name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Grind.Ring.intCast | Init.Grind.Ring.Basic | [
"IntCast",
"Lean.Grind.Ring"
] | true |
CategoryTheory.BasedCategory.bicategory._proof_6 | Mathlib.CategoryTheory.FiberedCategory.BasedCategory | [
"CategoryTheory.NatTrans.vcomp",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.BasedFunctor",
"CategoryTheory.BasedNatIso.id",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.BasedNatTrans.toNatTran... | false |
GaloisConnection.liftOrderBot._proof_1 | Mathlib.Order.GaloisConnection.Defs | [
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"PartialOrder",
"GaloisConnection.l_le",
"Bot.bot",
"LE.le",
"bot_le",
"Preorder",
"GaloisConnection"
] | false |
Fin.reverseInduction.go._f | Init.Data.Fin.Lemmas | [
"Fin.reverseInduction._proof_1",
"Fin.succ",
"False.elim",
"Fin.reverseInduction._proof_9",
"cast",
"Fin.mk",
"instOfNatNat",
"LE.le",
"instLENat",
"Fin.val",
"dite",
"Nat.below",
"instHAdd",
"Fin.reverseInduction._proof_5",
"HAdd.hAdd",
"Fin.reverseInduction.go.match_1",
"Nat",
"L... | false |
optionCoe | Init.Data.Option.Coe | [
"Option.some",
"Coe.mk",
"Coe",
"Option"
] | true |
_private.Mathlib.Combinatorics.SimpleGraph.Sum.0.SimpleGraph.sum.match_1.eq_2 | Mathlib.Combinatorics.SimpleGraph.Sum | [
"SimpleGraph.sum.match_1",
"Sum",
"Sum.inl",
"Sum.inr",
"Eq.refl",
"Eq"
] | true |
CategoryTheory.instCategoryCostructuredArrow._proof_1 | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"inferInstance",
"CategoryTheory.Comma",
"CategoryTheory.commaCategory",
"CategoryTheory.discreteCategory",
"PUnit",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Categor... | false |
List.Perm | Init.Data.List.Basic | [
"List.Perm.cons",
"List.Perm.swap",
"List.Perm.trans",
"List",
"List.Perm.nil"
] | true |
Subsemigroup.unop_eq_bot | Mathlib.Algebra.Group.Subsemigroup.MulOpposite | [
"Subsemigroup.instBot",
"MulOpposite",
"Mul",
"Function.Injective.eq_iff'",
"Bot.bot",
"Subsemigroup.unop_injective",
"Iff",
"Subsemigroup.unop",
"Subsemigroup",
"Subsemigroup.unop_bot",
"Eq",
"MulOpposite.instMul"
] | true |
CategoryTheory.ShortComplex.SnakeInput.naturality_δ_assoc | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.SnakeInput.naturality_δ",
"CategoryTheory.Category.assoc",
"CategoryTheory.ShortComplex.SnakeInput.L₃",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex.Hom.τ₁",
"CategoryTheory.Short... | true |
CategoryTheory.StrictBicategory.category | Mathlib.CategoryTheory.Bicategory.Strict.Basic | [
"CategoryTheory.Category.mk",
"CategoryTheory.Bicategory.Strict",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory.Strict.id_comp",
"CategoryTheory.Bicategory.Strict.assoc",
"CategoryTheory.Bicategory",
"CategoryTheory.Bicategory.Strict.comp_id",
"CategoryTheory.Category"
] | true |
Std.DHashMap.Internal.Raw₀.size_le_size_insert | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.DHashMap.Raw.WF.insert₀",
"Std.DHashMap.Internal.Raw.WF.out",
"congrArg",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw₀.toListModel_insert",
"id",
"instOfNatNat",
"Std.DHashMap.Internal.Raw.WFImp",
"LE.le",
"Std.Internal.List.insertEntry",
"instLENat",... | true |
cfcTac | Mathlib.Tactic.ContinuousFunctionalCalculus | [
"Lean.ParserDescr.nonReservedSymbol",
"instOfNatNat",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1"
] | true |
CategoryTheory.Yoneda.yoneda_faithful | Mathlib.CategoryTheory.Yoneda | [
"CategoryTheory.Functor",
"CategoryTheory.Yoneda.fullyFaithful",
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.yoneda",
"CategoryTheory.Functor.FullyFaithful.faithful",
"CategoryTheory.types",
"CategoryTheory.Category.opposite",
"CategoryTheory.Functor.Faithful",
"CategoryTheory.C... | true |
SNum.zero.elim | Mathlib.Data.Num.Bitwise | [
