSpaces._mutual._proof_5 | Init.Data.String.Extra | [
"PSum.casesOn",
"String.Pos.next",
"String",
"invImage",
"PSum",
"PSum.inr",
"PSigma.casesOn",
"id",
"instOfNatNat",
"PSum.inl",
"String.instLTPos",
"Nat",
"LT.lt",
"String.Pos",
"String.Pos.IsAtEnd",
"PSigma.mk",
"of_eq_true",
"String.Pos.lt_next._simp_1",
"String.Pos.instWellFo... | false |
Bundle.Pretrivialization.preimage_symm_proj_inter | Mathlib.Topology.FiberBundle.Trivialization | [
"Set.instSProd",
"Set.ext",
"Eq.mpr",
"and_true",
"SProd.sprod",
"congrArg",
"Set.univ",
"Iff.rfl",
"Membership.mem",
"PartialEquiv.symm",
"_private.Mathlib.Topology.FiberBundle.Trivialization.0.Bundle.Pretrivialization.preimage_symm_proj_inter._simp_1_3",
"id",
"Prod.mk",
"_private.Mathli... | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.Option.bind_dmap_left | Std.Data.Internal.List.Associative | [
"Option.casesOn",
"Option.some",
"Option.bind",
"Option.none",
"Eq.ndrec",
"Option.pbind",
"Eq.refl",
"_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.Option.dmap",
"Eq.symm",
"Eq",
"Option"
] | true |
Set.Icc_diff_pi_univ_Ioo_subset | Mathlib.Order.Interval.Set.Pi | [
"Eq.mpr",
"_private.Mathlib.Order.Interval.Set.Pi.0.Set.Icc_diff_pi_univ_Ioo_subset._simp_1_1",
"Pi.preorder",
"Preorder.toLT",
"Function.update",
"and_true",
"_private.Mathlib.Order.Interval.Set.Pi.0.Set.Icc_diff_pi_univ_Ioo_subset._simp_1_4",
"congrArg",
"and_self",
"true_or",
"LinearOrder",
... | true |
Multipliable.map_iff_of_equiv | Mathlib.Topology.Algebra.InfiniteSum.Basic | [
"MulEquiv.instEquivLike",
"Continuous",
"Monoid.toMulOneClass",
"SummationFilter",
"MulEquiv.instMulEquivClass",
"Function.comp",
"MulOne.toMul",
"Multipliable",
"MulEquivClass",
"TopologicalSpace",
"MulOneClass.toMulOne",
"Multipliable.map_iff_of_leftInverse",
"Iff",
"EquivLike",
"CommM... | true |
TensorProduct.rightComm._proof_11 | Mathlib.LinearAlgebra.TensorProduct.Associator | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddCommMonoidWithOne.toAddMonoidWithOne... | false |
div_pos_iff_of_pos_right | Mathlib.Algebra.Order.Field.Basic | [
"Iff.mpr",
"GroupWithZero.toMonoidWithZero",
"DivInvMonoid.toInv",
"Preorder.toLT",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"DivInvOneMonoid.toInvOneClass",
"MulZeroClass.toMul",
"IsStrictOrderedRing.toMulPosStrictMono",
"Monoid.toMulOneClass"... | true |
_private.Std.Time.Format.Basic.0.Std.Time.GenericFormat.format.match_1 | Std.Time.Format.Basic | [
"Std.Time.Awareness.only",
"Std.Time.Awareness.casesOn",
"Std.Time.Awareness.any",
"Std.Time.TimeZone",
"Std.Time.GenericFormat",
"Std.Time.Awareness"
] | false |
_private.Lean.Elab.PatternVar.0.Lean.Elab.Term.CollectPatternVars.isNextArgAccessible | Lean.Elab.PatternVar | [
"Lean.ConstructorVal",
"Lean.Elab.Term.CollectPatternVars.Context.paramDeclIdx",
"Lean.Elab.Term.CollectPatternVars.Context",
"GE.ge",
"instLENat",
"dite",
"Array",
"GetElem.getElem",
"Unit",
"_private.Lean.Elab.PatternVar.0.Lean.Elab.Term.CollectPatternVars.isNextArgAccessible.match_1",
"Array.... | true |
ContinuousLinearMap.mk._flat_ctor | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic | [
