name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
ArithmeticFunction.prodPrimeFactors | Mathlib.NumberTheory.ArithmeticFunction.Misc | [
"CommMonoidWithZero.toCommMonoid",
"Nat.instMulZeroClass",
"instOfNatNat",
"CommMonoidWithZero.toMonoidWithZero",
"ZeroHom.mk",
"ArithmeticFunction.prodPrimeFactors._proof_1",
"Finset.prod",
"MonoidWithZero.toMulZeroOneClass",
"CommMonoidWithZero",
"Nat",
"ArithmeticFunction",
"Zero.toOfNat0",... | true |
Std.Internal.IO.Async.Waiter.race | Std.Internal.Async.Select | [
"ST.Ref.modifyGet",
"IO.RealWorld",
"instDecidableEqBool",
"Prod.mk",
"MonadLiftT",
"instBEqOfDecidableEq",
"Std.Internal.IO.Async.Waiter",
"Bool.true",
"BEq.beq",
"ST",
"IO.Promise",
"Bool",
"Monad.toBind",
"Bind.bind",
"IO.Error",
"Std.Internal.IO.Async.Waiter.promise",
"Except",
... | true |
WithTop.add_left_cancel | Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | [
"Ne",
"instHAdd",
"WithTop.top",
"HAdd.hAdd",
"IsLeftCancelAdd",
"Iff.mp",
"Top.top",
"Eq",
"WithTop.add",
"Add",
"WithTop.add_left_inj",
"WithTop"
] | true |
Std.ExtHashMap.getElem_map | Std.Data.ExtHashMap.Lemmas | [
"Std.ExtHashMap.mem_of_mem_map",
"GetElem?.toGetElem",
"instLawfulHashableOfLawfulBEq",
"Std.ExtHashMap.inner",
"Std.ExtDHashMap.Const.get_map",
"LawfulBEq",
"Membership.mem",
"Std.ExtHashMap",
"GetElem.getElem",
"Hashable",
"instEquivBEqOfLawfulBEq",
"Std.ExtHashMap.instGetElem?Mem",
"Std.E... | true |
MeasureTheory.Measure.InnerRegularWRT.comap | Mathlib.MeasureTheory.Measure.Regular | [
"Iff.mpr",
"Eq.mpr",
"MeasureTheory.Measure",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Exists",
"Eq.mp",
"HasSubset.Subset.trans",
"Set.image_subset_range",
"id",
"Set.instIsTransSubset",
"HasSubset.Subset",
"MeasureTheory.Measure.InnerRegularWRT",
"And.casesOn",
"Measu... | true |
_private.Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas.0.IsDedekindDomain.HeightOneSpectrum.iInf_localization_eq_bot.match_1_1 | Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas | [
"CommRing",
"CommSemiring.toSemiring",
"MaximalSpectrum.mk",
"MaximalSpectrum",
"Ideal",
"CommRing.toCommSemiring",
"MaximalSpectrum.casesOn",
"Ideal.IsMaximal"
] | false |
Lean.Widget.InfoPopup.exprExplicit | Lean.Server.FileWorker.WidgetRequests | [
"Lean.Widget.InfoPopup",
"Lean.Widget.CodeWithInfos",
"Option"
] | true |
IsLocalRing.instCommRingResidueField._aux_32 | Mathlib.RingTheory.LocalRing.ResidueField.Defs | [
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"Submodule.Quotient.addCommGroup._aux_1",
"IsLocalRing.maximalIdeal",
"IsLocalRing",
"CommRing.toCommSemiring",
"IsLocalRing.ResidueField",
"Ring.toAddCommGroup",
"CommRing.toRing",
"Ring.toSemiring"
] | false |
Continuous.nnnorm' | Mathlib.Analysis.Normed.Group.Continuity | [
"NNReal.instTopologicalSpace",
"Continuous",
"NNNorm.nnnorm",
"SeminormedGroup",
"Continuous.comp",
"PseudoMetricSpace.toUniformSpace",
"SeminormedGroup.toPseudoMetricSpace",
"NNReal",
"TopologicalSpace",
"SeminormedGroup.toNNNorm",
"continuous_nnnorm'",
"UniformSpace.toTopologicalSpace"
] | true |
ENat.le_ceil_self | Mathlib.Algebra.Order.Floor.Extended | [
"le_rfl",
"ENat.ceil_le",
"instPreorderENat",
"ENat.ceil",
"ENat.toENNReal",
"LE.le",
"instLEENat",
"ENat",
"ENNReal.instLE",
"ENNReal",
"Iff.mp"
] | true |
NonUnitalSubring.mk_le_mk | Mathlib.RingTheory.NonUnitalSubring.Defs | [
"AddGroup.toSubtractionMonoid",
"NonUnitalNonAssocRing",
"NegZeroClass.toNeg",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup",
"PartialOrder.toPreorder",
"AddSubsemigroup.carrier",
"Preorder.toLE",
"NonUnitalSubring",
"AddCommGroup.toAddGroup",
"Membership.mem",
... | true |
_private.Mathlib.Util.Notation3.0.Mathlib.Notation3._aux_Mathlib_Util_Notation3___elabRules_Mathlib_Notation3_notation3_1.match_3 | Mathlib.Util.Notation3 | [
"Lean.TSyntax",
"Lean.Syntax",
"Prod.mk",
"List.cons",
"Array",
"Lean.SyntaxNodeKind",
"Prod",
"Prod.casesOn",
