name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.NonPreadditiveAbelian.neg_add_cancel | Mathlib.CategoryTheory.Abelian.NonPreadditive | [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.NonPreadditiveAbelian",
"id",
"CategoryTheory.NonPreadditiveAbelian.toHasZeroMorphisms",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"CategoryTheory.NonPreadditiveAbelian.hasNeg",
"instHAdd",
"HAdd.h... | true |
CategoryTheory.Subobject.mapIsoToOrderIso | Mathlib.CategoryTheory.Subobject.Basic | [
"CategoryTheory.Subobject.mapIsoToOrderIso._proof_3",
"RelIso.mk",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CategoryTheory.Subobject.map",
"Equiv.mk",
"CategoryTheory.Iso",
"OrderIso",
"Preorder.smallCategory",
"CategoryTheory.Subobject.mapIsoToOrderIso._proof_4",
"LE.le",
"CategoryTheory.... | true |
Mathlib.Meta.Multiset.ProveZeroOrConsResult.cons | Mathlib.Tactic.NormNum.BigOperators | [
"Mathlib.Meta.Multiset.ProveZeroOrConsResult.cons",
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level.succ",
"Mathlib.Meta.Multiset.ProveZeroOrConsResult",
"Lean.Name.mkStr1",
"List.nil"
] | true |
AffineEquiv.arrowCongr._proof_1 | Mathlib.LinearAlgebra.AffineSpace.AffineEquiv | [
"AffineMap.ext",
"AffineEquiv.linear",
"CommRing",
"AffineMap.instFunLike",
"Equiv.instEquivLike",
"AffineMap.instAddCommGroup",
"AddMonoid.toAddSemigroup",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AffineEquiv.arrowCongrₗ",
"AffineEquiv.equivLike",
"AddCommGrou... | false |
ContinuousNeg.mk._flat_ctor | Mathlib.Topology.Algebra.Group.Defs | [
"ContinuousNeg.mk",
"Continuous",
"ContinuousNeg",
"TopologicalSpace",
"Neg",
"Neg.neg"
] | false |
PrimrecPred.comp | Mathlib.Computability.Primrec.Basic | [
"Primrec.primrecPred",
"Primrec",
"Primcodable.bool",
"DecidablePred",
"Primrec.comp",
"Primcodable",
"Bool",
"_private.Mathlib.Computability.Primrec.Basic.0.PrimrecPred.comp.match_1_1",
"Decidable.decide",
"PrimrecPred"
] | true |
PosNum.lor._unsafe_rec | Mathlib.Data.Num.Bitwise | [
"PosNum.lor.match_1",
"PosNum.bit1",
"PosNum.lor._unsafe_rec",
"PosNum.bit0",
"PosNum"
] | false |
OrderDual.instAddCancelCommMonoid | Mathlib.Algebra.Order.Group.Synonym | [
"AddCancelCommMonoid.mk",
"AddCancelCommMonoid",
"OrderDual.instAddCancelCommMonoid._proof_1",
"AddCancelCommMonoid.toAddCommMonoid",
"OrderDual",
"OrderDual.instAddCommMonoid"
] | true |
Std.DTreeMap.Internal.Zipper.prependMapGE._unsafe_rec | Std.Data.DTreeMap.Internal.Zipper | [
"Ord",
"Ordering",
"_private.Std.Data.DTreeMap.Internal.Zipper.0.Std.DTreeMap.Internal.Impl.pruneLE.match_1",
"Std.DTreeMap.Internal.Zipper",
"Ord.compare",
"Std.DTreeMap.Internal.Zipper.cons",
"Unit",
"Nat",
"_private.Std.Data.DTreeMap.Internal.Zipper.0.Std.DTreeMap.Internal.Impl.pruneLE.match_3",
... | false |
CochainComplex.mappingCocone.lift._proof_3 | Mathlib.Algebra.Homology.HomotopyCategory.MappingCocone | [
"Eq.mpr",
"HomologicalComplex.instCategory",
"CochainComplex.HomComplex.instAddCommGroupCochain",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CochainComplex.HomComplex.Cochain.comp",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWi... | false |
IsSMulRegular.of_mul_eq_one | Mathlib.Algebra.Regular.SMul | [
"Monoid",
"Eq.mpr",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"id",
"MulOne.toMul",
"IsScalarTower.left",
"IsSMulRegular.of_mul",
"MulOneClass.toMulOne",
"MulAction",
"IsSMulRegular",
"Monoid.toSemigroup",
"One.toOfNat1",
"SemigroupAction.toSMul",
"MulAction.to... | true |
frequently_nhds_iff | Mathlib.Topology.Neighborhoods | [
"congrArg",
"Membership.mem",
"Exists",
"nhds",
"Filter.Frequently",
"iff_self",
"TopologicalSpace",
"And",
"Iff",
"Filter.HasBasis.frequently_iff",
"True",
"Iff.trans",
"of_eq_true",
"congrFun'",
"IsOpen",
"nhds_basis_opens",
"Set.instMembership",
"and_imp._simp_1",
"Eq.trans",
... | true |
Lean.ImportState.ctorIdx | Lean.Environment | [