"instHSMul",
"Continuous",
"DistribMulAction.toDistribSMul",
"ContinuousLinearMap.mk",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"ContinuousLinearMap.cont._autoParam",
"autoParam",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace... | false |
_private.Lean.Meta.Sym.Pattern.0.Lean.Meta.Sym.isLevelDefEqS._sparseCasesOn_4 | Lean.Meta.Sym.Pattern | [
"Lean.Level.ctorIdx",
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Lean.Level.mvar",
"Lean.Level.param",
"Nat.hasNotBit",
"Lean.Level.imax",
"instOfNatNat",
"Lean.Level",
"Nat.land",
"Lean.Level.zero",
"Nat",
"Bool",
"Lean.Level.rec",
"Lean.Name",
"Eq.refl",
"Lean.Level.succ",
"OfN... | false |
Lean.Meta.Grind.Arith.Linear.IneqCnstrProof.notCoreOfNat.sizeOf_spec | Lean.Meta.Tactic.Grind.Arith.Linear.Types | [
"Lean.Meta.Grind.Arith.Linear.LinExpr",
"Lean.Grind.Linarith.Expr._sizeOf_inst",
"Lean.Meta.Grind.Arith.Linear.IneqCnstrProof",
"Lean.Expr",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"instSizeOfNat",
"OfNat.ofNat",
"Eq",
"Lean.Meta.Grind.Ar... | true |
LinearMap.coprod_inl_inr | Mathlib.LinearAlgebra.Prod | [
"LinearMap.id",
"LinearMap.coprod",
"LinearMap.inl",
"AddMonoid.toAddSemigroup",
"LinearMap.ext",
"congrArg",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"Prod.mk",
"zero_add",
"LinearMap",
"Prod.fst",
"AddCommMonoid",
"AddZero.toZero",
"instHAdd",
... | true |
RingCon.congrₐ._proof_1 | Mathlib.RingTheory.Congruence.Hom | [
"RingEquiv.toEquiv",
"HMul.hMul",
"RingCon.instMulQuotient",
"RingCon",
"Distrib.toAdd",
"RingCon.Quotient",
"RingEquiv.map_mul'",
"Equiv.toFun",
"RingCon.instAddQuotient",
"instDistribOfSemiring",
"Distrib.toMul",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semiring",
"NonUnitalNonAs... | false |
Lean.SerialMessage.endPos._inherited_default | Lean.Message | [
"id",
"Lean.Position",
"Option.none",
"Option"
] | false |
CategoryTheory.Factorisation.terminal_ι | Mathlib.CategoryTheory.Category.Factorisation | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Factorisation.ι",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Factorisation.terminal",
"Eq",
"CategoryTheory.Category"
] | true |
Manifold.definition._@.Mathlib.Geometry.Manifold.Riemannian.PathELength.4077471356._hygCtx._hyg.102 | Mathlib.Geometry.Manifold.Riemannian.PathELength | [
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"iInf",
"mfderiv",
"PiLp.normedSpace",
"fact_one_le_two_ennreal",
"instAddMonoidWithOneENat",
"NormedSpace",
"Real.denselyNormedField",
"Real.instZero",
"Manifold.definition._proof_1._@.Mathlib.Geometry.Manifold.... | false |
_private.Mathlib.RingTheory.DedekindDomain.Different.0.Submodule.traceDual_top'._simp_1_5 | Mathlib.RingTheory.DedekindDomain.Different | [
"Submodule",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Membership.mem",
"Exists",
"Algebra.toModule",
"Submodule.one",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"RingHom.instFunLike",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Submodul... | false |