"Lean.Name.mkStr1",
"List.nil"
] | false |
_private.Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM.0.UniformConvergenceCLM.topologicalSpace_mono._simp_1_2 | Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM | [
"UniformSpace",
"AddCommGroup.toAddCommMonoid",
"UniformConvergenceCLM.instUniformSpace",
"UniformConvergenceCLM.instTopologicalSpace",
"AddCommGroup.toAddGroup",
"RingHom",
"NormedField.toField",
"AddCommGroup",
"UniformConvergenceCLM.uniformity_toTopologicalSpace_eq",
"IsUniformAddGroup",
"Fie... | false |
subset_seqClosure | Mathlib.Topology.Sequences | [
"tendsto_const_nhds",
"Membership.mem",
"nhds",
"HasSubset.Subset",
"seqClosure",
"Filter.atTop",
"TopologicalSpace",
"And",
"Filter.Tendsto",
"Nat.instPreorder",
"Nat",
"And.intro",
"Exists.intro",
"Function.const",
"Set.instMembership",
"Set.instHasSubset",
"Set"
] | true |
CategoryTheory.ShiftedHom.opEquiv' | Mathlib.CategoryTheory.Shift.ShiftedHomOpposite | [
"CategoryTheory.Iso.homToEquiv",
"CategoryTheory.Functor",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Equiv.trans",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.shiftFunctor",
"Equiv",
"CategoryTheory.ShiftedHom"... | true |
_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.AnalyzeResult | Lean.Elab.Extra | [
"_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.AnalyzeResult.mk"
] | true |
Std.DTreeMap.Internal.Impl.get?.match_1.congr | Std.Data.DTreeMap.Internal.Model | [
"Ordering.gt",
"Ordering",
"Eq.rec",
"Ordering.eq",
"funext",
"Ordering.lt",
"Eq.refl",
"Eq",
"Std.DTreeMap.Internal.Impl.get?.match_1",
"Eq.trans"
] | true |
RingEquiv.ringKrullDim | Mathlib.RingTheory.KrullDimension.Basic | [
"WithBot",
"CommSemiring.toSemiring",
"ringKrullDim_eq_of_ringEquiv",
"Distrib.toAdd",
"instDistribOfSemiring",
"CommSemiring",
"Distrib.toMul",
"ENat",
"ringKrullDim",
"RingEquiv",
"Eq"
] | true |
CochainComplex.HomComplex.Cochain.fromSingleMk.congr_simp | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexSingle | [
"CochainComplex.HomComplex.Cochain._proof_1",
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CochainComplex.singleFunctor",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"CochainC... | true |
_private.Mathlib.Probability.Decision.Risk.Defs.0.ProbabilityTheory.bayesRisk_of_isEmpty'._simp_1_1 | Mathlib.Probability.Decision.Risk.Defs | [
"Subtype",
"IsEmpty",
"isEmpty_subtype",
"propext",
"Eq",
"Not"
] | false |
_private.Mathlib.Analysis.SpecialFunctions.Pow.NNReal.0.Mathlib.Meta.Positivity.evalNNRealRpow.match_1 | Mathlib.Analysis.SpecialFunctions.Pow.NNReal | [
"Lean.Level.ctorIdx",
"Mathlib.Meta.Positivity.Strictness",
"Lean.Expr.const",
"Lean.Meta.MetaM",
"Nat.hasNotBit",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Lean.Level.zero",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Level.instOfNat",
"OfNat.ofNat",
"_private.Mathlib.Ana... | false |
_private.Batteries.Lean.EStateM.0.EStateM.bind.match_1.splitter | Batteries.Lean.EStateM | [
"EStateM.Result",
"EStateM.bind.match_1",
"EStateM.Result.ok",
"EStateM.Result.error"
] | true |
Substring.Raw.Valid.drop | Batteries.Data.String.Lemmas | [
"Substring.Raw.ValidFor.valid",
"Substring.Raw.Valid.validFor",
"Exists",
"Substring.Raw.ValidFor",
"Substring.Raw.drop",
"Substring.Raw",
"instHAppendOfAppend",
"List",
"Substring.Raw.Valid",
"List.drop",
"Nat",
"Substring.Raw.ValidFor.drop",
"Char",
"List.instAppend",
"List.take",
"_... | true |
LocallyConstant.coe_const | Mathlib.Topology.LocallyConstant.Basic | [
"LocallyConstant",
"TopologicalSpace",
"Function.const",
"LocallyConstant.instFunLike",
"Eq",
"DFunLike.coe",
"rfl",
"LocallyConstant.const"
] | true |
AffineSubspace.coe_direction_eq_vsub_set_right | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | [
"Eq.mpr",
"Submodule",
"Set.vsub",
"AddMonoid.toAddSemigroup",
"congrArg",
"AffineSubspace.vsub_mem_direction",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Exists",