"PULift.up",
"SNum.ctorElim",
"SNum",
"SNum.ctorIdx",
"Nat",
"Bool",
"SNum.zero",
"Eq.symm",
"Eq"
] | false |
ZFSet.instDefinable₁Singleton | Mathlib.SetTheory.ZFC.Basic | [
"ZFSet",
"ZFSet.Definable₁.mk",
"ZFSet.Definable₁",
"PSet",
"ZFSet.instDefinable₁Singleton._proof_1",
"ZFSet.instSingleton",
"PSet.instSingleton",
"Singleton.singleton"
] | true |
_private.Mathlib.Algebra.Category.Grp.Biproducts.0.AddCommGrpCat.biprodIsoProd_inv_comp_desc._simp_1_2 | Mathlib.Algebra.Category.Grp.Biproducts | [
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddCommGrpCat.biprodIsoProd",
"CategoryTheory.Limits.biprod",
"AddCommGrpCat.carrier",
"CategoryTheory.Limits.biprod.snd",
"AddGroup.toSubNegMonoid",
"Add... | false |
AndThen.noConfusion | Init.Prelude | [
"HEq.refl",
"AndThen",
"Unit",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Eq",
"AndThen.noConfusionType",
"AndThen.casesOn"
] | false |
_private.Mathlib.Order.Partition.Equipartition.0.Finpartition.IsEquipartition.exists_partPreservingEquiv._simp_1_4 | Mathlib.Order.Partition.Equipartition | [
"Fin.val",
"Nat",
"propext",
"Fin",
"Eq",
"Fin.val_eq_val"
] | false |
String.firstDiffPos.eq_1 | Batteries.Data.String.Lemmas | [
"String",
"String.firstDiffPos",
"String.Pos.Raw",
"String.rawEndPos",
"String.firstDiffPos.loop",
"String.Pos.Raw.min",
"Eq.refl",
"String.instOfNatRaw",
"OfNat.ofNat",
"Eq"
] | true |
Lean.Meta.Grind.SolverTerms.below | Lean.Meta.Tactic.Grind.Types | [
"Lean.Expr",
"Lean.Meta.Grind.SolverTerms.rec",
"PProd",
"PUnit",
"Nat",
"Lean.Meta.Grind.SolverTerms"
] | false |
CategoryTheory.Pseudofunctor.Grothendieck.map._proof_4 | Mathlib.CategoryTheory.Bicategory.Grothendieck | [
"CategoryTheory.Pseudofunctor.StrongTrans.naturality",
"CategoryTheory.LocallyDiscrete.categoryStruct",
"CategoryTheory.Cat.Hom₂.comp_app",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Pseudofunctor.Grothendieck.Hom.ext",
"CategoryTheory.Functor",
"CategoryTheory.Iso.inv_hom_id",
"Cate... | false |
CategoryTheory.MorphismProperty.instCategoryLocalization._proof_9 | Mathlib.CategoryTheory.Localization.Construction | [
"CategoryTheory.MorphismProperty",
"Quiver.mk",
"CategoryTheory.CategoryStruct.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Localization.Construction.LocQuiver",
"CategoryTheory.Paths.categoryPaths",
"CategoryTheory.Paths",
"CategoryTheory.Category.assoc._autoParam",
... | false |
_private.Mathlib.RingTheory.Valuation.ValuativeRel.Basic.0.ValuativeRel.ValueGroupWithZero.embed._simp_2 | Mathlib.RingTheory.Valuation.ValuativeRel.Basic | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"LE.le",
"And",
"le_antisymm_iff",
"propext",
"Eq.symm",
"Eq"
] | false |
Set.Ioi_subset_Ici | Mathlib.Order.Interval.Set.Basic | [
"Set.Ioi",
"Set.Ici",
"Set.Ioi_subset_Ici_self",
"Preorder.toLE",
"HasSubset.Subset.trans",
"Set.instIsTransSubset",
"HasSubset.Subset",
"LE.le",
"Set.Ioi_subset_Ioi",
"Preorder",
"Set.instHasSubset",
"Set"
] | true |
Lean.SMap.stage₁._default | Lean.Data.SMap | [
"id",
"Bool.true",
"Bool",
"Hashable",
"BEq"
] | false |
_private.Init.Prelude.0.Nat.div_rec_lemma.match_1_1 | Init.Prelude | [
"instOfNatNat",
"LE.le",
"instLENat",
"And.casesOn",
"And",
"Nat",
"And.intro",
"LT.lt",
"instLTNat",
"OfNat.ofNat"
] | false |
nhdsKer_eq_iff_isOpen | Mathlib.Topology.AlexandrovDiscrete | [
"Eq.rec",
"TopologicalSpace",
"Iff",
"IsOpen.nhdsKer_eq",
"AlexandrovDiscrete",
"Iff.intro",
"isOpen_nhdsKer",
"nhdsKer",
"IsOpen",
"Eq",
"Set"
] | true |
IsCoveringMap.liftPath.congr_simp | Mathlib.Topology.Homotopy.Lifting | [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"Eq.rec",
"Real.semiring",
"Set.Elem",
"IsCoveringMap.liftPath",
"TopologicalSpace",
"Eq.ndrec",
"Zero.toOfNat0",
"Eq.refl",
"Real.pseudoMet... | true |