_private.Mathlib.RingTheory.Spectrum.Prime.FreeLocus.0.Module.isLocallyConstant_rankAtStalk_freeLocus._simp_1_3 | Mathlib.RingTheory.Spectrum.Prime.FreeLocus | [
"Monoid",
"Monoid.toMulOneClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"Submonoid.instPartialOrder",
"Submonoid.powers",
"propext",
"Submonoid.instSetLike",
"Eq",
"SetLike.instMembership",
"Submonoid",
"Submonoid.powers_le"
] | false |
EuclideanGeometry.Sphere.IsTangentAt.inner_right_eq_zero_of_mem | Mathlib.Geometry.Euclidean.Sphere.Tangent | [
"InnerProductSpace.toNormedSpace",
"Real",
"EuclideanGeometry.Sphere.mem_orthRadius_iff_inner_right",
"Inner.inner",
"EuclideanGeometry.Sphere.IsTangentAt",
"Real.instZero",
"Real.instRCLike",
"NormedSpace.toModule",
"EuclideanGeometry.Sphere",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Rea... | true |
AddGrpCat.hasZeroObject | Mathlib.Algebra.Category.Grp.Zero | [
"CategoryTheory.Limits.HasZeroObject.mk",
"AddGrpCat.instCategory",
"PUnit.addCommGroup",
"AddCommGroup.toAddGroup",
"AddGrpCat",
"instSubsingletonPUnit",
"AddGrpCat.isZero_of_subsingleton",
"PUnit",
"CategoryTheory.Limits.HasZeroObject",
"Exists.intro",
"AddGrpCat.of",
"CategoryTheory.Limits.... | true |
mabs.unexpander | Mathlib.Algebra.Order.Group.Unbundled.Abs | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Array.mkArray0",
"Lea... | true |
Task.pure.injEq | Init.Core | [
"Task",
"Task.pure.inj",
"Eq.propIntro",
"Task.pure",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
CategoryTheory.Functor.LeftExtension.isPointwiseLeftKanExtensionOfIsIsoOfIsLocalization | Mathlib.CategoryTheory.Functor.Derived.PointwiseRightDerived | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.Functor.LeftExtension",
"CategoryTheory.IsIso",
"CategoryTheory.Functor.isPointwiseLeftKanExtensionOfIsoOfIsLocalization",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.StructuredArrow.hom"... | true |
CategoryTheory.Abelian.SpectralObject.recOn | Mathlib.Algebra.Homology.SpectralObject.Basic | [
"CategoryTheory.Abelian.SpectralObject.mk",
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject._proof_8",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Functo... | false |
MeasureTheory.Measure.haar.is_left_invariant_addIndex | Mathlib.MeasureTheory.Measure.Haar.Basic | [
"AddGroup.toSubtractionMonoid",
"Set.image_image",
"Eq.mpr",
"NegZeroClass.toNeg",
"instSeparatelyContinuousAddOfContinuousAdd",
"congrArg",
"Set.image_id'",
"HEq.refl",
"MeasureTheory.Measure.haar.addIndex",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership... | true |
minpoly.rootsOfMinPolyPiType._proof_3 | Mathlib.FieldTheory.Minpoly.Field | [
"IsNoetherianRing.strongRankCondition",
"PrincipalIdealRing.isNoetherianRing",
"Field.toDivisionRing",
"Field.instIsLocalRing",
"DivisionRing.toRing",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"StrongRankCondition",
"IsLocalRing.toNontrivial",
"EuclideanDomain.to_principal_ideal_domain"... | false |
UInt64.toNat_sub | Init.Data.UInt.Lemmas | [
"instPowNat",
"UInt64",
"BitVec.toNat_sub",
"HSub.hSub",
"Nat.instMod",
"instHMod",
"instSubNat",
"instOfNatNat",
"UInt64.toNat",
"instNatPowNat",
"instHAdd",
