name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
List.append._sunfold | Init.Prelude | [
"List.cons",
"List.append",
"List.append.match_1",
"List"
] | false |
Ideal.instNormalizedGCDMonoid._proof_7 | Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas | [
"CommRing",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring",
"OrderBot.toBot",
"Submodule.completeLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CommSemiring.toCommMonoidWithZero",
"SemilatticeInf.toPartialOrder",
"CompleteLattice.toConditionallyCompleteLattice",
"Bot.bot",
... | false |
Mathlib.MoveAdd.pairUp | Mathlib.Tactic.MoveAdd | [
"List.brecOn",
"Lean.Syntax",
"Lean.Expr",
"Lean.Meta.MetaM",
"List",
"Bool",
"Mathlib.MoveAdd.pairUp._f",
"Prod"
] | true |
CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionOfMonoidalFunctorToEndofunctorMop._proof_5 | Mathlib.CategoryTheory.Monoidal.Action.End | [
"CategoryTheory.Functor",
"CategoryTheory.MonoidalOpposite.unmop",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.MonoidalOpposite",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"Quiver.Hom.unmop",
"CategoryTheory.Functor.map",
"cong... | false |
_private.Lean.Compiler.LCNF.Basic.0.Lean.Compiler.LCNF.updateOsetImp | Lean.Compiler.LCNF.Basic | [
"Lean.Compiler.LCNF.Arg",
"Lean.Compiler.LCNF.instInhabitedCode",
"_private.Lean.Compiler.LCNF.Basic.0.Lean.Compiler.LCNF.updateOsetImp.match_1",
"Lean.Compiler.LCNF.Code.oset",
"panicWithPosWithDecl",
"ptrEq",
"Bool.and",
"Lean.FVarId",
"instDecidableEqBool",
"instOfNatNat",
"Lean.Compiler.LCNF... | true |
ArchimedeanClass.stdPart_neg | Mathlib.Algebra.Order.Ring.StandardPart | [
"Eq.mpr",
"NegZeroClass.toNeg",
"Classical.ofNonempty",
"Real",
"dite_congr",
"RingHomClass.toAddMonoidHomClass",
"ArchimedeanClass.instFieldFiniteResidueField",
"Real.instZero",
"IsOrderedRing",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"ArchimedeanClass.instLinea... | true |
LaurentSeries.instLaurentSeriesComplete | Mathlib.RingTheory.LaurentSeries | [
"Int.instAddCommGroup",
"Filter.instMembership",
"Int.instAddCommMonoid",
"Multiplicative.linearOrder",
"Int.instIsStrictOrderedRing",
"CompleteSpace",
"Cauchy",
"Int.instLinearOrder",
"PartialOrder.toPreorder",
"LaurentSeries.Cauchy.limit",
"Preorder.toLE",
"Membership.mem",
"Field.toDivisi... | true |
Pi.isAtom_iff_eq_single | Mathlib.Order.Atoms | [
"Pi.preorder",
"Preorder.toLT",
"Function.update",
"congrArg",
"CovBy",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"Exists",
"PartialOrder",
"Pi.instOrderBot",
"Pi.instBotForall",
"_private.Mathlib.Order.Atoms.0.Pi.isAtom_iff_eq_single._simp_1_1",
"Bot.bot"... | true |
List.decidableInfix._unsafe_rec | Mathlib.Data.List.Infix | [
"Decidable.isTrue",
"False",
"List.instDecidableIsPrefixOfDecidableEq",
"Decidable",
"Exists",
"List.decidableInfix.match_3",
"List.cons",
"List.decidableInfix._proof_5",
"List.IsInfix",
"instHAppendOfAppend",
"List",
"List.infix_cons_iff",
"List.IsPrefix",
"List.decidableInfix.match_1",
... | false |
Cardinal.lift_le_aleph_ofNat | Mathlib.SetTheory.Cardinal.Aleph | [
"Cardinal.aleph",
"Ordinal.partialOrder",
"Cardinal",
"PartialOrder.toPreorder",
"Cardinal.lift",
"Preorder.toLE",
"AddMonoidWithOne.toNatCast",
"LE.le",
"Cardinal.instLE",
"Ordinal.addMonoidWithOne",
"Iff",
"Nat",
"Cardinal.lift_le_aleph_natCast",
"OrderEmbedding",
"OfNat.ofNat",
"DFu... | true |
FiniteDimensional.of_injective | Mathlib.LinearAlgebra.FiniteDimensional.Defs | [
"PrincipalIdealRing.isNoetherianRing",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"DivisionRing.toDivisionSemiring",
"AddCommGroup",
"Module.Finite.of_injective",
"DivisionRing.toRing",
"DivisionSemiring.isPrincipalIdealRing",
"LinearMap",
"FiniteDimensional",
