name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
contDiffWithinAt_inter | Mathlib.Analysis.Calculus.ContDiff.Defs | [
"Filter.instMembership",
"NormedSpace",
"contDiffWithinAt_inter'",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"nhds",
"Set.instInter",
"mem_nhdsWithin_of_mem_nhds",
"Inter.inter",
"Iff",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"ENat",
"NontriviallyNormedField",
"Nontrivial... | true |
_private.Mathlib.LinearAlgebra.RootSystem.Defs.0.RootPairing.isFixedPt_reflectionPerm_iff._simp_1_2 | Mathlib.LinearAlgebra.RootSystem.Defs | [
"RootPairing.reflectionPerm_eq_iff_smul_root",
"RootPairing.pairing",
"CommRing",
"instHSMul",
"Equiv.instEquivLike",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"A... | false |
BoxIntegral.Integrable.convergenceR | Mathlib.Analysis.BoxIntegral.Basic | [
"Real.instLE",
"Real",
"Set.Ioi",
"BoxIntegral.Integrable",
"NormedSpace",
"Real.instZero",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Real.decidableLT",
"PseudoMetricSpace.toUniformSpace",
"ContinuousLinearMap.addCommMonoid",
"Real.instLT",
"BoxIntegral.integralSum._proof_1",
... | true |
CategoryTheory.Monoidal.rightUnitor_hom_app | Mathlib.CategoryTheory.Monoidal.FunctorCategory | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Monoidal.functorCategoryMonoidalStruct",
"CategoryTheory.MonoidalCategoryStruct.t... | true |
Array.getElem?_zipWith | Init.Data.Array.Zip | [
"Eq.mpr",
"List.zipWith",
"List.getElem?_toArray",
"congrArg",
"List.instGetElem?NatLtLength",
"Option.some",
"Array.casesOn",
"id",
"List.toArray",
"Array",
"Option.none",
"List",
"Nat",
"congr",
"LT.lt",
"Array.getElem?_zipWith.match_1",
"Eq.ndrec",
"List.zipWith_toArray",
"Eq.... | true |
_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.ExpandedFieldVal.proj.injEq | Lean.Elab.StructInst | [
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.ExpandedFieldVal.proj",
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.ExpandedFieldVal",
"Eq.propIntro",
"Lean.injEq_helper",
"_private.Lean.Elab.StructInst.0.Lean.Elab.Term.StructInst.ExpandedFieldVal.proj.inj",
"Lean.FVarId",
"Lea... | true |
ModuleCat.localizedModuleMap._proof_2 | Mathlib.Algebra.Category.ModuleCat.Localization | [
"IsScalarTower.to_smulCommClass'",
"CommRing",
"OreLocalization.instAlgebra",
"ModuleCat",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Algebra.id",
"Localization",
"DistribSMul.toSMulZeroCla... | false |
_private.Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic.0.InnerProductGeometry.sin_angle_mul_norm_mul_norm._simp_1_3 | Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic | [
"False",
"eq_false",
"four_ne_zero",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
SkewMonoidAlgebra.instNonAssocRing._proof_9 | Mathlib.Algebra.SkewMonoidAlgebra.Basic | [
"Monoid",
"AddMonoid.toZero",
"instOfNatNat",
"NatCast.natCast",
"SkewMonoidAlgebra.instNonAssocSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Nat",
"MulSemiringAction",
"SkewMonoidAlgebra",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",... | false |
Std.ExtDHashMap.Const.getKey!_insertManyIfNewUnit_list_of_not_mem_of_mem | Std.Data.ExtDHashMap.Lemmas | [
"Eq.mpr",
"Std.DHashMap.Const.insertManyIfNewUnit",
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Std.ExtDHashMap.getKey!",
"List.Pairwise",
"congrArg",
"instForInOfForIn'",
"Membership.mem",
"inferInstance",
"id",
"Std.ExtDHashMap.inductionOn",
"Std.ExtDHashMap.mk",
"Id",
"... | true |
MvPFunctor.castLastB | Mathlib.Data.PFunctor.Multivariate.M | [
"Eq.recOn",
"MvPFunctor",
"PFunctor.B",
"instOfNatNat",
"MvPFunctor.A",
"instHAdd",
"HAdd.hAdd",
"Nat",
"MvPFunctor.last",
"instAddNat",
"OfNat.ofNat",
"Eq"
] | true |
mul_le_mul_left | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"HMul.hMul",
"Function.swap",
"Mul",
"MulRightMono",
"LE.le",
"CovariantClass.elim",
"LE",
"instHMul"
] | true |
Finsupp.support_smul_eq | Mathlib.Data.Finsupp.SMul | [