"HMod.hMod",
"instHSub",
"HPow.hPow",
"HAdd.hAdd",
"Nat",
"instSubUInt64",
"instAddNat",
"instHPow",
"OfNat.ofNat",
"... | true |
Int64.shiftLeft | Init.Data.SInt.Basic | [
"Int64.ofUInt64",
"BitVec.instOfNat",
"HShiftLeft.hShiftLeft",
"UInt64.ofBitVec",
"BitVec",
"Int64",
"instOfNatNat",
"Nat",
"BitVec.instHShiftLeft",
"Int64.toBitVec",
"BitVec.smod",
"OfNat.ofNat"
] | true |
_private.Lean.Meta.Match.Match.0.Lean.Meta.Match.getMkMatcherInputInContext.match_1 | Lean.Meta.Match.Match | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"_private.Lean.Meta.Match.Match.0.Lean.Meta.Match.withEqs.go._sparseCasesOn_1",
"Nat",
"Option"
] | false |
AddMonCat.FilteredColimits.coconeMorphism | Mathlib.Algebra.Category.MonCat.FilteredColimits | [
"CategoryTheory.Functor",
"AddMonCat.FilteredColimits.colimit",
"AddMonCat.instConcreteCategoryAddMonoidHomCarrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Limits.Types.TypeMax.colimitCocone",
"AddMonoid.toAddZeroClass",
"Catego... | true |
Std.ExtTreeSet.instSDiffOfTransCmp | Std.Data.ExtTreeSet.Basic | [
"Ordering",
"Std.TransCmp",
"Std.ExtTreeSet.diff",
"Std.ExtTreeSet",
"SDiff.mk",
"SDiff"
] | true |
_private.Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Pseudo.0.CategoryTheory.Pseudofunctor.StrongTrans.naturality_naturality_hom._simp_1_1 | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Pseudo | [
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsIso.inv_comp_eq",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.inv",
"CategoryTheory.Category.toCategoryStruct",
"Eq.symm",
"Eq",
"CategoryTheory.Category"
] | false |
Lean.reservedNamePredicatesExt | Lean.ResolveName | [
"Inhabited.default",
"Lean.instInhabitedEnvExtension",
"Array",
"Bool",
"Lean.Name",
"Lean.EnvExtension",
"Lean.Environment"
] | true |
Mathlib.Tactic.ToDual.abbreviationDict | Mathlib.Tactic.Translate.ToDual | [
"String",
"Prod.mk",
"Std.HashMap.ofList",
"Std.HashMap",
"instHashableString",
"instBEqOfDecidableEq",
"List.cons",
"instDecidableEqString",
"Prod",
"List.nil"
] | true |
Filter.Tendsto.logb | Mathlib.Analysis.SpecialFunctions.Log.Base | [
"Real",
"Real.instZero",
"PseudoMetricSpace.toUniformSpace",
"nhds",
"Ne",
"Real.logb",
"ContinuousAt.tendsto",
"Filter.Tendsto",
"Zero.toOfNat0",
"Real.pseudoMetricSpace",
"Real.continuousAt_logb",
"Filter.Tendsto.comp",
"OfNat.ofNat",
"UniformSpace.toTopologicalSpace",
"Filter"
] | true |
Nat.dvd_prime_two_le | Mathlib.Data.Nat.Prime.Defs | [
"Nat.Prime",
"Dvd.dvd",
"instOfNatNat",
"Nat.dvd_prime",
"LE.le",
"instLENat",
"Iff",
"Nat.instDvd",
"Not.elim",
"Nat",
"Iff.trans",
"or_iff_right_of_imp",
"Or",
"OfNat.ofNat",
"Eq",
"Nat.ne_of_gt"
] | true |
_private.Mathlib.Computability.RegularExpressions.0.RegularExpression.deriv.match_1.eq_2 | Mathlib.Computability.RegularExpressions | [
"RegularExpression",
"RegularExpression.char",
"RegularExpression.comp",
"RegularExpression.plus",
"RegularExpression.epsilon",
"RegularExpression.star",
"RegularExpression.zero",
"Eq.refl",
"RegularExpression.deriv.match_1",
"Eq"
] | true |