"RingHomInvPair.ids",... | true |
Array.instOrientedCmpCompareLex | Init.Data.Order.Ord | [
"List.instOrientedCmpCompareLex",
"Array.compareLex_eq_compareLex_toList",
"congrArg",
"Std.OrientedCmp.mk",
"Ordering",
"Std.OrientedCmp",
"Ordering.swap",
"Array.toList",
"Array",
"List",
"Array.compareLex",
"congr",
"True",
"eq_self",
"of_eq_true",
"List.compareLex",
"_private.Ini... | true |
Bundle.Trivialization.nhds_eq_inf_comap | Mathlib.Topology.FiberBundle.Trivialization | [
"Eq.mpr",
"Bundle.Trivialization.toFun'",
"congrArg",
"Filter.instCompleteLatticeFilter",
"PartialOrder.toPreorder",
"instTopologicalSpaceProd",
"Preorder.toLE",
"Function.comp",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"nhds",
"CompleteLattice.toConditionallyCompleteLattice",
"id"... | true |
Lean.Lsp.instHashableMarkupKind.hash | Lean.Data.Lsp.Basic | [
"UInt64.instOfNat",
"UInt64",
"_private.Lean.Data.Lsp.Basic.0.Lean.Lsp.instHashableMarkupKind.hash.match_1",
"Lean.Lsp.MarkupKind",
"Unit",
"OfNat.ofNat"
] | true |
_private.Mathlib.Combinatorics.Matroid.Basic.0.Matroid.ext_indep._simp_1_1 | Mathlib.Combinatorics.Matroid.Basic | [
"Matroid.IsBase",
"Matroid.Indep",
"Set.instLE",
"propext",
"Maximal",
"Matroid.isBase_iff_maximal_indep",
"Eq",
"Matroid",
"Set"
] | false |
CategoryTheory.IsModHom | Mathlib.CategoryTheory.Monoidal.Mod | [
"CategoryTheory.IsModHom.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalLeftAction",
"CategoryTheory.ModObj",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.MonObj",
"CategoryTheory.Category"
] | true |
NonUnitalSemiring.ext_iff | Mathlib.Algebra.Ring.Ext | [
"HMul.hMul",
"HEq.refl",
"NonUnitalSemiring.ext",
"Eq.casesOn",
"Distrib.toAdd",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"And.casesOn",
"instHAdd",
"And",
"Iff",
"Distrib.toMul",
"HAdd.hAdd",
"NonUnitalSemiring",
"And.intro",
"Iff.intro",
"Eq.ndrec",
"NonUnitalNonAssocSemiri... | true |
Flow.IsFactorOf.self | Mathlib.Dynamics.Flow | [
"Flow.IsFactorOf",
"Iff.mpr",
"AddMonoid.toAddSemigroup",
"Flow",
"id",
"TopologicalSpace",
"AddSemigroup.toAdd",
"AddMonoid",
"Exists.intro",
"Flow.isSemiconjugacy_id_iff_eq",
"Flow.IsSemiconjugacy",
"Eq.refl",
"ContinuousAdd",
"Eq"
] | true |
MeasureTheory.«_aux_Mathlib_MeasureTheory_Measure_MeasureSpaceDef___macroRules_MeasureTheory_term∀ᵐ_,__1» | Mathlib.MeasureTheory.Measure.MeasureSpaceDef | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax... | false |
RingCat.Colimits.Prequotient.recOn | Mathlib.Algebra.Category.Ring.Colimits | [
"RingCat.Colimits.Prequotient.one",
"CategoryTheory.Functor",
"RingCat.Colimits.Prequotient.neg",
"RingCat.Colimits.Prequotient.add",
"RingCat.Colimits.Prequotient.zero",
"CategoryTheory.SmallCategory",
"RingCat.Colimits.Prequotient",
"RingCat.Colimits.Prequotient.of",
"RingCat",
"RingCat.Colimits... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getKey!_insert._simp_1_3 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
Std.DHashMap.Internal.Raw₀.eraseMany_eq_eraseListₘ_toListModel | Std.Data.DHashMap.Internal.WF | [
"Pure.pure",
"Eq.mpr",
"Std.DHashMap.Internal.Raw₀.eraseListₘ",
"_private.Std.Data.DHashMap.Internal.Defs.0.Std.DHashMap.Internal.Raw₀.eraseManyEntries._proof_1",
"congrArg",
"instForInOfForIn'",
"Monad.toApplicative",
"List.map",
"Std.DHashMap.Raw",
"inferInstance",
"id",
"Subtype",
"ForIn.... | true |
HilbertBasis._sizeOf_inst | Mathlib.Analysis.InnerProductSpace.l2Space | [
"HilbertBasis",
"RCLike",
"SizeOf.mk",
"SizeOf",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"HilbertBasis._sizeOf_1",
"InnerProductSpace",
"NormedAddCommGroup"
] | false |
_private.Init.Data.Nat.Fold.0.Nat.dfold._proof_9 | Init.Data.Nat.Fold | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean.Omega.Int.add_congr",