"Finsupp.instFunLike",
"Finsupp.smulZeroClass",
"IsDomain",
"False",
"instHSMul",
"eq_false",
"congrArg",
"DistribMulAction.toDistribSMul",
"Finset",
"Finsupp.mem_support_iff._simp_1",
"AddMonoid.toAddZeroClass",
"Module.IsTorsionFree",
"Finset.ext",
"Finsupp.support",
"Membership.mem",
... | true |
AddSubgroup.addOrderOf_mk | Mathlib.GroupTheory.OrderOfElement | [
"addOrderOf",
"AddSubgroup.toAddGroup",
"Membership.mem",
"Subtype",
"AddSubgroup.addOrderOf_coe",
"Subtype.mk",
"AddSubgroup",
"AddGroup",
"AddGroup.toSubNegMonoid",
"AddSubgroup.instSetLike",
"Nat",
"SubNegMonoid.toAddMonoid",
"Eq.symm",
"Subtype.val",
"Eq",
"SetLike.instMembership"
... | true |
Int.neg_inj | Init.Data.Int.Lemmas | [
"Eq.mpr",
"congrArg",
"id",
"Int.instNegInt",
"Int",
"Iff",
"Iff.intro",
"Eq.refl",
"Int.neg_neg",
"Eq.symm",
"Eq",
"Neg.neg"
] | true |
_private.Init.Data.Iterators.Lemmas.Combinators.Monadic.Attach.0.Std.IterM.toArray_eq_match_step.match_1.eq_1 | Init.Data.Iterators.Lemmas.Combinators.Monadic.Attach | [
"Std.IterStep",
"Std.IterStep.skip",
"Unit",
"Std.IterStep.yield",
"Std.IterStep.done",
"Eq.refl",
"Std.IterM.toArray_eq_match_step.match_1",
"Std.IterM",
"Eq"
] | true |
FirstOrder.Language.DefinableSet.instSetLike._proof_1 | Mathlib.ModelTheory.Definability | [
"Set.Definable",
"Subtype.val_injective",
"Subtype",
"FirstOrder.Language.Structure",
"FirstOrder.Language",
"Function.Injective",
"Subtype.val",
"Set"
] | false |
_private.Mathlib.Computability.Primrec.Basic.0.Primrec.eq._simp_1_1 | Mathlib.Computability.Primrec.Basic | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"LE.le",
"And",
"le_antisymm_iff",
"propext",
"Eq"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph.0.SimpleGraph.Walk.exists_mem_support_mem_erase_mem_support_takeUntil_eq_empty._proof_1_3 | Mathlib.Combinatorics.SimpleGraph.Connectivity.Subgraph | [
"Iff.mpr",
"Iff.of_eq",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"Membership.mem",
"SimpleGraph",
"List",
"List.instMembership",
"Eq.refl"
] | false |
Lean.Lsp.instInhabitedCallHierarchyIncomingCall.default | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.CallHierarchyItem",
"Inhabited.default",
"Array",
"Array.instInhabited",
"Lean.Lsp.instInhabitedCallHierarchyItem",
"Lean.Lsp.CallHierarchyIncomingCall.mk",
"Lean.Lsp.CallHierarchyIncomingCall",
"Lean.Lsp.Range"
] | true |
CategoryTheory.Limits.hasLimitsOfShape_thinSkeleton | Mathlib.CategoryTheory.Limits.Skeleton | [
"CategoryTheory.ThinSkeleton.fromThinSkeleton_isEquivalence",
"CategoryTheory.Functor.createsLimitsOfIsEquivalence",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.ThinSkeleton.fromThinSkeleton",
"Preorder.smallCategory",
"CategoryTheory.ThinSkeleton"... | true |
FormalMultilinearSeries.unshift._proof_3 | Mathlib.Analysis.Calculus.FormalMultilinearSeries | [
"NormedCommRing.toNormedRing",
"NormedRing.toRing",
"NormedSpace",
"AddMonoid.toAddSemigroup",
"ContinuousLinearMap.topologicalAddGroup",
"ContinuousLinearMap.topologicalSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
... | false |
CategoryTheory.functorCategoryPreadditive._proof_18 | Mathlib.CategoryTheory.Preadditive.FunctorCategory | [
"CategoryTheory.Functor",
"instHSMul",
"CategoryTheory.functorCategoryPreadditive._proof_4",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"AddCommGroup.toAddGroup",
"CategoryTheory.functorCategoryPreadditive._proof_14",
"Int",
"CategoryTheory.NatTrans.... | false |
_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.isPath_iff_isSubwalk_imp_nil._proof_1_2 | Mathlib.Combinatorics.SimpleGraph.Paths | [
"Lean.Grind.Nat.lt_eq",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"Eq.mp",
"instOfNatNat",
"LE.le",
"instLENat",
"SimpleGraph",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.... | false |
AlgebraicGeometry.IsClosedImmersion.lift_fac_assoc | Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion | [
"CategoryTheory.Category.assoc",