_private.Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra.0.IntermediateField.fg_top_iff._simp_1_3 | Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra | [
"HMul.hMul",
"IsLocalization",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Membership.mem",
"Subtype",
"MulZeroOneClass.toMulOneClass",
"instDistribOfSemiring",
"instMulZeroOneClassOfSemiring",
"CommSemiring",
"IsLocalization.mk'_eq_iff_eq_mul",
"IsLocalization.... | false |
Function.IsFixedPt.eq | Mathlib.Logic.Function.Defs | [
"Function.IsFixedPt",
"Eq"
] | true |
CategoryTheory.MonoidalClosed.compTranspose | Mathlib.CategoryTheory.Monoidal.Closed.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.MonoidalCategory.tensorLeft",
"CategoryTheory.MonoidalCategoryStruct.whiskerRight",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
... | true |
Matrix.invertibleOfDetInvertible._proof_2 | Mathlib.LinearAlgebra.Matrix.NonsingularInverse | [
"Eq.mpr",
"Matrix.smul",
"MulOne.toOne",
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"Matrix.instMulOfFinty... | false |
Lean.Omega.IntList.sdiv | Init.Omega.IntList | [
"Int.instDiv",
"instHDiv",
"List.map",
"HDiv.hDiv",
"Int",
"Lean.Omega.IntList"
] | true |
Std.IterM.IsPlausibleNthOutputStep.yield | Init.Data.Iterators.Consumers.Monadic.Access | [
"Std.IterM.IsPlausibleNthOutputStep",
"Std.IterStep",
"Std.IterM.IsPlausibleStep",
"instOfNatNat",
"Std.Iterator",
"instHAdd",
"HAdd.hAdd",
"Std.IterStep.yield",
"Nat",
"instAddNat",
"Std.IterM",
"Std.IterM.IsPlausibleNthOutputStep.yield",
"OfNat.ofNat"
] | true |
Matrix.UnitaryGroup.toLinearEquiv._proof_6 | Mathlib.LinearAlgebra.UnitaryGroup | [
"Matrix.UnitaryGroup.toLinearEquiv._proof_1",
"Pi.Function.module",
"CommRing",
"Trans.trans",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"Submonoid.mul",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"DivInvOneMonoid.toInvOneClass",
"CommSemiring.... | false |
Lean.Elab.Command.withFreshMacroScope | Lean.Elab.Command | [
"Lean.Elab.Command.Context.fileName",
"Lean.Elab.Command.Context.snap?",
"Lean.Elab.Command.State.nextMacroScope",
"Lean.Elab.Command.Context.ref",
"Lean.Elab.Command.State.infoState",
"IO.instMonadLiftSTRealWorldBaseIO",
"Lean.Elab.Command.State.mk",
"Lean.Elab.Command.Context.macroStack",
"Lean.El... | true |
_private.Mathlib.Algebra.Homology.SpectralObject.SpectralSequence.0.CategoryTheory.Abelian.SpectralObject.spectralSequencePageSc'Iso._proof_15 | Mathlib.Algebra.Homology.SpectralObject.SpectralSequence | [
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"CategoryTheory.Abelian.SpectralObject.spectralSequencePageSc'Iso._auto_7",
"congrArg",
"Classical.byContradiction",
"Eq.mp",
"Lean.RArray.branch",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"Int.instNegInt",
"instOfNatNat",
"Int",
"Int.Linear.P... | false |
NumberField.Units.logEmbedding | Mathlib.NumberTheory.NumberField.Units.DirichletTheorem | [
"NumberField.InfinitePlace.instFunLikeReal",
"Units.val",
"NumberField.Units.logEmbedding._proof_2",
"Real",
"Equiv.instEquivLike",
"HMul.hMul",
"Algebra.algebraMap",
"NumberField.instCommRingRingOfIntegers",
"Real.instAddMonoid",
"CommSemiring.toSemiring",
"Additive",
"AddMonoid.toAddZeroClas... | true |
Field.Emb.cardinal_separableClosure | Mathlib.FieldTheory.PurelyInseparable.Basic | [
"Eq.mpr",
"MulOne.toOne",
"IntermediateField.isScalarTower_mid'",
"IsDomain.to_noZeroDivisors",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"HMul.hMul",
"Cardinal.instOne",
"CommRing.toNonUnitalCommRing",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"Field.embProd... | true |
_private.Mathlib.RingTheory.Spectrum.Maximal.Localization.0.PrimeSpectrum.iInf_localization_eq_bot.match_1_2 | Mathlib.RingTheory.Spectrum.Maximal.Localization | [
"CommRing",