"Nat",
"Lean.ImportState"
] | false |
TensorProduct.AlgebraTensorModule.map_smul_right | Mathlib.LinearAlgebra.TensorProduct.Tower | [
"TensorProduct.instDistribMulAction",
"IsScalarTower.to_smulCommClass'",
"LinearMap.restrictScalars",
"TensorProduct.leftHasSMul",
"instHSMul",
"instSMulOfMul",
"LinearMap.ext",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"TensorProduct.addMonoid",... | true |
Num.gcdAux.eq_1 | Mathlib.Data.Num.ZNum | [
"Num.gcdAux",
"instOfNatNat",
"Num",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
_private.Mathlib.Analysis.Asymptotics.Lemmas.0.Asymptotics.IsLittleO.tendsto_inv_smul_nhds_zero._simp_1_1 | Mathlib.Analysis.Asymptotics.Lemmas | [
"Norm.norm",
"Real",
"GroupWithZero.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Real.instInv",
"NormedDivisionRing.toNorm",
"DivisionSemiring.toGroupWithZero",
"NormedDivisionRing.toDivisionRing",
"DivisionMonoid.toDivInvOneMonoid",
"DivisionRing.toDivisionSemiring",
"norm_inv",
"Inv.... | false |
_private.Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion.0.Tactic.ComputeAsymptotics.Seq.dist_eq_one_of_head._simp_1_2 | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Corecursion | [
"Exists",
"instOfNatNat",
"Nat.find_eq_zero",
"DecidablePred",
"Nat",
"Nat.find",
"propext",
"OfNat.ofNat",
"Eq"
] | false |
CategoryTheory.Limits.cospanCompIso_hom_app_right | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingCospan.right",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Lim... | true |
CategoryTheory.Triangulated.SpectralObject.instCategory._proof_7 | Mathlib.CategoryTheory.Triangulated.SpectralObject | [
"CategoryTheory.Functor",
"CategoryTheory.Triangulated.SpectralObject",
"CategoryTheory.Triangulated.SpectralObject.instCategory._proof_2",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Triangulated.SpectralObject.δ",
"CategoryTheory.Triangulated.SpectralObject.instCategory._pr... | false |
_private.Mathlib.Algebra.GroupWithZero.WithZero.0.WithZero.monoidWithZeroHom_ext.match_1_1 | Mathlib.Algebra.GroupWithZero.WithZero | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"WithZero"
] | false |
stdOrthonormalBasis | Mathlib.Analysis.InnerProductSpace.PiL2 | [
"InnerProductSpace.toNormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedDivisionRing.toDivisionRing",
"NormedField.toField",
"NormedField.toNormedDivisionRing",
"Field.toSemifield",
"Fin.fintype",
"RCLike.toDenselyNormedField",
"RCLike",
"FiniteDimensional",
"Semifiel... | true |
AlgebraicGeometry.instModuleObjOppositeOpensCarrierTopObjFunctorTypeIsSheafGrothendieckTopologyStructureSheafInType_1._proof_3 | Mathlib.AlgebraicGeometry.StructureSheaf | [
"AlgebraicGeometry.StructureSheaf.Localizations",
"Subalgebra.instSetLike",
"CategoryTheory.Functor",
"Submodule.module._proof_1",
"Semigroup.toMul",
"CommRing",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"Pi.addCommMonoid",
"Opposite",
"HMul.hMul",
"TopologicalSpace.Opens.instPartia... | false |
CategoryTheory.Limits.FormalCoproduct.Hom.fromIncl_asSigma | Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic | [
"Eq.mpr",
"CategoryTheory.Limits.FormalCoproduct.Hom.asSigma",
"CategoryTheory.Limits.FormalCoproduct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.Limits.FormalCoproduct.hom_ext",
"CategoryTheory.Limits.FormalCoproduct.hom_ext._proof... | true |
Std.DTreeMap.Internal.Impl.getKey?_eq_some_getKey! | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Ord",
"Std.TransOrd",
"Option.some",
"Membership.mem",
"id",
"Std.DTreeMap.Internal.Impl.WF",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"implies_congr",
"Std.DTreeMap.Internal.Impl.getKey?",
"Bool",
"Std.DTreeMap.Internal.Impl.getKey!",
"Inhabited",
"Eq.refl",
"_pr... | true |
Submodule.tensorSpanEquivSpan | Mathlib.LinearAlgebra.Span.TensorProduct | [
"Submodule.tensorEquivSpan._proof_2",