MeasureTheory.Measure.compProd_sum_right | Mathlib.Probability.Kernel.Composition.MeasureCompProd | [
"Eq.mpr",
"Unit.unit",
"MeasureTheory.Measure",
"ProbabilityTheory.Kernel.IsSFiniteKernel.prodMkLeft",
"congrArg",
"MeasureTheory.Measure.compProd.eq_1",
"ProbabilityTheory.IsSFiniteKernel",
"ProbabilityTheory.Kernel.instFunLike",
"id",
"MeasurableSpace",
"Unit",
"ProbabilityTheory.Kernel.sum"... | true |
IsInvariantSubring.casesOn | Mathlib.Algebra.Ring.Action.Invariant | [
"Monoid",
"IsInvariantSubring.mk",
"instHSMul",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Membership.mem",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddZero.toZero",
"IsIn... | false |
ExteriorAlgebra.liftAlternatingEquiv_apply | Mathlib.LinearAlgebra.ExteriorAlgebra.OfAlternating | [
"AlternatingMap",
"CommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"QuadraticMap.instZero",
"Ring.toNonAssocRing",
"ExteriorAlgebra",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"instAlgebraCliffordAlgebra",
"Pi.module",
"QuadraticForm",
"LinearMap.instFunLike",
"Exterio... | true |
CategoryTheory.Limits.opCospan_inv_app | Mathlib.CategoryTheory.Limits.Shapes.Opposites.Pullbacks | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Limits.WalkingSpan",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Limits.opCospan",
"CategoryT... | true |
MeasureTheory.IsStoppingTime.measurableSet_ge_of_countable_range' | Mathlib.Probability.Process.Stopping | [
"Set.ext",
"Eq.mpr",
"MeasureTheory.IsStoppingTime",
"False",
"WithTop.top_ne_coe._simp_1",
"WithTop.instPartialOrder",
"Preorder.toLT",
"MeasureTheory.IsStoppingTime.measurableSet_eq_of_countable_range'",
"MeasurableSet",
"WithTop.instPreorder",
"congrArg",
"WithTop.coe_ne_top._simp_1",
"Li... | true |
FirstOrder.Language.LHom.constantsOnMap.match_1 | Mathlib.ModelTheory.LanguageMap | [
"False",
"False.elim",
"instOfNatNat",
"FirstOrder.Language.constantsOn",
"Nat",
"FirstOrder.Language.Functions",
"PEmpty.casesOn",
"Nat.zero",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
MeasureTheory.instPseudoEMetricSpaceMeasuredSets._proof_3 | Mathlib.MeasureTheory.Measure.MeasuredSets | [
"MeasureTheory.Measure",
"Lattice.toSemilatticeSup",
"_private.Mathlib.MeasureTheory.Measure.MeasuredSets.0.MeasureTheory.instPseudoEMetricSpaceMeasuredSets._proof_2",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"MeasureTheory.instSetLikeMeasuredSets",
"MeasurableSpace",
... | false |
Nat.lcm_eq_left_iff_dvd | Init.Data.Nat.Lcm | [
"Nat.gcd",
"Nat.lcm",
"Eq.mpr",
"Nat.mul_left_cancel_iff",
"Dvd.dvd",
"instHDiv",
"Nat.lcm_eq_mul_div",
"HMul.hMul",
"congrArg",
"Nat.dvd_zero._simp_1",
"Iff.rfl",
"id",
"HDiv.hDiv",
"instMulNat",
"instOfNatNat",
"Nat.gcd_pos_of_pos_left",
"Nat.gcd_dvd_mul",
"iff_self",
"GT.gt",
... | true |
List.eq_getElem_of_length_eq_three._proof_1 | Init.Data.List.Lemmas | [
"of_decide_eq_true",
"id",
"instOfNatNat",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
"Decidable.decide",
"Eq"
] | false |
CanonicallyOrderedCommMonoid.toUniqueAddUnits.eq_1 | Mathlib.Algebra.Order.Monoid.Canonical.Defs | [
"CanonicallyOrderedCommMonoid.toUniqueAddUnits._proof_1",