"CommSemiring.toSemiring",
"MaximalSpectrum.mk",
"MaximalSpectrum",
"Ideal",
"CommRing.toCommSemiring",
"MaximalSpectrum.casesOn",
"Ideal.IsMaximal"
] | false |
_private.Std.Sync.Channel.0.Std.CloseableChannel.Consumer._sizeOf_1 | Std.Sync.Channel | [
"IO.Promise._sizeOf_inst",
"_private.Std.Sync.Channel.0.Std.CloseableChannel.Consumer",
"Option._sizeOf_inst",
"_private.Std.Sync.Channel.0.Std.CloseableChannel.Consumer.rec",
"instOfNatNat",
"Std.Internal.IO.Async.Waiter",
"instHAdd",
"HAdd.hAdd",
"Nat",
"IO.Promise",
"SizeOf.sizeOf",
"instAd... | false |
unitarySubgroupUnitsEquiv._proof_3 | Mathlib.Algebra.Star.Unitary | [
"Monoid",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"unitary",
"StarMul",
"Membership.mem",
"MulOne.toMul",
"Subtype",
"MulOneClass.toMulOne",
"And.left",
"Subtype.prop",
"StarMul.toInvolutiveStar",
"One.toOfNat1",
"InvolutiveStar.toStar",
"Submonoid.instSetLike",
"OfNat.o... | false |
Lean.Grind.CommRing.Stepwise.superpose_cert.eq_1 | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Stepwise.superpose_cert",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.beq'",
"Lean.Grind.CommRing.Poly.mulMon_k",
"Int",
"Bool",
"Eq.refl",
"Lean.Grind.CommRing.Poly.combine_k",
"Eq",
"Lean.Grind.CommRing.Mon"
] | true |
Ideal.powQuotPowSuccLinearEquivMapMkPowSuccPow._simp_1 | Mathlib.RingTheory.Ideal.Quotient.Operations | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"Submodule.module._proof_1",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"DistribMulAction.toDistribSMul",
"Submodule.addCommMonoid",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"DistribSMul... | false |
CategoryTheory.ObjectProperty.IsVerdierRightLocalizing.fullyFaithful | Mathlib.CategoryTheory.Triangulated.LocalizingSubcategory | [
"CategoryTheory.ObjectProperty.triangulatedLocalizerMorphism._proof_1",
"CategoryTheory.Functor.FullyFaithful.ofIso",
"CategoryTheory.Localization.liftNatIso",
"CategoryTheory.Functor",
"CategoryTheory.Localization.Lifting.compLeft",
"CategoryTheory.ObjectProperty.IsTriangulated.toContainsZero",
"Catego... | true |
CategoryTheory.LaxBraidedFunctor.homMk._proof_1 | Mathlib.CategoryTheory.Monoidal.Braided.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.LaxBraidedFunctor.toFunctor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"inferInstance",
"CategoryTheory.Functor.LaxBraided.toLaxMonoidal",
"CategoryTheory.BraidedCategory",
... | false |
instAddCommMonoidEReal._proof_1 | Mathlib.Data.EReal.Basic | [
"Real",
"AddMonoid.toAddSemigroup",
"EReal",
"instAddMonoidEReal",
"WithTop.addCommMonoid",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Real.instAddCommMonoid",
"Eq",
"WithTop",
"WithBot.addCommMonoid._proof_1"
] | false |
Lean.Server.ModuleRefs.addRef | Lean.Server.References | [
"Lean.Lsp.instOrdRefIdent",
"Std.TreeMap.alter",
"Option.some",
"Lean.Server.Reference",
"Lean.Server.Reference.ident",
"Lean.Server.RefInfo.empty",
"Ord.compare",
"Lean.Server.ModuleRefs",
"Lean.Server.RefInfo.addRef",
"Unit",
"Lean.Server.RefInfo",
"Lean.Lsp.RefIdent",
"_private.Lean.Serve... | true |
Set.powersetCard.instAddActionElemFinset._proof_3 | Mathlib.GroupTheory.GroupAction.SubMulAction.Combination | [
"AddMonoid.toAddSemigroup",
"instVAddOfAdd",
"Finset",
"Finset.addActionFinset",
"AddMonoid.toAddZeroClass",
"Set.powersetCard.instAddActionElemFinset._aux_1",
"AddZeroClass.toAddZero",
"VAddAssocClass.left",
"Set.Elem",
"SubAddAction.addAction'._proof_1",
"VAdd.mk",
"HVAdd.hVAdd",
"AddActio... | false |
exists_eq_iInf_of_not_isPredPrelimit | Mathlib.Order.SuccPred.CompleteLinearOrder | [
"Preorder.toLT",
"iInf",
"PartialOrder.toPreorder",
"Exists",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"sInf_mem_of_not_isPredPrelimit",
"CompleteLinearOrder.toConditionallyCompleteLinearOrderBot",
"ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder",
"C... | true |
_private.Mathlib.MeasureTheory.Constructions.BorelSpace.Order.0.measure_eq_measure_preimage_add_measure_tsum_Ico_zpow._simp_1_1 | Mathlib.MeasureTheory.Constructions.BorelSpace.Order | [
"Membership.mem",
"Set.instSingletonSet",
"Set.mem_singleton_iff",
"propext",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Set"
] | false |
instSMulCommClassUniformOnFun | Mathlib.Topology.Algebra.UniformConvergence | [
"SMul",
"instSMulUniformOnFun",
"_private.Mathlib.Topology.Algebra.UniformConvergence.0.instSMulCommClassUniformOnFun._proof_1",
"UniformOnFun",
"SMulCommClass",
"Set"
] | true |
Nat.Partrec.Code.ofNatCode._unsafe_rec | Mathlib.Computability.PartrecCode | [
"lt_of_le_of_lt",
"Nat.Partrec.Code.rfind'",
"Nat.Partrec.Code.ofNatCode.match_1",
"Nat.unpair",
"Nat.Partrec.Code.right",
"Nat.Partrec.Code.ofNatCode.match_3",
"Nat.Partrec.Code",
"Nat.Partrec.Code.ofNatCode._unsafe_rec",
"Nat.div2",
"instOfNatNat",
"Nat.Partrec.Code.prec",
"Nat.Partrec.Code.... | false |
_private.Init.Data.String.Pattern.Basic.0.String.Slice.Pattern.instBEqSearchStep.beq._sparseCasesOn_2 | Init.Data.String.Pattern.Basic | [
"String.Slice.Pattern.SearchStep.ctorIdx",
"Nat.ne_of_beq_eq_false",
"String.Slice.Pattern.SearchStep",
"Nat.shiftRight",
"String.Slice",
"Nat.hasNotBit",
"instOfNatNat",
"String.Slice.Pattern.SearchStep.rejected",
"Nat.land",
"Nat",
"String.Slice.Pattern.SearchStep.matched",
"Bool",
"Eq.ref... | false |
Matrix.PosDef.posSemidef_add | Mathlib.LinearAlgebra.Matrix.PosDef | [
"Matrix.add",
"Ring.toNonAssocRing",
"Matrix",
"Matrix.addCommSemigroup",
"PartialOrder.toPreorder",
"AddLeftMono",
"Preorder.toLE",
"Eq.rec",
"PartialOrder",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"add_comm",
"NonAssocRing.toNonUnitalNonAssocRing",
"instDist... | true |
_private.Mathlib.RingTheory.Polynomial.Resultant.Basic.0.Polynomial.resultant_add_mul_monomial_right._proof_1_16 | Mathlib.RingTheory.Polynomial.Resultant.Basic | [
"Lean.RArray.leaf",
"False",
"Lean.Grind.ToInt.toInt",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Lean.Grind.Nat.lt_eq",
"Eq.mp",
"Lean.RArray.branch",
"Nat.ToInt.natCast_ofNat",
"Int.Linear.Expr.add",... | false |
_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.applyPartition_eq._simp_1_6 | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"beq_iff_eq",
"LawfulBEq",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"BEq",
"Eq"
] | false |
Lean.Json.Parser.natCoreNumDigits | Lean.Data.Json.Parser | [
"Inhabited.default",
"String",
"Nat",
"String.Pos",
"Std.Internal.Parsec.instInhabited",
"Prod",
"Std.Internal.Parsec.String.Parser",
"Sigma"
] | true |
TopologicalSpace.OpenNhdsOf.instPartialOrder._proof_1 | Mathlib.Topology.Sets.Opens | [
"TopologicalSpace.OpenNhdsOf.instSetLike",
"TopologicalSpace.OpenNhdsOf",
"Membership.mem",
"LE.le",
"TopologicalSpace",
"PartialOrder.ofSetLike._proof_1",
"LE.mk",
"SetLike.instMembership"
] | false |
AddSubsemigroup.copy | Mathlib.Algebra.Group.Subsemigroup.Defs | [
"AddSubsemigroup.instSetLike",
"AddSubsemigroup.copy._proof_1",
"AddSubsemigroup.mk",
"SetLike.coe",
"AddSubsemigroup",
"Eq",
"Add",
"Set"
] | true |
Aesop.BaseRuleSetMember.unfoldRule.inj | Aesop.RuleSet.Member | [
"Aesop.UnfoldRule",
"Aesop.BaseRuleSetMember.unfoldRule",
"Aesop.BaseRuleSetMember.unfoldRule.noConfusion",
"Aesop.BaseRuleSetMember",
"Eq"
] | true |
LinearMap.toContinuousLinearMap._proof_9 | Mathlib.Topology.Algebra.Module.FiniteDimension | [
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"CompleteSpace",
"ContinuousSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.mk",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"NormedDivisionRing.toDivi... | false |