"Lean.Om... | false |
CategoryTheory.Oplax.StrongTrans.Modification.whiskerRight_naturality | Mathlib.CategoryTheory.Bicategory.Modification.Oplax | [
"CategoryTheory.Oplax.OplaxTrans.Modification.whiskerRight_naturality",
"CategoryTheory.Oplax.StrongTrans.naturality",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Oplax.StrongTrans.app",
... | true |
_private.Mathlib.Topology.Spectral.Prespectral.0.PrespectralSpace.of_isOpenCover._simp_1_1 | Mathlib.Topology.Spectral.Prespectral | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
indicator_union_eventuallyEq | Mathlib.Order.Filter.IndicatorFunction | [
"Set.indicator",
"Set.indicator_union_of_notMem_inter",
"Filter.Eventually",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Set.instUnion",
"AddZeroClass.toAddZero",
"Filter.EventuallyEq",
"Set.instInter",
"Inter.inter",
"Filter.Eventually.mono",
"AddZero.toZero",
"instHAdd",
"Pi.instAdd",... | true |
Relation.ReflTransGen.below.refl | Mathlib.Logic.Relation | [
"Relation.ReflTransGen.below.refl",
"Relation.ReflTransGen.refl",
"Relation.ReflTransGen.below",
"Relation.ReflTransGen"
] | true |
_private.Std.Do.WP.SimpLemmas.0.Option.orElse.match_1.splitter | Std.Do.WP.SimpLemmas | [
"Option.some",
"Option.orElse.match_1",
"Option.none",
"Unit",
"Option"
] | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.getD_diff_of_contains_eq_false_left._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 |
_private.Mathlib.Probability.Process.LocalProperty.0.ProbabilityTheory.IsStable.locally_and_iff._simp_1_5 | Mathlib.Probability.Process.LocalProperty | [
"Set.indicator",
"Set.instInter",
"Inter.inter",
"Set.indicator_indicator",
"Eq.symm",
"Eq",
"Zero",
"Set"
] | false |
Submodule.finrank_sup_add_finrank_inf_eq | Mathlib.LinearAlgebra.FiniteDimensional.Lemmas | [
"IsNoetherianRing.strongRankCondition",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"Lattice.toSemilatticeSup",
"PrincipalIdealRing.isNoetherianRing",
"Ring.toNonAssocRing",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
... | true |
_private.Aesop.Tree.Data.0.Aesop.instDecidableEqGoalId.decEq._proof_2 | Aesop.Tree.Data | [
"False",
"Aesop.GoalId",
"Aesop.GoalId.mk.noConfusion",
"Nat",
"Aesop.GoalId.mk",
"Eq",
"Not"
] | false |
Std.Tactic.BVDecide.Gate.beq.sizeOf_spec | Std.Tactic.BVDecide.Bitblast.BoolExpr.Basic | [
"instOfNatNat",
"Std.Tactic.BVDecide.Gate._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"Std.Tactic.BVDecide.Gate",
"Eq.refl",
"Std.Tactic.BVDecide.Gate.beq",
"OfNat.ofNat",
"Eq"
] | true |
LieAlgebra.Orthogonal.indefiniteDiagonal_assoc | Mathlib.Algebra.Lie.Classical | [
"Eq.mpr",
"NegZeroClass.toNeg",
"Matrix.fromBlocks",
"False",
"CommRing",
"instFintypeSum",
"instDecidableTrue",
"Sum.inr_injective",
"Sum.ctorIdx",
"if_true",
"LieRing.toAddCommGroup",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"LieEquiv",
"instDecidableEqSum",
"False.elim",
... | true |
LinearMap.IsRefl.nondegenerate_iff_separatingRight | Mathlib.LinearAlgebra.SesquilinearForm.Basic | [
"Iff.mpr",
"Eq.mpr",
"Submodule",
"CommRing",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearMap.IsRefl.ker_eq_bot_iff_ker_flip_eq_bot",
"AddMonoid.toAddZeroClass",
"LinearMap.ker",
"AddZeroClass.toAddZero",
"AddCommGroup",
"... | true |
Function.mulSupport_one_add' | Mathlib.Algebra.GroupWithZero.Indicator | [
"One",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddLeftCancelMonoid",
"AddZeroClass.toAddZero",
"AddZero.toZero",
"instHAdd",
"AddSemigroup.toAdd",
"Pi.instAdd",
"HAdd.hAdd",
"Pi.instOne",
"Function.support",
"Function.mulSupport",
"One.toOfNat1",
"OfNat.ofNat",
"Functi... | true |
AlgebraicGeometry.IsOpenImmersion | Mathlib.AlgebraicGeometry.OpenImmersion | [