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Eq.mp",
"id",
"AlgebraicGeometry.Scheme.Hom.ker",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"AlgebraicGeometry.IsClosedImmer... | true |
CategoryTheory.MonoidalCategory.Arrow.PullbackHom.isInitialIso_hom_left | Mathlib.CategoryTheory.Monoidal.PushoutProduct | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.PullbackObjObj.π",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.Arrow.pullbackHom",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.PullbackObjObj.pt",
... | true |
Filter.Germ.LiftRel | Mathlib.Order.Filter.Germ.Basic | [
"Filter.Eventually",
"Filter.germSetoid",
"Filter.Germ.LiftRel._proof_1",
"Filter.Germ",
"Filter",
"Quotient.liftOn₂'"
] | true |
DivisorChain.eq_pow_second_of_chain_of_has_chain | Mathlib.RingTheory.ChainOfDivisors | [
"CommMonoidWithZero.toCommMonoid",
"Iff.mpr",
"Finset.mem_univ",
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Trans.trans",
"Dvd.dvd",
"StrictMono",
"Finset.univ",
"outParam",
"Finset.mem_image",
"LE.le.antisymm'",
"congrArg",
"Function.Injective.injOn",
"HEq.refl",
"Finset",
"Finset.card_le_ca... | true |
Lean.IR.CollectUsedDecls.collectFnBody | Lean.Compiler.IR.EmitUtil | [
"Lean.IR.CollectUsedDecls.M",
"Inhabited.default",
"instInhabitedOfMonad",
"instInhabitedPUnit",
"Lean.IR.CollectUsedDecls.State",
"Id",
"Lean.IR.FnBody",
"Unit",
"StateM",
"Id.instMonad",
"StateT.instMonad",
"instInhabitedReaderT",
"Lean.Environment"
] | true |
CategoryTheory.ComposableArrows.IsComplex.opcyclesToCycles_fac._auto_1 | Mathlib.Algebra.Homology.ExactSequenceFour | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
NNRat.cast_inj._simp_1 | Mathlib.Data.Rat.Cast.CharZero | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"NNRat.cast_inj",
"NNRat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"DivisionSemiring.toNNRatCast",
"CharZero",
"DivisionSemiring",
"propext",
"DivisionSemiring.toSemiring",
"NNRat.cast",
"Semiring.toNonAssocSemiring",
"Eq"
] | false |
SimplexCategory.δ₀Iter_δ'._auto_1 | Mathlib.AlgebraicTopology.SimplexCategory.DeltaZeroIter | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
UpperHalfPlane.atImInfty.eq_1 | Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty | [
"Real",
"UpperHalfPlane.atImInfty",
"Filter.atTop",
"UpperHalfPlane.im",
"UpperHalfPlane",
"Eq.refl",
"Eq",
"Filter",
"Real.instPreorder",
"Filter.comap"
] | true |
Cardinal.mk_sum | Mathlib.SetTheory.Cardinal.Defs | [
"Cardinal",
"ULift",
"Cardinal.lift",
"Cardinal.mk",
"Equiv.ulift",
"Sum",
"Cardinal.instAdd",
"instHAdd",
"Equiv.sumCongr",
"HAdd.hAdd",
"Equiv.symm",
"Eq",
"Cardinal.mk_congr"
] | true |
MeasureTheory.Measure.instRegularOfIsHaarMeasureOfCompactSpace | Mathlib.MeasureTheory.Measure.Haar.Unique | [
"Eq.mpr",
"instHSMul",
"MeasureTheory.Measure",
"IsScalarTower.right",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"Group",
"BorelSpace",
"inferInstance",
"MeasureTheory.IsFiniteMeasureOnCompacts",
"Algebra.id",
"id",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"WeaklyL... | true |
LinearIsometryEquiv.piLpCongrRight._proof_1 | Mathlib.Analysis.Normed.Lp.PiLp | [
"LinearIsometryEquiv.instEquivLike",
"WithLp",
"PiLp.instNorm",
"Norm.norm",
"Eq.mpr",
"Real.instPow",
"Real.partialOrder",
"Real.instLE",
"LinearEquiv.symm",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"SeminormedAddCommGroup",
"Pi.addCommMonoid",
"Finset.univ",
"LinearIsometryEquiv.nor... | false |
Lean.Widget.instFromJsonRpcEncodablePacket.fromJson._@.Lean.Widget.Types.3328362917._hygCtx._hyg.14 | Lean.Widget.Types | [
"Pure.pure",
"Lean.Json",
"Lean.Name.mkNum",
"Monad.toApplicative",
"String",
"Lean.Name.mkStr",
"Lean.Widget.RpcEncodablePacket.mk._@.Lean.Widget.Types.2243429567._hygCtx._hyg.1",
"Lean.Json.getObjValAs?",
"instOfNatNat",
"Applicative.toPure",
"ToString.toString",
"Except.instMonad",
"Lean.... | false |
preordToCat._proof_1 | Mathlib.Order.Category.Preord | [