"AffineSubspace.coe_direction_eq_vsub_set",
"CompleteLattice.toConditionallyCompleteLattice",
... | true |
EckmannHilton.IsUnital | Mathlib.GroupTheory.EckmannHilton | [
"EckmannHilton.IsUnital.mk"
] | true |
AlgebraicGeometry.instUniversallyClosedToImage | Mathlib.AlgebraicGeometry.Morphisms.Proper | [
"Eq.mpr",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.Scheme.Hom.image",
"AlgebraicGeometry.Scheme.Hom.imageι",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AlgebraicGeometry.Scheme.Hom.toImage_imageι",
"AlgebraicGeometry.UniversallyClosed.of_comp_of_isSeparated",
"Algeb... | true |
LocallyBoundedMap.instFunLike._proof_1 | Mathlib.Topology.Bornology.Hom | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Eq.rec",
"LE.le",
"LocallyBoundedMap",
"LocallyBoundedMap.mk",
"Eq.ndrec",
"Bornology.cobounded",
"Eq.refl",
"LocallyBoundedMap.casesOn",
"Eq.symm",
"LocallyBoundedMap.toFun",
"Eq",
"Bornology",
"Filter",
"Filter.comap",
"Filter.instPartia... | false |
RootPairing.GeckConstruction.ωConj | Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basic | [
"LieAlgebra.toModule",
"RootPairing.GeckConstruction.ωConj._proof_2",
"CommRing",
"instFintypeSum",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"RootPairing.Base",
"AddCommGroup.toAddCommMonoid... | true |
_private.Lean.Server.FileWorker.0.Lean.Server.FileWorker.importsLoadedRef | Lean.Server.FileWorker | [
"Classical.ofNonempty",
"Bool",
"_private.Lean.Server.FileWorker.0.Lean.Server.FileWorker.importsLoadedRef._proof_1",
"IO.Ref"
] | true |
Lean.Elab.Term.Quotation.match_syntax.expand | Lean.Elab.Quotation | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.TSyntax",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"_private.Lean.Elab.Quotation.0.Lean.Elab.Term.Quotation.match_syntax.expand.match_3",
"Lean.NameMap",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Bool.not",
"_private.Lean.Elab... | true |
_private.Mathlib.Computability.DFA.0.DFA.acceptsFrom_inter._simp_1_2 | Mathlib.Computability.DFA | [
"instCompleteAtomicBooleanAlgebraLanguage",
"CompleteLattice.toLattice",
"Membership.mem",
"SemilatticeInf.toMin",
"List",
"And",
"Language.mem_inf",
"propext",
"CompleteBooleanAlgebra.toCompleteLattice",
"Language.instMembershipList",
"Language",
"Eq",
"CompleteAtomicBooleanAlgebra.toComple... | false |
Lean.Compiler.LCNF.Decl.lambdaLifting | Lean.Compiler.LCNF.LambdaLifting | [
"Pure.pure",
"_private.Lean.Compiler.LCNF.LambdaLifting.0.Lean.Compiler.LCNF.Decl.lambdaLifting.match_1",
"Lean.Compiler.LCNF.Scope",
"Array.push",
"Lean.Compiler.LCNF.LambdaLifting.State.decls",
"Lean.Core.instMonadLiftIOCoreM",
"IO.instMonadLiftSTRealWorldBaseIO",
"Lean.Compiler.LCNF.LambdaLifting.S... | true |
PartOrdEmb.coe_comp | Mathlib.Order.Category.PartOrdEmb | [
"PartOrdEmb.str",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Function.comp",
"PartOrdEmb.instCategory",
"PartOrdEmb.carrier",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategory... | true |
_private.Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors.0.UniqueFactorizationMonoid.normalizedFactorsEquiv._simp_3 | Mathlib.RingTheory.UniqueFactorizationDomain.NormalizedFactors | [
"Monoid",
"Monoid.toMulOneClass",
"Irreducible",
"MulOne.toMul",
"MulEquivClass",
"MulOneClass.toMulOne",
"EquivLike",
"MulEquiv.irreducible_iff",
"propext",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | false |
Turing.Dir.right | Mathlib.Computability.TuringMachine.Tape | [
"Turing.Dir.right",
"Turing.Dir"
] | true |
_private.Mathlib.Order.CompleteBooleanAlgebra.0.sSup_disjoint_iff._simp_1_2 | Mathlib.Order.CompleteBooleanAlgebra | [
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"iSup",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"Bot.bot",
"BoundedOrder.toOrderBot",
"propext",
"CompleteSemilatticeSup.toSupSet",
"SemilatticeSup.toPartialOrder",
"CompleteLatti... | false |