"Unique.mk",
"Unique",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"PartialOrder",
"CanonicallyOrderedAdd",
"AddUnits.instInhabited",
"AddMonoid",
"AddZero.toAdd",
"Eq.refl",
"Ca... | true |
_private.Mathlib.RingTheory.Multiplicity.0.emultiplicity_le_emultiplicity_iff._simp_1_5 | Mathlib.RingTheory.Multiplicity | [
"le_refl",
"Preorder.toLE",
"LE.le",
"True",
"eq_true",
"Eq",
"Preorder"
] | false |
_private.Lean.Environment.0.Lean.Environment.isSafeDefinition.match_1 | Lean.Environment | [
"Lean.ConstantInfo.defnInfo",
"Lean.DefinitionVal.mk",
"Lean.ConstantVal",
"Lean.ConstantVal.casesOn",
"Lean.ReducibilityHints",
"Lean.Expr",
"Lean.DefinitionSafety.safe",
"Nat.hasNotBit",
"_private.Lean.Environment.0.Lean.Environment.isSafeDefinition._sparseCasesOn_2",
"Lean.ConstantVal.mk",
"L... | false |
AddCommMagma.to_isCommutative | Mathlib.Algebra.Group.Defs | [
"AddCommMagma",
"add_comm",
"instHAdd",
"HAdd.hAdd",
"IsAddCommutative.mk",
"IsAddCommutative",
"Std.Commutative.mk",
"AddCommMagma.toAdd"
] | true |
Lean.Omega.Coeffs.dot_nil_right | Init.Omega.Coeffs | [
"Int",
"Lean.Omega.IntList.dot_nil_right",
"instOfNat",
"Lean.Omega.Coeffs",
"Lean.Omega.Coeffs.dot",
"OfNat.ofNat",
"Eq",
"List.nil"
] | true |
_private.Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks.0.CategoryTheory.Limits.PreservesPushout.inl_iso_inv._simp_1_2 | Mathlib.CategoryTheory.Limits.Preserves.Shapes.Pullbacks | [
"CategoryTheory.Iso.comp_inv_eq",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Iso.hom",
"Eq",
"CategoryTheory.Iso.inv",
"CategoryTheory.Category"
] | false |
CategoryTheory.ObjectProperty.IsClosedUnderFiniteProducts.casesOn | Mathlib.CategoryTheory.ObjectProperty.FiniteProducts | [
"CategoryTheory.ObjectProperty.IsClosedUnderFiniteProducts.mk",
"Finite",
"CategoryTheory.ObjectProperty.IsClosedUnderFiniteProducts",
"CategoryTheory.ObjectProperty.IsClosedUnderFiniteProducts.rec",
"CategoryTheory.ObjectProperty.IsClosedUnderLimitsOfShape",
"CategoryTheory.discreteCategory",
"Category... | false |
SemiRingCat.of.injEq | Mathlib.Algebra.Category.Ring.Basic | [
"Eq.propIntro",
"SemiRingCat.of.inj",
"Lean.injEq_helper",
"HEq.homo_ndrec",
"And",
"Eq.ndrec",
"Semiring",
"Eq.refl",
"HEq",
"SemiRingCat",
"SemiRingCat.of",
"Eq"
] | true |
FormalMultilinearSeries.hasFiniteFPowerSeriesOnBall_of_finite | Mathlib.Analysis.Analytic.CPolynomialDef | [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"le_refl",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"FormalMultilinearSeries.hasSum_of_finite",
"ENNReal.zero_lt_top",
"NormedSpace",
"congrArg",
"FormalMultilinearSeries",
"NormedAddCommGroup.toMetricSpa... | true |
CategoryTheory.Pseudofunctor.Grothendieck.mapCompIso | Mathlib.CategoryTheory.Bicategory.Grothendieck | [
"CategoryTheory.Pseudofunctor.Grothendieck.mapCompIso._proof_1",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pseudofunctor.Grothendieck.map",
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.Pseudofunctor.Grothendieck",
"CategoryTheory.F... | true |
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