"CategoryTheory.Cat.category",
"OrderHom.monotone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.toCatHom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Cat.of",
"id",
"Preord.instCategory",
"Preorder.smallCategory",
"Preord.str",
"CategoryTheory.Cat",... | false |
CategoryTheory.IsSplitEpi.exists_splitEpi | Mathlib.CategoryTheory.EpiMono | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsSplitEpi",
"Nonempty",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.SplitEpi",
"CategoryTheory.Category"
] | true |
_private.Batteries.Data.String.Lemmas.0.String.Legacy.mkIterator.eq_1 | Batteries.Data.String.Lemmas | [
"String.Legacy.Iterator.mk",
"String",
"String.Pos.Raw",
"String.Legacy.mkIterator",
"Eq.refl",
"String.Legacy.Iterator",
"String.instOfNatRaw",
"OfNat.ofNat",
"Eq"
] | true |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital.0._auto_280 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Lean.Environment.AddConstAsyncResult.mainEnv | Lean.Environment | [
"Lean.Environment.AddConstAsyncResult",
"Lean.Environment"
] | true |
_private.Mathlib.Algebra.Homology.Factorizations.CM5a.0.CochainComplex.Plus.modelCategoryQuillen.cm5a_cof.isIso_functor_map_hom_h_f._proof_1_1 | Mathlib.Algebra.Homology.Factorizations.CM5a | [
"Lean.RArray.leaf",
"False",
"Classical.byContradiction",
"Nat.not_le_eq",
"Lean.RArray.branch",
"id",
"False.casesOn",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.Linear.Expr.num",
"Bool.true",
"instHAdd",
"Nat.Linear.ExprCnstr.eq_false_of_isUnsat",
"HAdd.hAdd",
"Nat",
"Bool",
"Lea... | false |
Lean.Meta.Grind.TopSort.State.permMark._default | Lean.Meta.Tactic.Grind.EqResolution | [
"Lean.Expr.instBEq",
"Std.HashSet",
"Lean.Expr",
"id",
"Lean.Expr.instHashable",
"EmptyCollection.emptyCollection",
"Std.HashSet.instEmptyCollection"
] | false |
linearIndepOn_finset_iff | Mathlib.LinearAlgebra.LinearIndependent.Defs | [
"dite_cond_eq_true",
"Eq.mpr",
"dite_congr",
"instHSMul",
"Finset.univ",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Finset",
"AddMonoid.toAddZeroClass",
"instInhabitedTrue",
"Module.toMulActionWithZero",
"Classical.propDecidable",
"AddCommGroup.toAddGrou... | true |
Lean.Server.TransientWorkerILean.hasRefs | Lean.Server.References | [
"Bool.not",
"Option.any",
"Lean.Server.TransientWorkerILean.isSetupFailure?",
"Lean.Server.TransientWorkerILean",
"Bool"
] | true |
Polynomial.derivRootWeight.eq_1 | Mathlib.Analysis.Complex.Polynomial.GaussLucas | [
"Norm.norm",
"Polynomial.eval",
"Real",
"instHDiv",
"Real.instZero",
"Real.instDivInvMonoid",
"HSub.hSub",
"Complex.instZero",
"Complex.instNorm",
"HDiv.hDiv",
"instOfNatNat",
"Pi.single",
"Nat.cast",
"Polynomial",
"Monoid.toPow",
"Real.instOne",
"Real.instMonoid",
"instHSub",
"H... | true |
_private.Mathlib.Topology.Sets.VietorisTopology.0.TopologicalSpace.vietoris.isCompact_aux._simp_1_4 | Mathlib.Topology.Sets.VietorisTopology | [
"Set.instInter",
"Inter.inter",
"Set.inter_iUnion",
"Eq.symm",
"Eq",
"Set.iUnion",
"Set"
] | false |
Std.DTreeMap.Internal.Impl.getKeyD_diff_of_contains_eq_false_right | Std.Data.DTreeMap.Internal.Lemmas | [
"Std.DTreeMap.Internal.Impl.getKeyD",
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Std.DTreeMap.Internal.Impl.getKeyD_eq_getKeyD",
"Bool.not",
"Ord",
"Std.instLawfulBEqOrd",
"congrArg",
"Std.Internal.List.getKeyD",
"Std.DTreeMap.Internal.Impl.contains_eq_containsKey",
"Std.Internal.List.getKeyD_... | true |
UniformFun.lipschitzWith_ofFun_iff | Mathlib.Topology.MetricSpace.UniformConvergence | [
"LipschitzWith",
"Equiv.instEquivLike",
"UniformFun.instPseudoEMetricSpace",
"Equiv",
"NNReal",
"PseudoEMetricSpace",
"Iff",
"UniformFun",
"UniformFun.lipschitzWith_iff",
"DFunLike.coe",
"EquivLike.toFunLike",
"UniformFun.ofFun"
] | true |
Std.DTreeMap.Internal.Cell.ofEq.eq_1 | Std.Data.DTreeMap.Internal.Model | [
"Std.DTreeMap.Internal.Cell.ofEq",
"Ord",
"Std.DTreeMap.Internal.Cell.mk",
"Std.OrientedOrd",