"CategoryTheory.MorphismProperty",
"AlgebraicGeometry.Scheme.Hom.toLRSHom",
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgebraicGeometry.LocallyRingedSpace.IsOpenImmersion",
"CategoryTheory.Category.toCategoryStruct",
"AlgebraicGeometry.Scheme.instCategory",
... | true |
FinPartOrd.mk.inj | Mathlib.Order.Category.FinPartOrd | [
"And",
"Fintype",
"PartOrd",
"And.intro",
"PartOrd.carrier",
"HEq",
"FinPartOrd.mk.noConfusion",
"Eq",
"FinPartOrd.mk",
"FinPartOrd"
] | true |
smoothSheaf.eval_surjective | Mathlib.Geometry.Manifold.Sheaf.Smooth | [
"CategoryTheory.Limits.Types.hasColimitsOfSize",
"NormedSpace",
"instTopENat",
"contDiffGroupoid",
"TopologicalSpace.Opens.instChartedSpace",
"TopologicalSpace.OpenNhds.instOrderTop",
"TopCat.PrelocalPredicate.pred",
"PartialOrder.toPreorder",
"smoothSheaf.eval",
"TopologicalSpace.Opens",
"Preor... | true |
Lean.Elab.Tactic.Do.ProofMode.elabMAssumption._regBuiltin.Lean.Elab.Tactic.Do.ProofMode.elabMAssumption_1 | Lean.Elab.Tactic.Do.ProofMode.Assumption | [
"Lean.Elab.Tactic.tacticElabAttribute",
"IO",
"Unit",
"Lean.Elab.Tactic.Tactic",
"Lean.Name.mkStr6",
"Lean.Elab.Tactic.Do.ProofMode.elabMAssumption",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
isBounded_ge_nhds | Mathlib.Topology.Order.LiminfLimsup | [
"Preorder.toLE",
"nhds",
"GE.ge",
"Filter.IsBounded",
"BoundedGENhdsClass.isBounded_ge_nhds",
"TopologicalSpace",
"BoundedGENhdsClass",
"Preorder"
] | true |
_private.Lean.Meta.Match.Match.0.Lean.Meta.Match.processConstructor.match_5 | Lean.Meta.Match.Match | [
"Lean.Expr",
"Nat.hasNotBit",
"List.cons",
"List",
"List.ctorIdx",
"_private.Lean.Meta.Match.Match.0.Lean.Meta.Match.isNextVar._sparseCasesOn_1"
] | false |
AddActionHom.mk.injEq | Mathlib.GroupTheory.GroupAction.Hom | [
"Eq.propIntro",
"VAdd",
"AddActionHom",
"AddActionHom.mk.inj",
"HVAdd.hVAdd",
"AddActionHom.mk",
"instHVAdd",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
stronglyMeasurable_bot_iff | Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic | [
"MeasureTheory.stronglyMeasurable_const",
"MeasureTheory.StronglyMeasurable.approx",
"Exists.choose_spec",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"congrArg",
"exists_const._simp_1",
"Pi.uniqueOfIsEmpty",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"instArchimedeanNat",
"Filt... | true |
OrderDual.instMeasurableInf₂ | Mathlib.MeasureTheory.Order.Lattice | [
"MeasurableInf₂",
"OrderDual.instMinOfMax",
"MeasurableSup₂.measurable_sup",
"Max",
"instMeasurableSpaceOrderDual",
"MeasurableSpace",
"MeasurableInf₂.mk",
"MeasurableSup₂",
"OrderDual"
] | true |
MeasureTheory.LevyProkhorov.probabilityMeasureHomeomorph._proof_2 | Mathlib.MeasureTheory.Measure.LevyProkhorovMetric | [
"MeasureTheory.LevyProkhorov",
"MeasureTheory.ProbabilityMeasure",
"MeasurableSpace",
"MeasureTheory.LevyProkhorov.toMeasure",
"MeasureTheory.LevyProkhorov.ofMeasure",
"Eq",
"rfl"
] | false |
_private.Aesop.RuleTac.Tactic.0.Aesop.RuleTac.tacGenImpl.match_13 | Aesop.RuleTac.Tactic | [
"MProd.casesOn",
"String",
"MProd.mk",
"Array",
"Aesop.RuleApplication",
"MProd",
"Prod",
"Lean.Exception"
] | false |
Aesop.NormSimpRule.instHashable | Aesop.Rule | [
"Aesop.RuleName",
"Hashable.mk",
"Hashable.hash",
"Aesop.NormSimpRule",
"Hashable",
"Aesop.RuleName.instHashable",
"Aesop.NormSimpRule.name"
] | true |
Lean.Meta.SynthInstance.TableEntry.recOn | Lean.Meta.SynthInstance | [
"Lean.Meta.SynthInstance.Answer",
"Lean.Meta.SynthInstance.Waiter",
"Array",
"Lean.Meta.SynthInstance.TableEntry",
"Lean.Meta.SynthInstance.TableEntry.mk",
"Lean.Meta.SynthInstance.TableEntry.rec"
] | false |