"Submodule",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"Submodule.addCommMonoid",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
... | true |
Dvd.intro | Mathlib.Algebra.Divisibility.Basic | [
"Semigroup",
"Semigroup.toMul",
"Dvd.dvd",
"HMul.hMul",
"semigroupDvd",
"Exists.intro",
"Eq.symm",
"Eq",
"instHMul"
] | true |
CategoryTheory.Functor.IsEventuallyConstantTo.cone | Mathlib.CategoryTheory.Limits.Constructions.EventuallyConstant | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsCofiltered",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.IsEventuallyConstantTo",
"CategoryTheory.NatTrans.mk",
"CategoryTheory.Category.toCategoryStruct",... | true |
mem_uniformity_isClosed | Mathlib.Topology.UniformSpace.Basic | [
"Filter.instMembership",
"UniformSpace",
"uniformity_hasBasis_closed",
"Filter.HasBasis.mem_iff",
"SetRel",
"uniformity",
"instTopologicalSpaceProd",
"Membership.mem",
"Exists",
"_private.Mathlib.Topology.UniformSpace.Basic.0.mem_uniformity_isClosed.match_1_1",
"id",
"HasSubset.Subset",
"IsC... | true |
CategoryTheory.LocallyDiscrete.mk.inj | Mathlib.CategoryTheory.Bicategory.LocallyDiscrete | [
"CategoryTheory.LocallyDiscrete.mk",
"CategoryTheory.LocallyDiscrete",
"CategoryTheory.LocallyDiscrete.mk.noConfusion",
"eq_of_heq",
"HEq",
"Eq"
] | true |
_private.Std.Data.ExtDHashMap.Basic.0.Std.ExtDHashMap.get._proof_2 | Std.Data.ExtDHashMap.Basic | [
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"instLawfulHashableOfLawfulBEq",
"Std.DHashMap.Equiv",
"LawfulBEq",
"Membership.mem",
"Eq.rec",
"Std.DHashMap.instMembership",
"Std.DHashMap.Equiv.mem_iff",
"Std.ExtDHashMap.mk",
"Iff.mp",
"Std.ExtDHashMap",
"Hashable",
"instEquivBE... | false |
RingCat.Colimits.Prequotient._sizeOf_1 | Mathlib.Algebra.Category.Ring.Colimits | [
"CategoryTheory.Functor",
"instSizeOfDefault",
"CategoryTheory.SmallCategory",
"RingCat.Colimits.Prequotient",
"instOfNatNat",
"RingCat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"RingCat.instCategory",
"SizeOf.sizeOf",
"RingCat.Colimits.Prequotient.rec",
"instAddNat",
"SizeOf",
"OfNat.ofNat",
... | false |
ContinuousLinearMap.continuousConstSMul | Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap | [
"Monoid",
"NormedCommRing.toSeminormedCommRing",
"Bornology.IsVonNBounded",
"ContinuousLinearMap.topologicalSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"setOf",
"AddCommGroup.toAddGroup",
"RingHom",
"NormedField.toField",
"AddZeroClass.... | true |
LieIdeal.map_sup_ker_eq_map | Mathlib.Algebra.Lie.Ideal | [
"LieHom",
"LieAlgebra.toModule",
"LieSubmodule.instSetLike",
"Eq.mpr",
"Submodule",
"CommRing",
"Lattice.toSemilatticeSup",
"LieIdeal.map._proof_1",
"LieRing.toAddCommGroup",
"le_sup_left",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
... | true |
SimpleGraph.Copy.isoSubgraphMap._simp_4 | Mathlib.Combinatorics.SimpleGraph.Copy | [
"True",
"propext",
"forall_true_iff",
"Eq"
] | false |
Lean.Lsp.instHashableResolvableCompletionItemData.hash | Lean.Data.Lsp.LanguageFeatures | [
"UInt64.instOfNat",
"mixHash",
"UInt64",
"Lean.Lsp.CompletionIdentifier",
"Lean.Lsp.instHashableCompletionIdentifier",
"Lean.Lsp.instHashablePosition",
"instHashableNat",
"instHashableString",
"Lean.Lsp.DocumentUri",
"Hashable.hash",
"Nat",
"Lean.Lsp.Position",
"Lean.Lsp.ResolvableCompletion... | true |
Lean.Compiler.LCNF.LambdaLifting.Context.allowEtaContraction | Lean.Compiler.LCNF.LambdaLifting | [
"Lean.Compiler.LCNF.LambdaLifting.Context",
"Bool"
] | true |
MeasureTheory.ofReal_setAverage | Mathlib.MeasureTheory.Integral.Average | [
"MeasureTheory.ae",
"NormedCommRing.toSeminormedCommRing",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"instHDiv",
"MeasurableSet",
"Real.instZero",
"ENNReal.ofReal",
"congrArg",
"Set.univ",
"MeasureTheory.Measure.restrict_apply",
"PseudoMetricSpace.toUniformSpace",
"MeasureTheory.Meas... | true |