"Option.some",
"Ordering",
"Ordering.eq",
"Std.DTreeMap.Internal.Cell",
"Eq.refl",
"Sigma.mk",
"Std.DTreeMap.Internal.Cell.ofEq._proof_1",
"Eq",
"Sigma"
] | true |
Std.ExtDTreeMap.Const.size_le_size_insertMany_list | Std.Data.ExtDTreeMap.Lemmas | [
"Eq.mpr",
"Std.ExtDTreeMap.mk",
"Std.DTreeMap.Const.size_le_size_insertMany_list",
"Std.DTreeMap",
"congrArg",
"instForInOfForIn'",
"Ordering",
"inferInstance",
"id",
"LE.le",
"Std.TransCmp",
"instLENat",
"Id",
"Std.DTreeMap.Const.insertMany",
"Membership",
"Std.ExtDTreeMap.Const.inser... | true |
_private.Mathlib.RingTheory.IsPrimary.0.Submodule.isPrimary_iff_zero_divisor_quotient_imp_nilpotent_smul._simp_1_3 | Mathlib.RingTheory.IsPrimary | [
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"PartialOrder",
"Bot.bot",
"LE.le",
"propext",
"eq_bot_iff",
"Eq"
] | false |
Partition.instIsTransRel | Mathlib.Order.Partition.Basic | [
"Eq.mpr",
"_private.Mathlib.Order.Partition.Basic.0.Partition.instSymmRel.match_1",
"congrArg",
"IsTrans.mk",
"Partition.eq_of_mem_of_mem",
"Membership.mem",
"id",
"IsTrans",
"And",
"Partition",
"And.intro",
"Exists.intro",
"CompleteBooleanAlgebra.toCompleteLattice",
"Partition.instSetLike... | true |
LocallyFiniteOrder.toLocallyFiniteOrderTop._proof_1 | Mathlib.Order.Interval.Finset.Defs | [
"Eq.mpr",
"congrArg",
"Finset",
"Iff.rfl",
"and_iff_left",
"Preorder.toLE",
"Membership.mem",
"Finset.mem_Icc",
"id",
"LE.le",
"Finset.Icc",
"OrderTop",
"And",
"Iff",
"OrderTop.toTop",
"Finset.instSetLike",
"le_top",
"propext",
"LocallyFiniteOrder",
"Top.top",
"Eq",
"SetLik... | false |
_private.Batteries.Data.RBMap.Lemmas.0.Batteries.RBMap.contains_iff_find?._simp_1_2 | Batteries.Data.RBMap.Lemmas | [
"Exists",
"Prod.mk",
"propext",
"Prod",
"Prod.exists",
"Eq"
] | false |
Prod.continuousNeg | Mathlib.Topology.Algebra.Group.Basic | [
"ContinuousNeg.mk",
"Continuous.fst'",
"ContinuousNeg.continuous_neg",
"Continuous.snd'",
"instTopologicalSpaceProd",
"ContinuousNeg",
"Prod.fst",
"TopologicalSpace",
"Neg",
"Prod.instNeg",
"Prod",
"Prod.snd",
"Neg.neg",
"Continuous.prodMk"
] | true |
_private.Init.System.IO.0.System.FilePath.isDir.match_1 | Init.System.IO | [
"Except.ok",
"Except.error",
"IO.FS.Metadata",
"IO.Error",
"Except.casesOn",
"Except"
] | false |
CategoryTheory.SimplicialObject.Augmented.σ₀Iter_hom_app_assoc | Mathlib.AlgebraicTopology.SimplicialObject.DeltaZeroIter | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Comma.right",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.SimplicialObject.const",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"Eq.mp",
"Categor... | true |
Lean.Meta.Grind.Action.andAlso | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.Action",
"Lean.Meta.Grind.ActionCont"
] | true |
_private.Mathlib.RingTheory.Unramified.Finite.0.Algebra.FormallyUnramified.iff_exists_tensorProduct._simp_1_4 | Mathlib.RingTheory.Unramified.Finite | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"Algebra",
"Algebra.toModule",
"KaehlerDifferential.ideal",
"NonUnitalNonAssocRing.toNonUnitalN... | false |
_private.Lean.Elab.Tactic.Do.ProofMode.RenameI.0.Lean.Elab.Tactic.Do.ProofMode.elabMRenameI | Lean.Elab.Tactic.Do.ProofMode.RenameI | [
"Pure.pure",
"Unit.unit",
"Lean.MVarId.withContext",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Tactic.Do.ProofMode.mStartMainGoal",
"Lean.Elab.Tactic.Do.ProofMode.MGoal.toExpr",
"Lean.instMonadMCtxOfMonadLift",
"IO.mkRef",
"Lean.Core.instMonadLiftIOCoreM",
"Lean.Elab.Term.instMonadTermEla... | true |
SimpleGraph.Connected.rec | Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected | [
"SimpleGraph.Connected.mk",
"SimpleGraph.Preconnected",
"SimpleGraph.Connected",
"SimpleGraph",
"Nonempty"
] | false |
Functor.supp.eq_1 | Mathlib.Data.PFunctor.Univariate.Basic | [
"Functor",
"setOf",
"Functor.supp",
"Functor.Liftp",
"Eq.refl",
"Eq",
"Set"
] | true |
CategoryTheory.Limits.colimitHomIsoLimitYoneda_inv_comp_π_assoc | Mathlib.CategoryTheory.Limits.IndYoneda | [