pointedToBipointedCompBipointedToPointedSnd_hom_app_toFun | Mathlib.CategoryTheory.Category.Bipointed | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"pointedToBipointed",
"Pointed",
"CategoryTheory.Functor.id",
"bipointedToPointedSnd",
"Pointed.largeCategory",
"Bipointed",
"pointedToBipointedCompBipointedToPointedSnd",
"Eq.refl",
"CategoryTheory.Iso... | true |
Subring.topologicalClosure._proof_5 | Mathlib.Topology.Algebra.Ring.Basic | [
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"AddMonoid.toAddZeroClass",
"AddSubsemigroup.carrier",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subring.toAddSubgroup",
"IsSemitopologicalRing",
"AddSubmonoid.toAddSubsemigroup",
"AddSubgroup.topologicalClosure",
"NonAssocRing.toNonUnitalN... | false |
SimpleGraph.Iso.connectedComponentEquiv | Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected | [
"SimpleGraph.Iso.connectedComponentEquiv._proof_2",
"SimpleGraph.Iso",
"SimpleGraph.ConnectedComponent.map",
"SimpleGraph.Adj",
"Equiv.mk",
"Equiv",
"SimpleGraph.ConnectedComponent",
"SimpleGraph",
"SimpleGraph.Iso.symm",
"RelIso.toRelEmbedding",
"SimpleGraph.Iso.connectedComponentEquiv._proof_1... | true |
_private.Mathlib.Tactic.Widget.LibraryRewrite.0.Mathlib.Tactic.LibraryRewrite.ExtState.default._proof_1 | Mathlib.Tactic.Widget.LibraryRewrite | [
"instNonemptyOfMonad",
"Lean.Meta.RefinedDiscrTree",
"Mathlib.Tactic.LibraryRewrite.RewriteLemma",
"ST.instNonemptyRef",
"IO.RealWorld",
"instMonadOption",
"Lean.Meta.instInhabitedRefinedDiscrTree",
"instNonemptyOfInhabited",
"Nonempty",
"ST.Ref",
"Option"
] | false |
ENNReal.inv_limsup | Mathlib.Topology.Instances.ENNReal.Lemmas | [
"OrderIso.invENNReal",
"OrderIso.limsup_apply",
"Filter.liminf",
"Filter.isBounded_le_of_top",
"Filter.map",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"OrderIso",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"Filter.limsup",
"Inv.inv",
... | true |
Hyperreal.instLinearOrder._proof_24 | Mathlib.Analysis.Real.Hyperreal | [
"Hyperreal.instLinearOrder._aux_13",
"LT.mk",
"Real",
"Preorder.toLT",
"PartialOrder.toPreorder",
"Hyperreal.instLinearOrder._proof_7",
"Classical.propDecidable",
"Ord.mk",
"Preorder.mk",
"Ordering",
"SemilatticeInf.toPartialOrder",
"Hyperreal.instLinearOrder._proof_5",
"DistribLattice.toLat... | false |
one_lt_sq_iff₀ | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic | [
"MulOne.toOne",
"Preorder.toLT",
"MulZeroClass.toMul",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"one_lt_pow_iff_of_nonneg",
"ZeroLEOneClass",
"instOfNatNat",
"LE.le",
"MulZeroOneClass.toMulOneClass",
"Monoid.toPow",
"MulOneClass.toMulOne",
"Iff",
"MonoidWithZero",
"Na... | true |
Group.IsFinitelyPresented.rec | Mathlib.GroupTheory.FinitelyPresentedGroup | [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"Group",
"Group.IsFinitelyPresented",
"Exists",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MonoidHom.ker",
"MulOneClass.toMulOne",
"And",
"Group.IsFinitelyPresented.mk",
"Nat",
"Subgroup.IsNormalClosureFG",
"Fin",
"DF... | false |
Turing.PartrecToTM2.trPosNum.eq_3 | Mathlib.Computability.TuringMachine.ToPartrec | [
"Turing.PartrecToTM2.Γ'",
"PosNum.bit1",
"Turing.PartrecToTM2.trPosNum",
"Turing.PartrecToTM2.Γ'.bit1",
"List.cons",
"List",
"Eq.refl",
"PosNum",
"Eq"
] | true |
_private.Mathlib.Combinatorics.Additive.ApproximateSubgroup.0.IsApproximateSubgroup.image._simp_1_1 | Mathlib.Combinatorics.Additive.ApproximateSubgroup | [
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"DivisionMonoid",
"DivInvMonoid.toMonoid",
"DivisionMonoid.toDivInvMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Inv.inv",
"Set.inv",
"Set.image",
"In... | false |
CategoryTheory.ComposableArrows.fourδ₄Toδ₃_app_zero | Mathlib.CategoryTheory.ComposableArrows.Four | [
"CategoryTheory.ComposableArrows.fourδ₄Toδ₃",