_private.Mathlib.SetTheory.ZFC.Rank.0.PSet.rank_sUnion_le.match_1_3 | Mathlib.SetTheory.ZFC.Rank | [
"PSet.instMembership",
"Membership.mem",
"Exists",
"PSet",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro"
] | false |
Ring.DirectLimit.hom_ext | Mathlib.Algebra.Colimit.Ring | [
"CommRing",
"HMul.hMul",
"FreeCommRing",
"Ring.instCommRingDirectLimit",
"Ideal.Quotient.ringHom_ext",
"AddGroupWithOne.toAddGroup",
"FreeCommRing.hom_ext",
"congrArg",
"CommSemiring.toSemiring",
"Ideal.Quotient.mk",
"setOf",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"instCommRing... | true |
_private.Mathlib.ModelTheory.Encoding.0.FirstOrder.Language.Term.listDecode_encode_list._simp_1_9 | Mathlib.ModelTheory.Encoding | [
"zero_le",
"LE.le",
"LE",
"IsBotZeroClass",
"True",
"eq_true",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
_private.Mathlib.CategoryTheory.Comma.StructuredArrow.Small.0.CategoryTheory.StructuredArrow.small_inverseImage_proj_of_locallySmall._simp_2 | Mathlib.CategoryTheory.Comma.StructuredArrow.Small | [
"CategoryTheory.ObjectProperty.ofObj",
"CategoryTheory.ObjectProperty.ofObj_iff",
"Exists",
"propext",
"CategoryTheory.CategoryStruct",
"Eq"
] | false |
CoeHTCT.mk.noConfusion | Init.Coe | [
"CoeHTCT.mk",
"id",
"CoeHTCT.noConfusion",
"CoeHTCT",
"heq_of_eq",
"Eq.refl",
"HEq",
"Eq"
] | false |
CategoryTheory.MonadicRightAdjoint.recOn | Mathlib.CategoryTheory.Monad.Adjunction | [
"CategoryTheory.Functor",
"CategoryTheory.Monad.comparison",
"CategoryTheory.MonadicRightAdjoint.mk",
"CategoryTheory.MonadicRightAdjoint",
"CategoryTheory.Adjunction",
"CategoryTheory.Functor.IsEquivalence",
"CategoryTheory.Adjunction.toMonad",
"CategoryTheory.Monad.Algebra.eilenbergMoore",
"Catego... | false |
CentroidHom.instRing._proof_3 | Mathlib.Algebra.Ring.CentroidHom | [
"NonUnitalNonAssocRing",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"NonUnitalNonAssocSemiring.toDistribSMul",
"AddZeroClass.toAddZero",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"DistribSMul.toSMulZeroClass",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddZero.toZero",
"Nat",
... | false |
Mathlib.Tactic.Ring.Common.const_pos | Mathlib.Tactic.Ring.Common | [
"Nat.le_of_ble_eq_true",
"Nat.rawCast",
"Nat.ble",
"instOfNatNat",
"Nat.instAddMonoidWithOne",
"Bool.true",
"Nat",
"LT.lt",
"Bool",
"instLTNat",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
LieRing.ofAssociativeRing | Mathlib.Algebra.Lie.OfAssociative | [
"Ring.toNonAssocRing",
"Ring.instBracket",
"LieRing.ofAssociativeRing._proof_4",
"LieRing.ofAssociativeRing._proof_6",
"NonAssocRing.toNonUnitalNonAssocRing",
"LieRing.ofAssociativeRing._proof_2",
"LieRing",
"LieRing.mk",
"Ring.toAddCommGroup",
"LieRing.ofAssociativeRing._proof_8",
"Ring"
] | true |
TensorProduct.finsuppRight | Mathlib.LinearAlgebra.DirectSum.Finsupp | [
"LinearEquiv.symm",
"Finsupp.module",
"instAddCommMonoidDirectSum",
"DirectSum.instModule",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"Algebra",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"Distrib... | true |
CategoryTheory.ShortComplex.isColimitColimitCocone | Mathlib.Algebra.Homology.ShortComplex.Limits | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.ShortComplex.isColimitπ₂MapCoconeColimitCocone",
"CategoryTheory.ShortComplex.colimitCocone",
"CategoryTheory.ShortComplex",
"CategoryTheory.Functor.comp",
"CategoryTheory.ShortComplex.π₁",
"CategoryTheory.ShortComplex... | true |
Mathlib.Command.MinImports.getSyntaxNodeKinds._unsafe_rec | Mathlib.Tactic.MinImports | [
"Mathlib.Command.MinImports.getSyntaxNodeKinds._unsafe_rec",
"Lean.NameSet",
"Lean.SourceInfo",
"Lean.Syntax",
"Array.map",
"_private.Mathlib.Tactic.MinImports.0.Mathlib.Command.MinImports.getSyntaxNodeKinds.match_1",
"instOfNatNat",
"Lean.NameSet.append",
"Substring.Raw",
"Array.foldl",
"Array"... | false |