"CategoryTheory.Limits.limit.π",
"CategoryTheory.yoneda_preservesLimit",
"CategoryTheory.Functor.op",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheo... | true |
_private.Batteries.Lean.Meta.UnusedNames.0.Lean.LocalContext.getUnusedUserNames.loop.match_1 | Batteries.Lean.Meta.UnusedNames | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
CategoryTheory.Limits.Cocone.category._proof_10 | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.Cocone.category._proof_3",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.CoconeMorphism.hom",
"Eq.rec",
"CategoryTheory.Limits.CoconeMorp... | false |
_private.Mathlib.Geometry.Euclidean.Similarity.0.EuclideanGeometry.similar_of_side_angle_side._proof_1_2 | Mathlib.Geometry.Euclidean.Similarity | [
"instLawfulOrderLT_mathlib",
"Lean.RArray.leaf",
"Lean.Grind.Field.toCommRing",
"False",
"Real.partialOrder",
"Real.instLE",
"Real",
"Lean.Grind.CommRing.Mon.mult",
"Lean.Grind.CommRing.diseq_to_eq",
"instHDiv",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"HMul.hMul",
"GroupWit... | false |
instCountablePLift | Mathlib.Data.Countable.Defs | [
"Function.Injective.countable",
"Equiv.instEquivLike",
"Equiv",
"PLift",
"Equiv.plift",
"Countable",
"Equiv.injective",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
generatePiSystem_subset_self | Mathlib.MeasureTheory.PiSystem | [
"IsPiSystem",
"Membership.mem",
"generatePiSystem.rec",
"HasSubset.Subset",
"Set.instInter",
"Inter.inter",
"Set.Nonempty",
"Set.instMembership",
"generatePiSystem",
"Set.instHasSubset",
"Set"
] | true |
Mathlib.Linter.linter.style.longLine | Mathlib.Tactic.Linter.Style | [
"Inhabited.default",
"instInhabitedBool",
"Lean.Option",
"Lean.instInhabitedOption",
"Bool"
] | true |
Lean.Elab.macroAttribute._regBuiltin.Lean.Elab.macroAttribute.declRange_3 | Lean.Elab.Util | [
"Lean.addBuiltinDeclarationRanges",
"Lean.DeclarationRange.mk",
"IO",
"Lean.Name.mkStr3",
"instOfNatNat",
"Unit",
"Lean.Position.mk",
"Nat",
"OfNat.ofNat",
"Lean.DeclarationRanges.mk"
] | false |
_private.Mathlib.Analysis.Distribution.TestFunction.0.TestFunction.instIsTopologicalAddGroup.match_1 | Mathlib.Analysis.Distribution.TestFunction | [
"Real.partialOrder",
"Real",
"NormedSpace",
"ContinuousSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PartialOrder.toPreorder",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"TopologicalSpace.Opens",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Real.semiri... | false |
ProbabilityTheory.Kernel.iIndepFun.comp | Mathlib.Probability.Independence.Kernel.IndepFun | [
"MeasureTheory.ae",
"Eq.mpr",
"MeasureTheory.Measure",
"MeasurableSet",
"Iff.of_eq",
"congrArg",
"Set.iInter",
"Finset",
"Filter.Eventually",
"Measurable",
"setOf",
"Function.comp",
"Membership.mem",
"Filter.mp_mem",
"Eq.mp",
"ProbabilityTheory.Kernel.instFunLike",
"id",
"Finset.pr... | true |
CategoryTheory.Limits.isTerminalEquivUnique._proof_5 | Mathlib.CategoryTheory.Limits.Shapes.IsTerminal | [
"Inhabited.default",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"False.elim",
"Unique",
"Aesop.BuiltinRules.pEmpty_false",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.isTerminalEqui... | false |
PFunctor.Approx.sCorec._unsafe_rec | Mathlib.Data.PFunctor.Univariate.M | [
"PFunctor",
"PFunctor.A",
"PFunctor.Obj",
"PFunctor.B",
"PFunctor.Approx.sCorec._unsafe_rec",
"Sigma.fst",
"PFunctor.Approx.CofixA.intro",
"PFunctor.Approx.CofixA",
"Nat",
"PFunctor.Approx.sCorec.match_1",
"PFunctor.Approx.CofixA.continue",
"Sigma.snd"
] | false |
_private.Std.Data.DTreeMap.Internal.Zipper.0.Std.DTreeMap.Internal.RxoIterator.step_cons_of_isLT | Std.Data.DTreeMap.Internal.Zipper | [
"Eq.mpr",
"Std.DTreeMap.Internal.RxoIterator.step",
"Std.IterStep",
"Ord",
"congrArg",
"Std.DTreeMap.Internal.RxoIterator",
"id",
"Ordering.isLT",
"_private.Std.Data.DTreeMap.Internal.Zipper.0.Std.DTreeMap.Internal.RxoIterator.step.eq_2",
"instDecidableEqBool",