"instNeZeroNatHAdd_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreorder",
"CategoryTheory.CategoryStruct.id",
"Fin.instOfNat",
"Preorder.smallCategory",
"instOfNatNat",
"instHAdd",
"Fin.instPartialOrder",
"HAdd.hAdd"... | true |
Lean.Doc.PostponedCheck.mk | Lean.Elab.DocString.Builtin.Postponed | [
"Lean.Doc.PostponedCheck.mk",
"Array",
"Lean.Doc.PostponedCheck",
"Lean.Name",
"Lean.Doc.PostponedImport",
"Dynamic"
] | true |
BoxIntegral.Prepartition.sum_fiberwise | Mathlib.Analysis.BoxIntegral.Partition.Basic | [
"Eq.mpr",
"BoxIntegral.Prepartition.filter",
"BoxIntegral.Prepartition",
"HEq.refl",
"Finset",
"Finset.sum_fiberwise_of_maps_to",
"Classical.propDecidable",
"Membership.mem",
"Eq.casesOn",
"BoxIntegral.Prepartition.boxes",
"AddCommMonoid",
"Finset.instSetLike",
"eq_of_heq",
"Eq.ndrec",
"... | true |
Set.instSupSet | Mathlib.Order.SetNotation | [
"setOf",
"Membership.mem",
"Exists",
"SupSet.mk",
"SupSet",
"And",
"Set.instMembership",
"Set"
] | true |
CategoryTheory.GradedObject.Monoidal.ιTensorObj₃._proof_2 | Mathlib.CategoryTheory.GradedObject.Monoidal | [
"AddMonoid.toAddSemigroup",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"AddMonoid",
"Eq",
"rfl"
] | false |
RingCat.limitRing._proof_26 | Mathlib.Algebra.Category.Ring.Limits | [
"AddGroup.toSubtractionMonoid",
"Equiv.ring._proof_3",
"RingCat.limitRing._proof_22",
"CategoryTheory.Functor",
"Mul.mk",
"Semigroup.toMul",
"RingCat.limitRing._proof_12",
"Equiv.instEquivLike",
"One.mk",
"HMul.hMul",
"CategoryTheory.Limits.Types.Small.limitCone",
"RingCat.limitRing._aux_20",
... | false |
IsOpenMap.image_interior_subset | Mathlib.Topology.Maps.Basic | [
"Set.mapsTo_image",
"IsOpenMap",
"HasSubset.Subset",
"TopologicalSpace",
"interior",
"Set.image",
"IsOpenMap.mapsTo_interior",
"Set.MapsTo.image_subset",
"Set.instHasSubset",
"Set"
] | true |
DividedPowers.OfInvertibleFactorial.dividedPowers | Mathlib.RingTheory.DividedPowers.RatAlgebra | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"IsScalarTower.right",
"DividedPowers.OfInvertibleFactorial.dpow_mem",
"DividedPowers.OfInvertibleFactorial.dpow_comp",
"CommSemiring.toSemiring",
"DividedPowers.OfInvertibleFactorial.dpow_add",
"DividedPowers.OfInvertibleFactorial.dpow_z... | true |
Orientation.definition._proof_3._@.Mathlib.Analysis.InnerProductSpace.Orientation.2114562672._hygCtx._hyg.2 | Mathlib.Analysis.InnerProductSpace.Orientation | [
"instOfNatNat",
"Nat",
"OfNat.ofNat",
"Eq.symm",
"Eq"
] | false |
HahnSeries.order_eq_orderTop_of_ne_zero | Mathlib.RingTheory.HahnSeries.Basic | [
"HahnSeries.support",
"Iff.mpr",
"Eq.mpr",
"HahnSeries.order",
"congrArg",
"HahnSeries.orderTop",
"PartialOrder.toPreorder",
"PartialOrder",
"id",
"HahnSeries.instZero",
"Ne",
"WithTop.some",
"HahnSeries.support_nonempty_iff",
"HahnSeries.orderTop_of_ne_zero",
"HahnSeries.order_of_ne",
... | true |
Bundle.RiemannianBundle.mk._flat_ctor | Mathlib.Topology.VectorBundle.Riemannian | [
"Bundle.RiemannianMetric",
"Real",
"AddCommGroup.toAddCommMonoid",
"Bundle.RiemannianBundle.mk",
"AddCommGroup",
"Real.semiring",
"TopologicalSpace",
"Module",
"Bundle.RiemannianBundle"
] | false |
LieRing.lie_self | Mathlib.Algebra.Lie.Basic | [
"LieRing.toAddCommGroup",
"AddMonoid.toZero",
"Bracket.bracket",
"AddCommGroup.toAddGroup",
"LieRing",
"AddGroup.toSubNegMonoid",
"Zero.toOfNat0",
"LieRing.toBracket",
"SubNegMonoid.toAddMonoid",
"OfNat.ofNat",
"Eq"
] | true |
_private.Mathlib.Tactic.Translate.Core.0.Mathlib.Tactic.Translate.applyReplacementFun.visitApp.match_3 | Mathlib.Tactic.Translate.Core | [
"_private.Mathlib.Tactic.Translate.Core.0.Mathlib.Tactic.Translate.findPrefixTranslation?.go._sparseCasesOn_1",
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Lean.StructureInfo",