_private.Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas.0.RootPairing.RootPositiveForm.rootLength_le_of_pairingIn_eq._proof_1_6 | Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas | [
"CommRing",
"AddGroupWithOne.toAddGroup",
"AddGroupWithOne.toAddMonoidWithOne",
"instFaithfulSMulIntOfCharZero",
"Int",
"CharZero",
"FaithfulSMul",
"AddGroup.toSubNegMonoid",
"CommRing.toRing",
"Ring.toAddGroupWithOne",
"SubNegMonoid.toZSMul"
] | false |
Aesop.instInhabitedGoalId.default | Aesop.Tree.Data | [
"Inhabited.default",
"Aesop.GoalId",
"instInhabitedNat",
"Nat",
"Aesop.GoalId.mk"
] | true |
Lean.Parser.getAlias | Lean.Parser.Extension | [
"Pure.pure",
"IO.instMonadLiftSTRealWorldBaseIO",
"Monad.toApplicative",
"instMonadLiftT",
"IO",
"Lean.NameMap.find?",
"ST.Ref.get",
"IO.RealWorld",
"instMonadEIO",
"Applicative.toPure",
"ST",
"Lean.Name",
"Monad.toBind",
"Bind.bind",
"IO.Error",
"IO.Ref",
"instMonadLiftTOfMonadLift"... | true |
Lean.Data.AC.ContextInformation.mk | Init.Data.AC | [
"Lean.Data.AC.ContextInformation",
"Lean.Data.AC.ContextInformation.mk",
"Nat",
"Bool"
] | true |
Lean.Meta.Grind.AC.ProofM | Lean.Meta.Tactic.Grind.AC.Proof | [
"ReaderT",
"Lean.Meta.Grind.AC.ProofM.State",
"IO.RealWorld",
"Lean.Meta.Grind.AC.ACM",
"StateRefT'",
"Lean.Meta.Grind.AC.ProofM.Context"
] | true |
Filter.cardinalInterFilter_sup | Mathlib.Order.Filter.CardinalInter | [
"CardinalInterFilter",
"Cardinal",
"CardinalInterFilter.of_cardinalInterFilter_of_le",
"inf_le_right",
"SemilatticeInf.toMin",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"Cardinal.instConditionallyCompleteLinearOrderBot",
"Max.max",
"ConditionallyCompleteLinearOrderBot.toCond... | true |
ContDiffWithinAt.mono | Mathlib.Analysis.Calculus.ContDiff.Defs | [
"NormedSpace",
"ContDiffWithinAt.mono_of_mem_nhdsWithin",
"nhdsWithin",
"PseudoMetricSpace.toUniformSpace",
"HasSubset.Subset",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"self_mem_nhdsWithin",
"ENat",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"ContDiffWithinAt",
"... | true |
Qq.Impl.mkNAryFunctionType._unsafe_rec | Qq.Match | [
"Lean.MetavarKind.natural",
"instMonadControlTOfPure",
"Lean.Meta.State",
"Lean.Meta.withLocalDeclD",
"Qq.Impl.mkNAryFunctionType._unsafe_rec",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"_private.Qq.Match.0.Qq.Impl.mkNAryFunctionType.match_1",
"Applicative.toPure",
"List.toArray",
"List.... | false |
FormalGroup.𝔾ₐ._proof_3 | Mathlib.RingTheory.FormalGroup.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Nat.instMulZeroClass",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"Fin.instNonUnitalCommRing",
"Fin.instNeZeroHAddNatOfNat_mathlib_1",... | false |
_private.Mathlib.Analysis.SpecificLimits.Basic.0.tendsto_nat_floor_atTop._simp_1_1 | Mathlib.Analysis.SpecificLimits.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"Nat.le_floor_iff",
"AddMonoidWithOne.toNatCast",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"LE.le",
"instLENat",
"Nat.cast",
"FloorSemiring",
"Nat",
"propext",
"Semiring",
"Nat.floor"... | false |
CategoryTheory.MonadIso.toNatIso | Mathlib.CategoryTheory.Monad.Basic | [
"CategoryTheory.Monad",
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.Iso",
"CategoryTheory.Monad.toFunctor",
"CategoryTheory.Functor.mapIso",
"CategoryTheory.monadToFunctor",
"CategoryTheory.instCategoryMonad",
"CategoryTheory.Category"
] | true |
TopModuleCat.noConfusionType | Mathlib.Algebra.Category.ModuleCat.Topology.Basic | [
"ContinuousSMul",
"ModuleCat",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"TopologicalSpace",
"AddZero.toZero",
"TopModuleCat",
"ModuleCat.isAddCommGroup",
"... | false |
_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite.0.SimpleGraph.odd_ncard_oddComponents._simp_1_2 | Mathlib.Combinatorics.SimpleGraph.Connectivity.Finite | [
"Set.Elem",
"Set.toFinset",
"Set.ncard_eq_toFinset_card'",
"Fintype",
"Nat",
"Finset.card",
"Set.ncard",
"Eq.symm",
"Eq",
"Set"
] | false |