"Std.DTreeMap.Internal.Zipper.prep... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.EdgeDisjointTriangles.card_edgeFinset_le._simp_1_5 | Mathlib.Combinatorics.SimpleGraph.Triangle.Basic | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
Finset.finsuppAntidiag_insert.match_3 | Mathlib.Algebra.Order.Antidiag.Finsupp | [
"Finset.HasAntidiagonal",
"Finset",
"AddMonoid.toAddZeroClass",
"Finset.finsuppAntidiag",
"Subtype.casesOn",
"Finsupp.update",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"Prod.fst",
"AddCommMonoid",
"Subtype.mk",
"AddZero.toZero",
"Finset.instSetLike",
"AddCommMonoid.toAddMon... | false |
neg_lt_sub_iff_lt_add | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"lt_add_neg_iff_add_lt",
"neg_add_lt_iff_lt_add",
"congrArg",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"AddRightStrictMono",
"HSub.hSub",
"AddZeroClass.toAddZero",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
... | true |
Finsupp.basisSingleOne | Mathlib.LinearAlgebra.Finsupp.VectorSpace | [
"Module.Basis.ofRepr",
"Semiring.toModule",
"Finsupp.module",
"Finsupp.instAddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Module.Basis",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semiring",
"LinearEquiv.refl",
"Semiring.toNonAssocSemiring",
"Finsupp",
"MulZeroClass.toZero... | true |
Aesop.Frontend.Priority.int.elim | Aesop.Frontend.RuleExpr | [
"PULift.up",
"Int",
"Nat",
"Aesop.Frontend.Priority.int",
"Aesop.Frontend.Priority",
"Eq.symm",
"Eq",
"Aesop.Frontend.Priority.ctorElim",
"Aesop.Frontend.Priority.ctorIdx"
] | false |
Lean.Elab.mkMessageCore | Lean.Elab.Exception | [
"Lean.MessageData",
"Lean.FileMap.toPosition",
"String",
"Lean.FileMap",
"Lean.Message",
"Option.some",
"Lean.MessageSeverity",
"Lean.Position",
"String.Pos.Raw",
"Bool.false",
"Lean.BaseMessage.mk"
] | true |
Int.decidableLELT._proof_3 | Mathlib.Data.Int.Range | [
"congrArg",
"_private.Mathlib.Data.Int.Range.0.Int.decidableLELT._simp_2",
"Membership.mem",
"Int",
"LE.le",
"_private.Mathlib.Data.Int.Range.0.Int.decidableLELT._simp_1",
"iff_self",
"Int.instLTInt",
"Int.range",
"List",
"And",
"Iff",
"List.instMembership",
"implies_congr",
"LT.lt",
"... | false |
TopCommRingCat.instConcreteCategorySubtypeRingHomαContinuousCoe._proof_3 | Mathlib.Topology.Category.TopCommRingCat | [
"Continuous",
"CommSemiring.toSemiring",
"TopCommRingCat.instCategory",
"RingHom",
"CategoryTheory.CategoryStruct.id",
"id",
"Subtype",
"TopCommRingCat.isTopologicalSpace",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"TopCommRingCat.instFunLikeSubtypeRingHomαContinuousCoe",
"TopCommRingC... | false |
Lean.Elab.Do.withDeadCode | Lean.Elab.Do.Basic | [
"Lean.Elab.Do.CodeLiveness",
"instMonadWithReaderOfMonadWithReaderOf",
"Lean.Elab.Do.Context.doBlockResultType",
"MonadWithReader.withReader",
"Lean.Elab.Do.Context.mutVarDefs",
"Lean.Elab.Do.Context.contInfo",
"instMonadWithReaderOfReaderT",
"Lean.Elab.Term.TermElabM",
"Lean.Elab.Do.DoElabM",
"Le... | true |
CategoryTheory.ShortComplex.instMonoICycles | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.leftHomologyData",
"CategoryTheory.Mono",
"CategoryTheory.ShortComplex.LeftHomologyData.instMonoI",
"CategoryTheory.ShortComplex",
"inferInstance",
"id",
"CategoryTheory.ShortComplex.HasLeftHomology",
"CategoryTheory.ShortComplex... | true |
instMulOneClassWithConvMatrix._proof_1 | Mathlib.LinearAlgebra.Matrix.WithConv | [
"MulOne.toOne",
"WithConv.toConv",
"Equiv.instEquivLike",
"HMul.hMul",
"instOneWithConvMatrix",
"congrArg",
"Matrix",
"WithConv.ofConv",
"Matrix.of",
"Matrix.of_one_hadamard",
"Equiv",
"MulOne.toMul",
"Matrix.hadamard",
"instMulWithConvMatrix",
"MulOneClass.toMulOne",
"Pi.instOne",
"... | false |
_private.Mathlib.Combinatorics.Matroid.Loop.0.Matroid.loopyOn_isLoopless_iff._simp_1_1 | Mathlib.Combinatorics.Matroid.Loop | [
"Matroid.E",
"Matroid.loopless_iff_forall_not_isLoop",
"Membership.mem",
"Matroid.Loopless",
"propext",