"Option"
] | false |
_private.Mathlib.Analysis.InnerProductSpace.Reproducing.0.RKHS.OfKernel.kerFunAux | Mathlib.Analysis.InnerProductSpace.Reproducing | [
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"UniformSpace.Completion.coe'",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"Finsupp.module",
"_... | true |
_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.emitLetDecl.emitFap.match_8 | Lean.Compiler.LCNF.EmitC | [
"Option.ctorIdx",
"Lean.Compiler.LCNF.Signature",
"Option.some",
"Nat.hasNotBit",
"Lean.Compiler.LCNF.Purity.impure",
"_private.Lean.Compiler.LCNF.EmitC.0.Lean.Compiler.LCNF.instEmitToStringName._sparseCasesOn_1",
"Option"
] | false |
instIsIntegrallyClosedPolynomialOfIsDomain | Mathlib.RingTheory.Polynomial.IsIntegral | [
"Iff.mpr",
"OreLocalization.instAddGroupOreLocalization",
"IsDomain",
"FractionRing.field",
"IsIntegrallyClosed.isIntegral_iff",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Subsemiring.instSetLike",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Module.Free.instFaithfulS... | true |
MessageType.warning.elim | Lean.Data.Lsp.Window | [
"PULift.up",
"MessageType.warning",
"MessageType.ctorElim",
"MessageType",
"Nat",
"Eq.symm",
"Eq",
"MessageType.ctorIdx"
] | false |
Lean.Compiler.InlineAttributeKind.alwaysInline | Lean.Compiler.InlineAttrs | [
"Lean.Compiler.InlineAttributeKind.alwaysInline",
"Lean.Compiler.InlineAttributeKind"
] | true |
lTensor.inverse_of_rightInverse._proof_5 | Mathlib.LinearAlgebra.TensorProduct.RightExactness | [
"CommRing",
"CommSemiring.toSemiring",
"RingHomCompTriple",
"CommRing.toCommSemiring",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring"
] | false |
ReaderT.instULiftableULiftULift | Mathlib.Control.ULiftable | [
"Equiv.trans",
"ReaderT",
"ULift",
"Equiv.ulift",
"ReaderT.uliftable'",
"Equiv.symm",
"ULiftable"
] | true |
Multiplicative.toAdd_eq_top._simp_1 | Mathlib.Algebra.Order.Monoid.Unbundled.TypeTags | [
"Multiplicative.orderTop",
"Equiv.instEquivLike",
"instLEMultiplicative",
"Equiv",
"Multiplicative.toAdd_eq_top",
"OrderTop",
"LE",
"Multiplicative",
"OrderTop.toTop",
"propext",
"Multiplicative.toAdd",
"Top.top",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | false |
_private.Mathlib.Order.Ideal.0.Order.Ideal.mem_sInf._simp_1_2 | Mathlib.Order.Ideal | [
"Set.iInter",
"Set.mem_iInter₂",
"Membership.mem",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Mathlib.Data.Nat.WithBot.0.Nat.WithBot.add_eq_two_iff._simp_1_1 | Mathlib.Data.Nat.WithBot | [
"WithBot.some",
"WithBot",
"instHAdd",
"HAdd.hAdd",
"WithBot.add",
"WithBot.coe_add",
"Eq.symm",
"Eq",
"Add"
] | false |
IsAdicComplete.of_lift | Mathlib.RingTheory.AdicCompletion.Basic | [
"Submodule",
"Submodule.Quotient.addCommMonoid",
"CommRing",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"IsScalarTower.right",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"Submodule.hasQuotient",
"AddCommGroup",
"AdicCompletion.in... | true |
Lean.SimplePersistentEnvExtensionDescr.addEntryFn | Lean.EnvExtension | [
"Lean.SimplePersistentEnvExtensionDescr"
] | true |
MemHolder.smul | Mathlib.Topology.MetricSpace.HolderNorm | [
"MemHolder.holderWith",
"instHSMul",
"HMul.hMul",
"MemHolder",
"NormedAddCommGroup.toMetricSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"AddMonoid.toAddZeroClass",
"SeminormedRing.toRing",
"AddCommGroup.toAddGroup",
... | true |
instUniformSpaceBool | Mathlib.Topology.UniformSpace.Basic | [
"UniformSpace",
"instBotUniformSpace",
"Bot.bot",
"Bool"
] | true |
CategoryTheory.Limits.IndObjectPresentation.yoneda_F | Mathlib.CategoryTheory.Limits.Indization.IndObject | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.IndObjectPresentation.yoneda",