_private.Aesop.Search.ExpandSafePrefix.0.Aesop.expandSafePrefixGoal._unsafe_rec | Aesop.Search.ExpandSafePrefix | [
"Pure.pure",
"Aesop.runFirstSafeRule",
"Lean.Core.instMonadTraceCoreM",
"Aesop.Goal.id",
"Aesop.BaseM",
"modifyThe",
"Functor.discard",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Aesop.SafeExpansionM",
"Aesop.instMonadStatsStateRefT'",
"Aesop.SafeExpan... | false |
Std.Tactic.BVDecide.BVExpr.bitblast.goCache._mutual._proof_55 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Expr | [
"Std.Sat.AIG.Decl",
"HMul.hMul",
"Std.Tactic.BVDecide.BVExpr.bitblast.instLawfulVecOperatorReplicateTargetBlastReplicate",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastReplicate",
"Std.Tactic.BVDecide.BVExpr.bitblast.ReplicateTarget",
"instMulNat",
"LE.le",
"instLENat",
"Subtype.mk",
"Std.Tactic.BVDe... | false |
ZNum.abs_toZNum | Mathlib.Data.Num.ZNum | [
"ZNum.abs",
"_private.Mathlib.Data.Num.ZNum.0.ZNum.abs_toZNum.match_1_1",
"Num.toZNum",
"Num",
"Unit",
"instZeroNum",
"Num.pos",
"Zero.toOfNat0",
"PosNum",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
Std.DTreeMap.Raw.isEmpty_eq_false_iff_exists_mem | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.instMembership",
"Ord.mk",
"Membership.mem",
"Exists",
"Ordering",
"Std.DTreeMap.Raw.isEmpty",
"Std.TransCmp",
"Iff",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Bool",
"Bool.false",
"Eq",
"Std.DTreeMap.Internal.Impl.isEmpty_eq_false_iff_exists_mem",
"Std.DTre... | true |
Array.map_fst_zip | Init.Data.Array.Zip | [
"congrArg",
"List.zip_toArray",
"List.map",
"List.map_toArray",
"Array.map",
"Eq.mp",
"Array.casesOn",
"id",
"List.zip",
"LE.le",
"instLENat",
"List.map_fst_zip",
"Prod.fst",
"List.toArray",
"Array",
"List",
"List.size_toArray",
"Nat",
"congr",
"True",
"eq_self",
"of_eq_tru... | true |
NonUnitalRingHom.srangeRestrict_surjective | Mathlib.RingTheory.NonUnitalSubsemiring.Basic | [
"NonUnitalRingHom.srange",
"NonUnitalRingHom.mem_srange",
"_private.Mathlib.RingTheory.NonUnitalSubsemiring.Basic.0.NonUnitalRingHom.srangeRestrict_surjective.match_1_3",
"Membership.mem",
"Exists",
"Subtype",
"NonUnitalSubsemiring.instNonUnitalSubsemiringClass",
"NonUnitalRingHom.instFunLike",
"Sub... | true |
HasStrictDerivAt.const_cpow | Mathlib.Analysis.SpecialFunctions.Pow.Deriv | [
"NormedCommRing.toSeminormedCommRing",
"Complex.log",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"HMul.hMul",
"IsTopologicalRing.toIsTopologicalSemiring",
"IsTopologicalSemiring.toContinuousMul",
"Complex.instNormedField",
"IsTopologicalDivisionRing.toIsTopologicalRing",
... | true |
Vector.instDecidableLTOfDecidableEq._proof_1 | Init.Data.Vector.Lex | [
"instLawfulBEq",
"Vector",
"Vector.lex_eq_true_iff_lt",
"instBEqOfDecidableEq",
"Vector.lex",
"Bool.true",
"Iff",
"Nat",
"LT.lt",
"Bool",
"Decidable.decide",
"Eq",
"DecidableLT",
"LT",
"Vector.instLT",
"DecidableEq"
] | false |
Set.Infinite.eq_1 | Mathlib.Data.Set.Finite.Basic | [
"Set.Finite",
"Eq.refl",
"Eq",
"Not",
"Set.Infinite",
"Set"
] | true |
_private.Init.Data.String.Decode.0.ByteArray.utf8DecodeChar?.assemble₂_eq_some_of_toBitVec._simp_1_7 | Init.Data.String.Decode | [
"BitVec",
"BitVec.lt_def",
"BitVec.toNat",
"instLTBitVec",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"Eq"
] | false |
«_aux_Mathlib_Algebra_Symmetrized___macroRules_term_ˢʸᵐ_1» | Mathlib.Algebra.Symmetrized | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMonad"... | false |
Std.Tactic.BVDecide.BVExpr.bitblast.blastReplicate.go_get_aux._unary | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.Replicate | [
"dite_cond_eq_true",
"Std.Sat.AIG.RefVec.get",
"Eq.mpr",
"False",
"Std.Sat.AIG.Fanin.gate",
"Decidable.casesOn",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Std.Sat.AIG.RefVec.append",