imaginaryPart_smul | Mathlib.LinearAlgebra.Complex.Module | [
"instTrivialStarReal",
"imaginaryPart_I_smul",
"Real",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"SemilinearMapClass.toMulActionSemiHomClass",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Complex.commRing",
"congrArg",
"DistribMulAction.toDistribSMul",
... | true |
Quiver.rec | Mathlib.Combinatorics.Quiver.Basic | [
"Quiver.mk",
"Quiver"
] | false |
AddSemigroupAction.mk | Mathlib.Algebra.Group.Action.Defs | [
"VAdd",
"AddSemigroup",
"HVAdd.hVAdd",
"AddSemigroupAction.mk",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"instHVAdd",
"AddSemigroupAction",
"Eq"
] | true |
List.range'_one | Init.Data.List.Basic | [
"List.range'",
"instOfNatNat",
"List.cons",
"List",
"Nat",
"OfNat.ofNat",
"Eq",
"rfl",
"List.nil"
] | true |
InnerProductSpace.Core.inner_self_eq_norm_mul_norm | Mathlib.Analysis.InnerProductSpace.Defs | [
"Norm.norm",
"Eq.mpr",
"Real",
"HMul.hMul",
"InnerProductSpace.Core.toNorm",
"AddMonoid.toAddSemigroup",
"Inner.inner",
"Real.instAddMonoid",
"congrArg",
"InnerProductSpace.Core.norm_eq_sqrt_re_inner",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddMonoid.toZero",
"Real.sq... | true |
Matroid.isColoop_iff_mem_coloops | Mathlib.Combinatorics.Matroid.Loop | [
"Iff.rfl",
"Matroid.coloops",
"Membership.mem",
"Matroid.IsColoop",
"Iff",
"Set.instMembership",
"Matroid",
"Set"
] | true |
Aesop.incrementIteration | Aesop.Search.SearchM | [
"Aesop.SearchM.State.iteration",
"modify",
"Aesop.SearchM.instMonadStateState",
"Aesop.SearchM.State.mk",
"Unit",
"Aesop.Queue",
"Aesop.SearchM",
"Aesop.SearchM.State",
"Aesop.SearchM.State.maxRuleApplicationDepthReached",
"Aesop.SearchM.State.queue",
"Aesop.Iteration.succ"
] | true |
Std.Time.Week.instLEOffset._aux_1 | Std.Time.Date.Unit.Week | [
"Rat.instOfNat",
"Rat.instMul",
"HMul.hMul",
"Rat",
"Std.Time.Internal.UnitVal",
"Int",
"LE.le",
"Std.Time.Internal.UnitVal.val",
"OfNat.ofNat",
"Std.Time.Week.Offset",
"Int.instLEInt",
"instHMul"
] | false |
CategoryTheory.SmallObject.SuccStruct.extendToSucc.map_comp | Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc | [
"CategoryTheory.SmallObject.SuccStruct.extendToSucc.map._proof_3",
"not_le",
"CategoryTheory.SmallObject.SuccStruct.extendToSucc.map._proof_4",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"Preorder.toLT",
"Order.succ",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom"... | true |
Metric.exists_continuous_real_forall_closedEBall_subset | Mathlib.Topology.MetricSpace.PartitionOfUnity | [
"_private.Mathlib.Topology.MetricSpace.PartitionOfUnity.0.Metric.exists_continuous_real_forall_closedEBall_subset._simp_1_1",
"Eq.mpr",
"Real",
"Set.Ioi",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Metric.exists_forall_closedEBall_subset_aux₂",
"Semiring.toModule",
"IsTopologicalRing.toIsTopolo... | true |
Complex.UnitDisc.coe_mul._simp_1 | Mathlib.Analysis.Complex.UnitDisc.Basic | [
"HMul.hMul",
"MulZeroClass.toMul",
"SemigroupWithZero.toMulZeroClass",
"Complex.instMul",
"Complex.UnitDisc.instSemigroupWithZero",
"Complex.UnitDisc.coe_mul",
"Complex.UnitDisc",
"Complex.UnitDisc.coe",
"Complex",
"Eq.symm",
"Eq",
"instHMul"
] | false |
SimpleGraph.Walk.concat_dropLast | Mathlib.Combinatorics.SimpleGraph.Walk.Operations | [
"False",
"congrArg",
"HEq.refl",
"SimpleGraph.Adj",
"False.elim",
"SimpleGraph.irrefl._simp_1",
"SimpleGraph.Walk",
"SimpleGraph.Walk.casesOn",
"Eq.mp",
"SimpleGraph.Walk.concat",
"SimpleGraph",
"SimpleGraph.Walk.cons",
"SimpleGraph.Walk.cons.congr_simp",
"SimpleGraph.Walk.nil",
"SimpleG... | true |
Dioph.reindex_dioph | Mathlib.NumberTheory.Dioph | [
"Dioph",
"Poly",
"congrArg",
"setOf",
"Function.comp",
"Membership.mem",
"Exists",
"_private.Mathlib.NumberTheory.Dioph.0.Dioph.reindex_dioph.match_1_1",
"Sum.casesOn",
"Sum",
"Poly.instFunLike",
"Sum.inl",
"Int",
"iff_self",
"funext",
"exists_congr",
"Iff",
"instOfNat",
"Sum.inr... | true |