ContinuousLinearMap.equivProdOfSurjectiveOfIsCompl._proof_4 | Mathlib.Analysis.Normed.Module.Complemented | [
"NormedCommRing.toNormedRing",
"Continuous",
"NormedRing.toRing",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"LinearMap.instFunLike",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceProd",
"NormedField.toField",
"ContinuousLin... | false |
Lean.Elab.InlayHintInfo.label | Lean.Elab.InfoTree.InlayHints | [
"Lean.Elab.InlayHintLabel",
"Lean.Elab.InlayHintInfo"
] | true |
Set.indicator_pi_one_apply | Mathlib.Algebra.BigOperators.GroupWithZero.Finset | [
"CommMonoidWithZero.toCommMonoid",
"SetLike.mem_coe._simp_1",
"MulOne.toOne",
"congrArg",
"Set.indicator",
"Finset",
"Classical.propDecidable",
"Membership.mem",
"Classical.decPred",
"Finset.prod_congr",
"CommMonoidWithZero.toMonoidWithZero",
"MulZeroOneClass.toMulOneClass",
"Finset.prod",
... | true |
Nat.eq_zero_of_two_mul_le | Init.Data.Nat.Lemmas | [
"HMul.hMul",
"instMulNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat",
"Decidable.byContradiction",
"instDecidableEqNat",
"OfNat.ofNat",
"Eq",
"Not",
"_private.Init.Data.Nat.Lemmas.0.Nat.eq_zero_of_two_mul_le._proof_1_1",
"instHMul"
] | true |
CategoryTheory.Abelian.Ext.hom | Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | [
"instCategoryDerivedCategory",
"DerivedCategory",
"Equiv.instEquivLike",
"CategoryTheory.Abelian",
"Equiv",
"CategoryTheory.ShiftedHom",
"Int",
"Int.instAddMonoid",
"DerivedCategory.instHasShiftInt",
"Nat.cast",
"CategoryTheory.HasExt",
"instOfNat",
"Nat",
"CategoryTheory.Abelian.Ext",
"... | true |
Std.DTreeMap.Internal.Impl.maxKey!.induct_unfolding | Std.Data.DTreeMap.Internal.Model | [
"Std.DTreeMap.Internal.Impl.maxEntry?.match_1.congr_eq_2",
"Eq.mpr",
"Std.DTreeMap.Internal.Impl.maxEntry?.match_1",
"congrArg",
"invImage",
"instSizeOfDefault",
"panicWithPosWithDecl",
"Std.DTreeMap.Internal.Impl.maxKey!._proof_1",
"Std.DTreeMap.Internal.Impl.maxKey!",
"Std.DTreeMap.Internal.Impl... | true |
Std.CancellationContext.token | Std.Sync.CancellationContext | [
"Std.CancellationContext",
"Std.CancellationToken"
] | true |
Equiv.Perm.disjoint_iff_eq_or_eq | Mathlib.GroupTheory.Perm.Support | [
"Equiv.instEquivLike",
"Iff.rfl",
"Iff",
"Equiv.Perm",
"Or",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike",
"Equiv.Perm.Disjoint"
] | true |
UniformConvergenceCLM.instAddCommGroup._proof_16 | Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM | [
"NormedCommRing.toNormedRing",
"UniformConvergenceCLM.instAddCommGroup._aux_14",
"NormedRing.toRing",
"AddMonoid.toAddSemigroup",
"AddCommGroup.toAddCommMonoid",
"Add.mk",
"Neg.mk",
"ContinuousLinearMap.addCommGroup._proof_1",
"HSub.hSub",
"AddMonoid.mk",
"AddCommGroup.toAddGroup",
"RingHom",
... | false |
_private.Lean.Compiler.NameMangling.0.Lean.Name.demangleAux.decodeNum._mutual._proof_11 | Lean.Compiler.NameMangling | [
"PSum.casesOn",
"String.Pos.next",
"instHDiv",
"String",
"invImage",
"PSum",
"String.push",
"String.pushn",
"PSum.inr",
"PSigma.casesOn",
"id",
"HDiv.hDiv",
"instOfNatNat",
"String.instLTPos",
"Nat",
"LT.lt",
"Nat.instDiv",
"String.endPos",
"String.Pos",
"PSigma.mk",
"of_eq_t... | false |
ProbabilityTheory.Kernel.integral_congr_ae₂ | Mathlib.Probability.Kernel.Integral | [
"MeasureTheory.ae",
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"MeasureTheory.integral_congr_ae",
"Filter.Eventually",
"setOf",
"Membership.mem",
"Filter.mp_mem",
"ProbabilityTheory.Kernel.instFunLike",
"Filter.EventuallyEq",
"id",
"MeasurableSpace",
"MeasureTheory.integral",
"Real.... | true |
CategoryTheory.ComposableArrows.homMk₄_app_four | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0._proof_246",
"_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0._auto_405",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ComposableArrows.map'._proof_8",
"CategoryTheory.ComposableArrows.homMk₄._proof_5",
"Partia... | true |