"HMul.hMul",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Vector",
"Lean.Omega.Const... | false |
AddCommMonCat.addCommMonoidObj._proof_11 | Mathlib.Algebra.Category.MonCat.Limits | [
"AddCommMonCat.addCommMonoidObj._proof_3",
"CategoryTheory.Functor",
"AddCommMonCat.instCategory",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.comp",
"AddCommMonCat",
"AddCommMonCat.addCommMonoidObj._aux_1",
"AddZeroClass.toAddZero",
"AddCommMonCat.instConcreteCategoryAddMonoidHomCarrier",
... | false |
div_mul_div_cancel | Mathlib.Algebra.Group.Basic | [
"Eq.mpr",
"instHDiv",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"mul_div_assoc",
"Group",
"id",
"MulOne.toMul",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"DivInvMonoid.toDiv",
"Eq.refl",
"div_mul_cancel",
"Eq.symm",
"Eq",
"instHM... | true |
Ring.inverse_eq_inv' | Mathlib.Algebra.GroupWithZero.Units.Basic | [
"GroupWithZero.toMonoidWithZero",
"GroupWithZero.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"GroupWithZero",
"Ring.inverse_eq_inv",
"DivisionMonoid.toDivInvOneMonoid",
"Ring.inverse",
"funext",
"Inv.inv",
"InvOneClass.toInv",
"Eq"
] | true |
Nat.instDiv | Init.Prelude | [
"Div",
"Nat.div",
"Div.mk",
"Nat"
] | true |
ContinuousAt.cfcₙ_nnreal | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity | [
"NNReal.instTopologicalSpace",
"cfcₙ",
"NNReal.instCommSemiring",
"IsSelfAdjoint",
"Real.partialOrder",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"instSMulOfMul",
"Filter.Eventually.self_of_nhds",
"NormedSpace",
"IsTopologicalRing.toIsTopologicalSemiring",
... | true |
_private.Lean.Elab.Tactic.Basic.0.Lean.Elab.Tactic.liftMetaTactic1.match_1 | Lean.Elab.Tactic.Basic | [
"Option.ctorIdx",
"Option.some",
"Lean.MVarId",
"Nat.hasNotBit",
"_private.Lean.Elab.Tactic.Basic.0.Lean.Elab.Tactic.withRestoreOrSaveFull._sparseCasesOn_1",
"Option"
] | false |
HomologicalComplex₂.d₁_eq' | Mathlib.Algebra.Homology.TotalComplex | [
"HomologicalComplex.instCategory",
"instHSMul",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex₂.toGradedObject",
"Units.instSMul",
"HomologicalComplex₂.HasTotal",
"AddCommGroup.toAddGroup",
"HomologicalComplex",
"Units",
"Prod.mk",
"In... | true |
CategoryTheory.Iso.commGroupIsoToMulEquiv._proof_2 | Mathlib.Algebra.Category.Grp.Basic | [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"CommGrpCat.instCategory",
"MonoidHom.ext",
"CommGrpCat.str",
"CategoryTheory.Iso",
"MonoidHom.comp",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"CommGrpCat.carrier",
"MonoidHom.id",
"... | false |
RelIso.sumLexComplLeft._proof_1 | Mathlib.Order.Hom.Lex | [
"Eq.mpr",
"False",
"Equiv.instEquivLike",
"trans",
"iff_false",
"Sum.lex_inr_inr._simp_1",
"congrArg",
"Sum.lex_inl_inl._simp_1",
"DecidableRel",
"iff_true",
"Subtype.casesOn",
"Sum.casesOn",
"Eq.mp",
"Sum",
"id",
"Equiv",
"Subtype",
"subrel_val._simp_1",
"Subrel",
"Sum.inl",
... | false |
AlgebraicGeometry.instFaithfulModuleCatCarrierModulesSpecOfFunctor | Mathlib.AlgebraicGeometry.Modules.Tilde | [
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme.Modules.instCategory",
"CommRingCat.carrier",
"ModuleCat",
"CommRingCat",
"CategoryTheory.Functor.FullyFaithful.faithful",
"CommRingCat.instCommRingObjForgetRingHomCarrier",
"AlgebraicGeometry.tilde.functor",
"ModuleCat.moduleCategory",
"CommRing... | true |
SSet.StrictSegalCore.ctorIdx | Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | [
"SSet",
"Nat",
"SSet.StrictSegalCore"
] | false |
CategoryTheory.Monoidal.Transported | Mathlib.CategoryTheory.Monoidal.Transport | [
"CategoryTheory.Equivalence",
"CategoryTheory.Category"
] | true |
Rat.smul_def | Mathlib.Algebra.Field.Defs | [
"instHSMul",
"HMul.hMul",
"DivisionRing.toRatCast",
"Rat.smulDivisionRing",
"Rat",
"DivisionRing.toDivisionSemiring",