"Eq",
"Set.instMembership",
"Matroid",
"Not",
"Matroid.IsLoop",
"Set"
] | false |
CategoryTheory.SmallObject.ιFunctorObj_eq | Mathlib.CategoryTheory.SmallObject.IsCardinalForSmallObjectArgument | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.SmallObject.relativeCellComplexιObj",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.SmallObject.FunctorObjIndex",
"Order.succ",
"Cardinal.IsRegular",
"CategoryT... | true |
CategoryTheory.Mon.limit._proof_3 | Mathlib.CategoryTheory.Monoidal.Internal.Limits | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Mon.instIsMonHomHom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Mon.Hom.hom",
"Cat... | false |
instLocallyFiniteOrderBotSubtypeLtOfDecidableLTOfLocallyFiniteOrder._proof_1 | Mathlib.Order.Interval.Finset.Defs | [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"Finset",
"Preorder.toLE",
"Membership.mem",
"Subtype.coe_le_coe",
"id",
"Subtype",
"LE.le",
"And",
"Finset.mem_Ioc'",
"Iff",
"Finset.instSetLike",
"Finset.mem_subtype",
"LT.lt",
"propext",
"LocallyFiniteOrder",
"congrFun'",
"Finset.subtyp... | false |
RingPreordering.supportAddSubgroup._proof_2 | Mathlib.Algebra.Order.Ring.Ordering.Defs | [
"neg_add_rev",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"SetLike.mem_coe._simp_1",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"AddSubmonoidClass.toAddMemClass",
"CommRing.toNonUnitalCommRing",
"Set.mem_neg._simp_1",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommS... | false |
Subgroup.map_subtype_le_map_subtype | Mathlib.Algebra.Group.Subgroup.Ker | [
"Subgroup.map",
"Subgroup.subtype",
"Subgroup.map_le_map_iff_of_injective",
"PartialOrder.toPreorder",
"Subgroup.subtype_injective",
"Group",
"Preorder.toLE",
"Membership.mem",
"Subtype",
"Subgroup",
"LE.le",
"Iff",
"Subgroup.instPartialOrder",
"Subgroup.toGroup",
"SetLike.instMembership... | true |
_private.Mathlib.Analysis.SpecialFunctions.Stirling.0.Stirling.log_stirlingSeq_bounded_aux._proof_1_2 | Mathlib.Analysis.SpecialFunctions.Stirling | [
"instLawfulOrderLT_mathlib",
"GroupWithZero.toMonoidWithZero",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.RArray.leaf",
"Lean.Grind.Field.toCommRing",
"False",
"Real.partialOrder",
"Real.instLE",
"Real",
"Lean.Grind.CommRing.Expr.var",
"Real.instZero",
"Lean.Grind.Order.le_eq_false_of_lt_k",
... | false |
LucasLehmer.X.add_snd | Mathlib.NumberTheory.LucasLehmer | [
"ZMod.commRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Distrib.toAdd",
"ZMod",
"instDistribOfSemiring",
"instHAdd",
"CommRing.toCommSemiring",
"HAdd.hAdd",
"Nat",
"LucasLehmer.X",
"AddCommSemigroup.toAddCommMagma",
"AddCommMonoid.toAddCommSemigroup",
"Eq",
"Prod.snd... | true |
_private.Mathlib.SetTheory.Ordinal.Veblen.0.Ordinal.cmp_veblenWith.match_1.eq_2 | Mathlib.SetTheory.Ordinal.Veblen | [
"Ordering.gt",
"Unit.unit",
"Ordinal.cmp_veblenWith.match_1",
"Ordering",
"Ordering.eq",
"Unit",
"Ordering.lt",
"Eq.refl",
"Eq"
] | true |
Lean.Expr.updateForall! | Lean.Expr | [
"panicWithPosWithDecl",
"Lean.Expr",
"instOfNatNat",
"Lean.instInhabitedExpr",
"Nat",
"Lean.mkForall",
"_private.Lean.Expr.0.Lean.Expr.getForallBody.match_1",
"Lean.Name",
"Lean.BinderInfo",
"OfNat.ofNat"
] | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_190 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"Equiv.instEquivLike",
"List.idxOfNth_lt_length_iff",
"instLawfulBEq",
"Lean.Grind.iff_eq",
"Lean.Grind.CommRing.Expr.var",
"Lean.Grind.Order.eq_of_le_of_le_0",
"congrArg",
"List.... | false |
HahnSeries.SummableFamily.embDomain | Mathlib.RingTheory.HahnSeries.Summable | [
"HahnSeries.SummableFamily.embDomain._proof_1",
"AddMonoid.toAddZeroClass",
"Classical.propDecidable",
"Membership.mem",
"AddZeroClass.toAddZero",
"PartialOrder",
"HahnSeries.instZero",
"dite",
"AddCommMonoid",
"Function.Embedding",
"AddZero.toZero",
"HahnSeries.SummableFamily.instFunLike",
... | true |
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