NontriviallyNormedField.ofNormNeOne | Mathlib.Analysis.Normed.Field.Basic | [
"Norm.norm",
"Real",
"NormedField.toField",
"Exists",
"NormedField.toNorm",
"Ne",
"Field.toSemifield",
"NormedField",
"Real.instOne",
"And",
"Semifield.toDivisionSemiring",
"NontriviallyNormedField.mk",
"DivisionSemiring.toSemiring",
"NontriviallyNormedField",
"One.toOfNat1",
"Zero.toO... | true |
_private.Lean.Elab.Tactic.ElabTerm.0.Lean.Elab.Tactic.evalSpecialize.match_1 | Lean.Elab.Tactic.ElabTerm | [
"Lean.MVarId",
"Lean.FVarId",
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
Mathlib.Tactic.Linarith.leftOfIneqProof | Mathlib.Tactic.Linarith.Verification | [
"Pure.pure",
"Mathlib.Ineq",
"Lean.Meta.State",
"_private.Mathlib.Tactic.Linarith.Verification.0.Mathlib.Tactic.Linarith.leftOfIneqProof.match_1",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Applicative.toPure",
"Lean.Core.CoreM",
"Lean.Meta.instMonadMetaM",
"StateRefT'",
"StateRefT'.inst... | true |
CategoryTheory.Presieve.HasPairwisePullbacks.mk | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.Presieve.HasPairwisePullbacks",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.Presieve.HasPairwisePullbacks.mk",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
tendsto_indicator_thickening_indicator_closure | Mathlib.Topology.MetricSpace.ThickenedIndicator | [
"Eq.mpr",
"Real",
"Set.Ioi",
"Pi.topologicalSpace",
"Real.instZero",
"congrArg",
"indicator_thickening_eventually_eq_indicator_closure",
"tendsto_const_nhds",
"Set.indicator",
"nhdsWithin",
"PseudoMetricSpace.toUniformSpace",
"nhds",
"id",
"tendsto_pi_nhds",
"PseudoEMetricSpace",
"Metr... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.minKey?_insert_le_minKey?._simp_1_2 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"beqOfOrd",
"Ordering",
"Std.DTreeMap.Internal.Impl.compare_ne_iff_beq_eq_false",
"Ordering.eq",
"Ne",
"Ord.compare",
"BEq.beq",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
Valuation.ofAddValuation._proof_4 | Mathlib.RingTheory.Valuation.Basic | [
"Equiv.instEquivLike",
"OrderDual.ofDual",
"Additive",
"Iff.rfl",
"PartialOrder.toPreorder",
"LinearOrderedCommMonoidWithZero.toLinearOrder",
"Preorder.toLE",
"Additive.toMul",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Equiv",
"LE.le",
"Multiplicative",
"Iff",
"Linear... | false |
Set.centralizer.eq_1 | Mathlib.Algebra.Group.Center | [
"HMul.hMul",
"setOf",
"Mul",
"Membership.mem",
"Set.centralizer",
"Eq.refl",
"Eq",
"Set.instMembership",
"instHMul",
"Set"
] | true |
_private.Lean.Meta.Sym.Simp.DiscrTree.0.Lean.Meta.Sym.pushAllArgs._unsafe_rec | Lean.Meta.Sym.Simp.DiscrTree | [
"Array.push",
"Lean.Expr",
"_private.Lean.Meta.Sym.Simp.DiscrTree.0.Lean.Meta.Sym.pushAllArgs.match_1",
"Array",
"_private.Lean.Meta.Sym.Simp.DiscrTree.0.Lean.Meta.Sym.pushAllArgs._unsafe_rec"
] | false |
_private.Mathlib.Algebra.BigOperators.Intervals.0.Fin.prod_Icc_div._proof_1_7 | Mathlib.Algebra.BigOperators.Intervals | [
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Int.Linear.norm_le",
"Lean.Grind.CommRing.Expr.var",
"Lean.Grind.ToInt.toInt",
"Lean.Grind.Order.le_eq_true_of_le_k",
"PartialOrder.toPreorder",
"Nat.ToInt.add_c... | false |
CategoryTheory.ObjectProperty.isColocal_iff_isIso | Mathlib.CategoryTheory.Localization.Bousfield | [
"CategoryTheory.Category.assoc",
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Exists",
"CategoryTheory.CategoryStruct.id",
"id",
"CategoryTheory.Category.comp_id",
"CategoryTheory.ObjectProperty.isColocal_of_isIso",
"And",
"Iff",
"Exists.casesO... | true |
_private.Lean.Elab.Tactic.Do.ProofMode.MGoal.0.Lean.Elab.Tactic.Do.ProofMode.parseHyp?._sparseCasesOn_1 | Lean.Elab.Tactic.Do.ProofMode.MGoal | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
_private.Batteries.Linter.UnreachableTactic.0.Batteries.Linter.UnreachableTactic.getTactics._sparseCasesOn_1 | Batteries.Linter.UnreachableTactic | [
"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 |