Real.arccos | Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse | [
"Real",
"instHDiv",
"Real.pi",
"Real.arcsin",
"Real.instDivInvMonoid",
"Real.instSub",
"HSub.hSub",
"HDiv.hDiv",
"Real.arcsin._proof_1",
"instHSub",
"DivInvMonoid.toDiv",
"OfNat.ofNat",
"instOfNatAtLeastTwo",
"Real.instNatCast"
] | true |
Subring.coe_intCast | Mathlib.Algebra.Ring.Subring.Defs | [
"Int.cast",
"Subring.instSetLike",
"Membership.mem",
"Subring.instSubringClass",
"Subtype",
"NonAssocRing",
"Int",
"AddGroupWithOne.toIntCast",
"NonAssocRing.toAddCommGroupWithOne",
"Subring",
"SubringClass.toNonAssocRing",
"Subtype.val",
"Eq",
"SetLike.instMembership",
"rfl",
"AddComm... | true |
MeasureTheory.self_subset_generateSetAlgebra | Mathlib.MeasureTheory.SetAlgebra | [
"MeasureTheory.generateSetAlgebra.base",
"HasSubset.Subset",
"MeasureTheory.generateSetAlgebra",
"Set.instHasSubset",
"Set"
] | true |
Polynomial.coeff_zero_eq_prod_roots_of_monic_of_splits | Mathlib.Algebra.Polynomial.Splits | [
"NegZeroClass.toNeg",
"IsDomain",
"CommRing",
"Polynomial.roots",
"HMul.hMul",
"CommSemiring.toSemiring",
"Multiset.prod",
"AddGroupWithOne.toAddMonoidWithOne",
"Polynomial.Splits.coeff_zero_eq_prod_roots_of_monic",
"SubtractionMonoid.toSubNegZeroMonoid",
"instOfNatNat",
"SubNegZeroMonoid.toNe... | true |
NormedField.completeSpace_iff_isComplete_closedBall | Mathlib.Analysis.Normed.Field.Lemmas | [
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"div_mul_cancel₀",
"Real.partialOrder",
"Real.instLE",
"Real",
"IsComplete",
"Preorder.toLT",
... | true |
AffineEquiv.ext_on | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic | [
"AffineEquiv.toAffineMap_inj",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"AffineEquiv.equivLike",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"CompleteLattice.toBoundedOrder",
"AddCommGroup",
"Set.EqOn",
"AffineMap",
"... | true |
CategoryTheory.MorphismProperty.IsStableUnderComonoid.rec | Mathlib.CategoryTheory.CopyDiscardCategory.Widesubcategory | [
"CategoryTheory.ComonObj.comul",
"CategoryTheory.MorphismProperty.IsStableUnderComonoid",
"CategoryTheory.MorphismProperty",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.ComonObj",
"CategoryTheory.ComonObj.counit",
"CategoryTheory.MorphismProperty.IsStableUnderComonoid.mk",
"CategoryTheory.Monoi... | false |
pow_div_pow_eventuallyEq_atTop | Mathlib.Analysis.Asymptotics.SpecificAsymptotics | [
"zpow_natCast",
"Preorder.toLT",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"GroupWithZero.toDivInvMonoid",
"CommRing.toNonUnitalCommRing",
"instNoMaxOrderOfNontrivial",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"HSub.hSub",
"IsStrictOrderedRing",
"DivInvMonoid.... | true |
Std.HashMap.isEmpty_union | Std.Data.HashMap.Lemmas | [
"Bool.and",
"Std.HashMap",
"Std.HashMap.instUnion",
"LawfulHashable",
"EquivBEq",
"Std.HashMap.isEmpty",
"Bool",
"Hashable",
"Std.DHashMap.isEmpty_union",
"Union.union",
"Std.HashMap.inner",
"BEq",
"Eq"
] | true |
MeasureTheory.Measure.ae_ae_of_ae_comp | Mathlib.Probability.Kernel.Composition.MeasureComp | [
"MeasureTheory.ae",
"Unit.unit",
"MeasureTheory.Measure",
"congrArg",
"ProbabilityTheory.Kernel.comp",
"Filter.Eventually",
"ProbabilityTheory.Kernel.ae_ae_of_ae_comp",
"Eq.mp",
"ProbabilityTheory.Kernel.instFunLike",
"MeasureTheory.Measure.comp_eq_comp_const_apply",
"MeasureTheory.Measure.bind"... | true |
Ultrafilter._sizeOf_inst | Mathlib.Order.Filter.Ultrafilter.Defs | [
"SizeOf.mk",
"SizeOf",
"Ultrafilter._sizeOf_1",
"Ultrafilter"
] | false |
CategoryTheory.Functor.LaxMonoidal.comp._proof_6 | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategoryStruct.leftUnitor",
"CategoryTheory.Functor.LaxMonoidal.ε",
"CategoryTheory.Functor.comp",
"CategoryTheo... | false |
_private.Mathlib.NumberTheory.ModularForms.NormTrace.0.term𝒬 | Mathlib.NumberTheory.ModularForms.NormTrace | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