"Rat.cast",
"instDistribOfSemiring",
"Distrib.toMul",
"DivisionSemiring.toSemiring",
"HSMul.hSMul",
"DivisionRing",
"DivisionRing.qsmul_def",
"Eq",
"instHMul"
] | true |
Set.mapsTo_iInter | Mathlib.Data.Set.Lattice.Image | [
"Set.forall_mem_range",
"Set.iInter",
"Membership.mem",
"Set.mapsTo_sInter",
"Iff",
"Set.MapsTo",
"Iff.trans",
"Set.range",
"Set.sInter",
"Set.instMembership",
"Set"
] | true |
Int16.decEq.match_1 | Init.Data.SInt.Basic | [
"Int16.casesOn",
"Int16",
"UInt16",
"Int16.ofUInt16"
] | false |
MeasureTheory.stronglyAdapted_predictablePart | Mathlib.Probability.Martingale.Centering | [
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"MeasureTheory.Filtration.seq",
"AddCommGroup.toAddCommMonoid",
"Finset",
"Finset.mem_range_succ_iff",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"Membership.mem",
"MeasureTheory.Filtration",
"Finset.stronglyMea... | true |
PresheafOfModules.instAddCommGroupModuleColimit._proof_21 | Mathlib.Algebra.Category.ModuleCat.Presheaf.ColimitFunctor | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"Opposite",
"AddCommGrpCat.instCategory",
"AddCommGroup.toAddGroup",
"CategoryTheory.Limits.IsColimit",
"Int",
"PresheafOfModules.instAddCommGroupModuleColimit._aux_17",
"Ab",
"Nat.cast",
"autoParam",
"AddCommGrpCat.carrier",
"RingCat... | false |
Std.DHashMap.Internal.Raw₀.Const.all_eq_false | Std.Data.DHashMap.Internal.RawLemmas | [
"Iff.mpr",
"Std.DHashMap.Raw.WF",
"Bool.not_false",
"Bool.not",
"Std.DHashMap.Internal.Raw₀.contains",
"Iff.of_eq",
"congrArg",
"Std.DHashMap.Internal.Raw₀.getKey",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw₀.all_eq_not_any_not",
"Exists",
"instOfNatNat",
"LawfulHashable",
"iff_self",
... | true |
_private.Lean.Meta.CtorIdxHInj.0.Lean.Meta.initFn._sparseCasesOn_1._@.Lean.Meta.CtorIdxHInj.1686831688._hygCtx._hyg.2 | Lean.Meta.CtorIdxHInj | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
Lean.Meta.FunInfo.ctorIdx | Lean.Meta.Basic | [
"Lean.Meta.FunInfo",
"Nat"
] | false |
StableUnderSpecialization.compl | Mathlib.Topology.Inseparable | [
"Iff.mpr",
"StableUnderSpecialization",
"Compl.compl",
"stableUnderGeneralization_compl_iff",
"Set.instCompl",
"TopologicalSpace",
"StableUnderGeneralization",
"Set"
] | true |
MeasureTheory.Measure.mapₗ_mk_apply_of_aemeasurable | Mathlib.MeasureTheory.Measure.Map | [
"dite_cond_eq_true",
"MeasureTheory.Measure.mapₗ",
"MeasureTheory.Measure",
"Semiring.toModule",
"IsScalarTower.right",
"AEMeasurable",
"congrArg",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"Classical.propDecidable",
"MeasureTheory.Measure.map_def",
"Algebra.id",
"AEMeasurable.mk",... | true |
FintypeCat.equivEquivIso_apply_inv | Mathlib.CategoryTheory.FintypeCat | [
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Finite",
"FintypeCat",
"FintypeCat.equivEquivIso",
"Equiv",
"CategoryTheory.Iso",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"CategoryTheory.types",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
... | true |
UniformSpace.Completion.coe_neg._simp_1 | Mathlib.Topology.Algebra.GroupCompletion | [
"AddGroup.toSubtractionMonoid",
"UniformSpace",
"NegZeroClass.toNeg",
"UniformSpace.Completion.coe'",
"instNegCompletion",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"IsUniformAddGroup",
"UniformSpace.Completion.coe_neg",
"AddGroup",
"Eq.symm",
"Eq",
"Neg.neg"... | false |
Opens.mayerVietorisSquare'._proof_2 | Mathlib.Topology.Sheaves.MayerVietoris | [
"CategoryTheory.Limits.Types.hasColimitsOfShape",
"CategoryTheory.GrothendieckTopology.Cover.shape",
"CategoryTheory.Functor",
"Opposite",
"TopologicalSpace.Opens.instPartialOrder",
"Opposite.small",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingMulticos... | false |
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