_private.Mathlib.Data.Vector.Basic.0.List.Vector.traverse._proof_1 | Mathlib.Data.Vector.Basic | [
"Eq.mpr",
"congrArg",
"List.Vector",
"id",
"List",
"Nat",
"Eq.refl",
"Eq",
"List.length"
] | false |
SeminormedGroup.toUniformSpace._inherited_default | Mathlib.Analysis.Normed.Group.Defs | [
"UniformSpace",
"Real.instLE",
"Real",
"Real.instZero",
"id",
"LE.le",
"Real.instAdd",
"instHAdd",
"UniformSpace.ofDist",
"HAdd.hAdd",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
Mathlib.Tactic.Push.instBEqHead | Mathlib.Tactic.Push.Attr | [
"Mathlib.Tactic.Push.instBEqHead.beq",
"BEq.mk",
"Mathlib.Tactic.Push.Head",
"BEq"
] | true |
CategoryTheory.PreZeroHypercover.instUniqueI₀Singleton | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover.instUniqueI₀Singleton._proof_3",
"Unique.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Unique",
"CategoryTheory.PreZeroHypercover.singleton",
"CategoryTheory.PreZeroHypercover.I₀",
"CategoryTheory.PreZeroHypercover.instUniqueI₀Singleton._aux_1",
"Cat... | true |
_private.Mathlib.RingTheory.SurjectiveOnStalks.0.RingHom.surjectiveOnStalks_iff_forall_maximal._simp_1_1 | Mathlib.RingTheory.SurjectiveOnStalks | [
"RingHom.instRingHomClass",
"CommRing",
"Semiring.toModule",
"HMul.hMul",
"CommSemiring.toSemiring",
"Localization.AtPrime",
"Localization.localRingHom",
"RingHom",
"Membership.mem",
"Exists",
"Ideal.IsPrime.comap",
"Ideal",
"instDistribOfSemiring",
"NonUnitalNonAssocSemiring.toAddCommMono... | false |
Std.Sat.AIG.rec | Std.Sat.AIG.Basic | [
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.Cache",
"instOfNatNat",
"Std.Sat.AIG.IsDAG",
"Array",
"GetElem.getElem",
"Std.Sat.AIG",
"Array.instGetElemNatLtSize",
"Nat",
"LT.lt",
"Hashable",
"instLTNat",
"Std.Sat.AIG.Decl.false",
"OfNat.ofNat",
"Eq",
"Array.size",
"Std.Sat.AIG.mk",
"DecidableE... | false |
Representation.freeLift_toLinearMap | Mathlib.RepresentationTheory.Equiv | [
"Monoid",
"LinearEquiv.symm",
"Representation",
"MonoidHom.instFunLike",
"Semiring.toModule",
"Finsupp.module",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Module.End.instSemiring",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"Representation.free",
... | true |
dite_dite_distrib_left | Mathlib.Logic.Lemmas | [
"Eq.mpr",
"dite_congr",
"congrArg",
"Decidable",
"dif_pos",
"id",
"dif_neg",
"dite",
"congr",
"Eq.mpr_not",
"Eq.refl",
"Eq.mpr_prop",
"Eq",
"Not"
] | true |
CategoryTheory.Limits.colimitQuotientCoproduct_epi | Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers | [
"CategoryTheory.Limits.ColimitCocone.cocone",
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasFiniteColimits_of_hasColimitsOfSize",
"CategoryTheory.Limits.colimit.isoColimitCocone",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver"... | true |
_private.Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme.0.AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asIdeal.prime.match_1_1 | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme | [
"SetLike",
"Membership.mem",
"Exists.casesOn",
"Nat",
"Exists.intro",
"SetLike.instMembership",
"SetLike.IsHomogeneousElem"
] | false |
Std.Iter.isSome_atIdxSlow?_repeat | Std.Data.Iterators.Lemmas.Producers.Repeat | [
"Nat.recAux",
"congrArg",
"Option.some",
"Std.Iter.repeat",
"instOfNatNat",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
"Std.Iter.atIdxSlow?_repeat",
"Nat",
"Std.Iterators.Types.RepeatIterator",
"True",
"eq_self",
"Bool",
"of_eq_true",
"instAddNat",
"congrFun'",
"Std.Iterators.Types.Repe... | true |
CategoryTheory.MorphismProperty.HasOfPostcompProperty.mk | Mathlib.CategoryTheory.MorphismProperty.Composition | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.HasOfPostcompProperty.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.HasOfPostcompProperty",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryThe... | true |
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