Lean.Elab.Term.expandShow | Lean.Elab.BuiltinNotation | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.SourceInfo",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMonad",
"Lean.TSyntax.raw",
"Lean.Macro.instMonadQuotationMacroM",
"inst... | true |
_private.Mathlib.Logic.Denumerable.0.Nat.Subtype.ofNat.match_1.eq_2 | Mathlib.Logic.Denumerable | [
"instOfNatNat",
"Unit",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq",
"Nat.Subtype.ofNat.match_1"
] | true |
_private.Init.Data.List.Sublist.0.List.append_subset._simp_1_1 | Init.Data.List.Sublist | [
"List.subset_def",
"List.instHasSubset",
"Membership.mem",
"HasSubset.Subset",
"List",
"List.instMembership",
"propext",
"Eq"
] | false |
oneLePart_eq_self._simp_2 | Mathlib.Algebra.Order.Group.PosPart | [
"Lattice",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"SemilatticeInf.toPartialOrder",
"LE.le",
"OneLePart.oneLePart",
"propext",
"One.toOfNat1",
"instOneLePart",
... | false |
birkhoffAverage_one' | Mathlib.Dynamics.BirkhoffSum.Average | [
"instOfNatNat",
"birkhoffAverage",
"AddCommMonoid",
"funext",
"DivisionSemiring",
"birkhoffAverage_one",
"Nat",
"DivisionSemiring.toSemiring",
"Module",
"OfNat.ofNat",
"Eq"
] | true |
Lean.Elab.Term.expandTermFor | Lean.Elab.Do.Switch | [
"_private.Lean.Elab.Do.Switch.0.Lean.Elab.Term.toDoElem",
"Lean.Name.mkStr4",
"Lean.Macro"
] | true |
_private.Mathlib.Analysis.SpecialFunctions.Log.NegMulLog.0.Real.strictConvexOn_mul_log._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Log.NegMulLog | [
"Preorder.toLT",
"NoMinOrder",
"Set.Nonempty",
"True",
"eq_true",
"Set.Iio",
"Eq",
"Set.nonempty_Iio",
"Preorder"
] | false |
Std.Time.Awareness.only.inj | Std.Time.Format.Basic | [
"Std.Time.Awareness.only",
"Std.Time.TimeZone",
"Std.Time.Awareness.only.noConfusion",
"Std.Time.Awareness",
"Eq"
] | true |
Std.DTreeMap.Internal.Impl.Const.size_alter! | Std.Data.DTreeMap.Internal.Lemmas | [
"Option.isNone",
"instDecidableNot",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"congrArg",
"Std.TransOrd",
"HSub.hSub",
"Membership.mem",
"Eq.mp",
"Std.DTreeMap.Internal.Impl.size",
"instDecidableEqBool",
"Std.DTreeMap.Internal.Impl.instDecidableMem",
"instSubNat",
"instO... | true |
Nat.one_lt_radical_iff | Mathlib.RingTheory.Radical.NatInt | [
"Eq.mpr",
"instNormalizedGCDMonoidNat",
"MulOne.toOne",
"Nat.Prime",
"Preorder.toLT",
"Dvd.dvd",
"Nat.Prime.one_lt",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"PartialOrder.toPreorder",
"_private.Mathlib.RingTheory.Radical.NatInt.0.Nat.one_lt_radical_iff.match_1_3",
"Nat.radical_eq_prod_... | true |
RingHom.comp | Mathlib.Algebra.Ring.Hom.Defs | [
"RingHom.comp._proof_4",
"MulOne.toOne",
"RingHom.mk",
"OneHom.mk",
"RingHom.comp._proof_3",
"RingHom",
"MonoidHom.mk",
"NonAssocSemiring.toMulZeroOneClass",
"MulZeroOneClass.toMulOneClass",
"NonUnitalRingHom.comp",
"MulOneClass.toMulOne",
"NonAssocSemiring",
"RingHom.instFunLike",
"RingHo... | true |
Sublattice.copy._proof_2 | Mathlib.Order.Sublattice | [
"Sublattice",
"Lattice",
"Sublattice.infClosed'",
"Eq.rec",
"SetLike.coe",
"Sublattice.instSetLike",
"InfClosed",
"Eq.symm",
"Eq",
"Lattice.toSemilatticeInf",
"Set"
] | false |
CategoryTheory.StrongMono.iff_of_arrow_iso | Mathlib.CategoryTheory.Limits.Shapes.StrongEpi | [
"CategoryTheory.StrongMono.of_arrow_iso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.StrongMono",
"CategoryTheory.Iso",
"CategoryTheory.instCategoryArrow",
"Iff",
"Iff.intro",
"CategoryTheory.Iso.symm",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Arro... | true |
LieModule.toEnd_pow_lie | Mathlib.Algebra.Lie.OfAssociative | [
"LieHom",
"LieAlgebra.toModule",
"Module.End.instRing",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"MulOne.toOne",
"CommRing",
"Nat.recAux",
"instHSMul",
"Nat.choose",
"Module.End.instMonoid",
"instSMulOfMul",