"CategoryTheory.Functor.category",
"CategoryTheory.yoneda",
"CategoryTheory.discreteCategory",
"PUnit",
"CategoryTheory.types",
"CategoryTheory.Category.opposite",
"Eq.refl",
"CategoryTheory.Functor.fromP... | true |
HurwitzZeta.hasSum_nat_completedSinZeta | Mathlib.NumberTheory.LSeries.HurwitzZetaOdd | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"CharP.cast_eq_zero",
"HasSum.congr_fun",
"AddGroup.toSubtractionMonoid",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Int.cast_neg",
"Distrib.leftDistribClass",
"Int.cast",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"GroupWithZero... | true |
HomologicalComplex.cylinder.ι₀.eq_1 | Mathlib.Algebra.Homology.HomotopyCofiber | [
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"DecidableRel",
"HomologicalComplex.instNegHom",
"HomologicalComplex",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.HasBinaryBiproduct",
"HomologicalComplex.cylinder.ι₀",
"ComplexShape",
"Cat... | true |
_private.Mathlib.Algebra.Group.UniqueProds.Basic.0.instAddI.eq_1 | Mathlib.Algebra.Group.UniqueProds.Basic | [
"ULift.add",
"_private.Mathlib.Algebra.Group.UniqueProds.Basic.0.I",
"Bool.rec",
"Bool",
"Eq.refl",
"Eq",
"_private.Mathlib.Algebra.Group.UniqueProds.Basic.0.instAddI",
"Add"
] | true |
Localization.mk_eq_mk' | Mathlib.RingTheory.Localization.Defs | [
"Localization.mk_eq_monoidOf_mk'",
"Localization.mk",
"OreLocalization.instAlgebra",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"Membership.mem",
"Algebra.id",
"Subtype",
"Localization",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"CommSemiring",
"IsLocalization... | true |
AlgebraicGeometry.SheafedSpace.GlueData.mk.sizeOf_spec | Mathlib.Geometry.RingedSpace.PresheafedSpace.Gluing | [
"AlgebraicGeometry.SheafedSpace.IsOpenImmersion",
"AlgebraicGeometry.SheafedSpace",
"CategoryTheory.GlueData.f",
"CategoryTheory.GlueData.J",
"Prod.mk",
"instOfNatNat",
"AlgebraicGeometry.SheafedSpace.GlueData._sizeOf_inst",
"CategoryTheory.GlueData",
"instHAdd",
"CategoryTheory.GlueData._sizeOf_i... | true |
String.Slice.Pos.splits_copy_iff._simp_1 | Init.Data.String.Lemmas.Splits | [
"String.Pos.Splits",
"String",
"String.Slice.Pos.copy",
"String.Slice",
"String.Slice.Pos.splits_copy_iff",
"String.Slice.copy",
"propext",
"String.Slice.Pos",
"Eq",
"String.Slice.Pos.Splits"
] | false |
LinearMap.BilinForm.Isometry._aux_Mathlib_LinearAlgebra_BilinearForm_Isometry___unexpand_LinearMap_BilinForm_Isometry_1 | Mathlib.LinearAlgebra.BilinearForm.Isometry | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
CategoryTheory.PreZeroHypercover.pullbackCoverOfRightIsoPullback₂._proof_1 | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.Limits.hasPullbackVertPaste",
"CategoryTheory.Limits.pullback",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.pullback.snd",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.PreZeroHypercover.X",
"CategoryTheo... | false |
ProofWidgets.ExprWithCtx.expr | ProofWidgets.Compat | [
"Lean.Expr",
"ProofWidgets.ExprWithCtx"
] | true |
_private.Mathlib.Analysis.Normed.Group.Quotient.0.Ideal.Quotient.semiNormedCommRing._simp_4 | Mathlib.Analysis.Normed.Group.Quotient | [
"Exists",
"Prod.mk",
"propext",
"Prod",
"Prod.exists",
"Eq"
] | false |
AddMemClass.mk._flat_ctor | Mathlib.Algebra.Group.Subsemigroup.Defs | [
"SetLike",
"AddMemClass.mk",
"outParam",
"Membership.mem",
"instHAdd",
"HAdd.hAdd",
"AddMemClass",
"SetLike.instMembership",
"Add"
] | false |
Vector.setIfInBounds.eq_1 | Init.Data.Vector.Lemmas | [
"Vector",
"Vector.setIfInBounds",
"Vector.setIfInBounds._proof_1",
"Vector.mk",
"Nat",
"Eq.refl",
"Array.setIfInBounds",
"Eq",
"Vector.toArray"
] | true |
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