"HMul.hMul",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"SemilinearMapClass.d... | true |
_private.Lean.Meta.Match.MatcherApp.Basic.0.Lean.Meta.matchMatcherApp?.match_7 | Lean.Meta.Match.MatcherApp.Basic | [
"Lean.ConstantInfo.inductInfo",
"Nat.hasNotBit",
"_private.Lean.Meta.Match.MatcherApp.Basic.0.Lean.Meta.matchMatcherApp?._sparseCasesOn_7",
"Lean.ConstantInfo.ctorIdx",
"Lean.ConstantInfo",
"Lean.InductiveVal"
] | false |
ArchimedeanClass.instLinearOrderFiniteElement._proof_6 | Mathlib.Algebra.Order.Ring.StandardPart | [
"AddValuation.toValuation",
"Equiv.instEquivLike",
"IsOrderedRing",
"LinearOrder",
"PartialOrder.toPreorder",
"instLinearOrderedCommGroupWithZeroMultiplicativeOrderDualOfLinearOrderedAddCommGroupWithTop",
"ArchimedeanClass.instLinearOrderedAddCommGroupWithTop",
"Membership.mem",
"SemilatticeInf.toPa... | false |
expNegInvGlue.zero_iff_nonpos._simp_1 | Mathlib.Analysis.SpecialFunctions.SmoothTransition | [
"Real.instLE",
"Real",
"Real.instZero",
"LE.le",
"expNegInvGlue",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"expNegInvGlue.zero_iff_nonpos"
] | false |
LinearMap.rank_le_range | Mathlib.LinearAlgebra.Dimension.LinearMap | [
"Cardinal",
"AddCommGroup.toAddCommMonoid",
"Submodule.rank_le",
"LinearMap.range",
"AddCommGroup",
"LE.le",
"LinearMap",
"Cardinal.instLE",
"LinearMap.rank",
"Module.rank",
"Module",
"RingHom.id",
"LinearMap.rank._proof_1",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Ring"
] | true |
TensorProduct.piRightInv | Mathlib.LinearAlgebra.TensorProduct.Pi | [
"LinearMap.id",
"Pi.addCommMonoid",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"TensorProduct.addCommMonoid",
"Pi.module",
"AddMonoid.toAddZeroClass",
"TensorProduct.piRightInv._proof_2",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"LinearMap.sin... | true |
List.Pairwise.below.rec | Init.Data.List.Basic | [
"List.Pairwise.cons",
"List.Pairwise.below.nil",
"List.Pairwise",
"Membership.mem",
"List.Pairwise.below",
"List.cons",
"List",
"List.Pairwise.nil",
"List.instMembership",
"List.Pairwise.below.cons",
"List.nil"
] | false |
_private.Mathlib.Algebra.GCDMonoid.Basic.0.dvd_gcd_iff.match_1_1 | Mathlib.Algebra.GCDMonoid.Basic | [
"Dvd.dvd",
"semigroupDvd",
"SemigroupWithZero.toSemigroup",
"CommMonoidWithZero.toMonoidWithZero",
"And.casesOn",
"MonoidWithZero.toSemigroupWithZero",
"And",
"CommMonoidWithZero",
"And.intro"
] | false |
CategoryTheory.hasLeftDualOfEquivalence | Mathlib.CategoryTheory.Monoidal.Rigid.OfEquivalence | [
"CategoryTheory.Functor",
"CategoryTheory.HasLeftDual.exact",
"CategoryTheory.Functor.IsEquivalence.full",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.HasLeftDual.mk",
"CategoryTheory.exactPairin... | true |
CategoryTheory.AddMon.Hom.mk._flat_ctor | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsAddMonHom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.AddMon.Hom",
"CategoryTheory.AddMon.Hom.mk",
"CategoryTheory.AddMon.addMon",
"CategoryTheory.AddMon.X",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheo... | false |
Set.Sized.upShadow | Mathlib.Combinatorics.SetFamily.Shadow | [
"Eq.mpr",
"Set.Sized",
"congrArg",
"Finset",
"Membership.mem",
"Exists",
"Finset.upShadow",
"id",
"Insert.insert",
"instOfNatNat",
"Finset.card_insert_of_notMem",
"Finset.instInsert",
"And.casesOn",
"instHAdd",
"And",
"Exists.casesOn",
"Fintype",
"SetLike.coe",
"Finset.instSetLik... | true |
CategoryTheory.Limits.coneOpEquiv_functor_map_hom | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.Cone",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"CategoryTheory.Limits.CoconeMorphism.hom",
"Quiver.Hom.unop",
"CategoryT... | true |
MeasurableSMul₂.measurable_smul | Mathlib.MeasureTheory.Group.Arithmetic | [
"instHSMul",
"MeasurableSMul₂",
"SMul",
"Measurable",
"MeasurableSpace",
"HSMul.hSMul",
"Function.uncurry",
"Prod",
"Prod.instMeasurableSpace"
] | true |
CategoryTheory.Core.functorToCore._proof_2 | Mathlib.CategoryTheory.Core | [
"CategoryTheory.Functor",
"CategoryTheory.Core.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Groupoid.inv",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Groupoid",
"CategoryTheory.Functor.map_inv",
"CategoryTheory.Core.of",
"CategoryTheory.Functo... | false |
LinearMap.instFunLike._proof_1 | Mathlib.Algebra.Module.LinearMap.Defs | [
"instHSMul",
"LinearMap.casesOn",
"DistribMulAction.toDistribSMul",
"AddHom",
"AddMonoid.toAddZeroClass",
"RingHom",
"Eq.rec",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.toAddHom",
"AddHom.funLike",
"LinearMap",
"AddCommMonoid",
"AddZero.toZero",
"RingHom.instFun... | false |
CategoryTheory.Limits.punitCoconeIsColimit._proof_4 | Mathlib.CategoryTheory.Limits.Unit | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.eqToHom",
"CategoryTheory.Functor.category",
"id",
"CategoryTheory.Limits.Cocone.ι",
"CategoryTheory.discreteCategory",
"PUnit",
"CategoryTheory.Limits.punitCoconeIsC... | false |
CategoryTheory.Limits.pullbackPullbackLeftIsPullback._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Assoc | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.pullback.snd",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.Limits.pullback.fst",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.t... | false |
NonUnitalSubalgebra.map_toSubmodule | Mathlib.Algebra.Algebra.NonUnitalSubalgebra | [
"Submodule",
"RingHomSurjective.ids",
"NonUnitalSubalgebra",
"NonUnitalAlgHomClass.instLinearMapClass",
"CommSemiring.toSemiring",
"NonUnitalSubalgebra.toSubmodule",
"NonUnitalSubalgebra.map",
"SetLike.coe_injective",
"LinearMapClass.linearMap",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCo... | true |
RingCat.Hom.noConfusion | Mathlib.Algebra.Category.Ring.Basic | [
"HEq.refl",
"RingCat.Hom.casesOn",
"RingCat.ring",
"RingHom",
"RingCat",
"RingCat.Hom.noConfusionType",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Eq",
"RingCat.carrier",
"RingCat.Hom"
] | false |
Lean.Meta.mkAbsurd | Lean.Meta.AppBuilder | [
"Pure.pure",
"Lean.Meta.State",
"Lean.mkApp4",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.Level",
"Lean.Meta.getLevel",
"Applicative.toPure",
"Lean.mkConst",
"List.cons",
"Lean.Core.CoreM",
"Lean.Meta.instMonadMetaM",
"StateRefT'",
"StateRefT'.instMonad",
"Monad.toBind",
"... | true |
RootPairing._sizeOf_inst | Mathlib.LinearAlgebra.RootSystem.Defs | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"RootPairing._sizeOf_1",
"CommRing.toCommSemiring",
"SizeOf.mk",
"SizeOf",
"Module",
"RootPairing"
] | false |
RingConGen.Rel.mul | Mathlib.RingTheory.Congruence.Defs | [
"RingConGen.Rel.mul",
"HMul.hMul",
"RingConGen.Rel",
"Mul",
"Add",
"instHMul"
] | true |
_private.Mathlib.Data.Set.Insert.0.Set.setOf_mem_list_eq_replicate._simp_1_4 | Mathlib.Data.Set.Insert | [
"List.replicate",
"Membership.mem",
"List",
"And",
"List.instMembership",
"Nat",
"propext",
"List.eq_replicate_iff",
"Eq",
"List.length"
] | false |
_private.Mathlib.GroupTheory.ArchimedeanDensely.0.LinearOrderedCommGroup.wellFoundedOn_setOf_ge_gt_iff_nonempty_discrete._simp_1_1 | Mathlib.GroupTheory.ArchimedeanDensely | [
"inv_le'",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulLeftMono",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"MulRightMono",
"LE.le",
"LE",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Inv.inv",
"... | false |
ComputablePred.halting_problem_not_re | Mathlib.Computability.Halting | [
"Iff.mpr",
"ComputablePred.computable_iff_re_compl_re'",
"Primcodable.ofDenumerable",
"Nat.Partrec.Code",
"REPred",
"And",
"ComputablePred.halting_problem",
"Nat",
"And.intro",
"Part.Dom",
"Nat.Partrec.Code.eval",
"ComputablePred.halting_problem_re",
"Nat.Partrec.Code.instDenumerable",
"Co... | true |
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