name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Data.Finset.Grade.0.CovBy.exists_finset_cons.match_1_1 | Mathlib.Data.Finset.Grade | [
"Finset.cons",
"Finset",
"Membership.mem",
"Exists",
"HasSubset.Subset",
"Exists.casesOn",
"Finset.instSetLike",
"Exists.intro",
"Finset.instHasSubset",
"Not",
"SetLike.instMembership"
] | false |
MeasureTheory.IsProjectiveMeasureFamily.eq_zero_of_isEmpty | Mathlib.MeasureTheory.Constructions.Projective | [
"Eq.mpr",
"MeasureTheory.Measure",
"Iff.of_eq",
"congrArg",
"true_or",
"Finset",
"Classical.propDecidable",
"Membership.mem",
"Exists",
"id",
"Subtype",
"exists_eq_or_imp._simp_1",
"Insert.insert",
"IsEmpty",
"Subtype.exists._simp_1",
"MeasureTheory.Measure.instZero",
"Finset.instIns... | true |
WithBot.Ioo_coe_coe | Mathlib.Order.Interval.Finset.Defs | [
"Function.Embedding.some",
"WithBot.instPreorder",
"WithBot.some",
"WithBot",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Finset.map",
"OrderBot",
"PartialOrder",
"WithBot.instLocallyFiniteOrder",
"LocallyFiniteOrder",
"Eq",
"Finset.Ioo",
"rfl",
"Option"
] | true |
CategoryTheory.Limits.StrongEpiMonoFactorisation.recOn | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.Limits.MonoFactorisation.I",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.StrongEpiMonoFactorisation",
"CategoryTheory.Limits.StrongEpiMonoFactorisation.mk",
"CategoryTheory.StrongEpi",
"CategoryTheory.Limits.MonoFactorisation",
"CategoryTheory.Limits.... | false |
Rat.intCast_lt_cast | Mathlib.Data.Rat.Cast.Order | [
"Int.cast",
"Eq.mpr",
"Rat.cast_intCast",
"Preorder.toLT",
"DivisionRing.toRatCast",
"congrArg",
"LinearOrder",
"Iff.rfl",
"Rat",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Rat.instIntCast",
"i... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.isEmpty_modify._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 |
_private.Mathlib.CategoryTheory.Functor.TypeValuedFlat.0.CategoryTheory.FunctorToTypes.fromOverSubfunctor._proof_1 | Mathlib.CategoryTheory.Functor.TypeValuedFlat | [
"Eq.mpr",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"_private.Mathlib.CategoryTheory.Functor.TypeValuedFlat.0.CategoryTheory.FunctorToTypes.fromOverSubfunctor._simp_1",
"CategoryTheory.O... | false |
CategoryTheory.Functor.mapContActionCongr_hom | Mathlib.CategoryTheory.Action.Continuous | [
"Monoid",
"CategoryTheory.Functor",
"TopCat.instCategory",
"CategoryTheory.Functor.mapContAction",
"Action.mkIso",
"ContinuousMap",
"CategoryTheory.Functor.category",
"CategoryTheory.Iso",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"CategoryTheory.Functor.mapContActionCongr",
"Category... | true |
_private.Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Lemmas.0.RootPairing.Base.root_sub_root_mem_of_mem_of_mem._simp_1_3 | Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Lemmas | [
"HSub.hSub",
"sub_left_inj",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
"Eq"
] | false |
faithfulVAdd_iff | Mathlib.Algebra.Group.Action.Faithful | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"SubtractionMonoid.toInvolutiveNeg",
"AddMonoid.toAddSemigroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddSemigroupAction.add_vadd",
"AddZeroClass.toAddZero",
"FaithfulVAdd.mk",
"neg_neg",
"id",
"FaithfulVAdd",
"SubtractionMonoid.toSubNegMonoid",
... | true |
ConditionallyCompleteLinearOrderedField.to_archimedean | Mathlib.Algebra.Order.CompleteField | [
"Mathlib.Tactic.Push.not_forall_eq",
"Mathlib.Tactic.Push.not_exists._simp_1",
"Iff.mpr",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.cast_succ",
"Mathlib.Tactic.Ring.Common.neg_mul",
"False",
"Mathlib.Meta.NormNum.instAd... | true |
LinearAlgebra.FreeProduct.rel_id | Mathlib.LinearAlgebra.FreeProduct.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"instAddCommMonoidDirectSum",
"LinearAlgebra.FreeProduct.FreeTensorAlgebra",
"DirectSum.instModule",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"Algebra",
"Algebra.toModule",
"Algebra.id",
"TensorAlgebra",
"AddCommMonoidWithOne.toAddMonoidWithO... | true |
Lean.EnumAttributes.casesOn | Lean.Attributes | [
"Lean.NameMap",
"Lean.AttributeImpl",
"Lean.EnumAttributes",
"Lean.PersistentEnvExtension",
"Lean.EnumAttributes.mk",
"List",
"Lean.Name",
"Lean.EnumAttributes.rec",
"Prod"
] | false |
SymbolicDynamics.FullShift.MulSubshift.isClosed | Mathlib.Dynamics.SymbolicDynamics.Basic | [
"Monoid",
"Pi.topologicalSpace",
"SymbolicDynamics.FullShift.MulSubshift.carrier",
"IsClosed",
"TopologicalSpace",
"SymbolicDynamics.FullShift.MulSubshift"
] | true |
AddMonoidHom.associator_eq_zero | Mathlib.Algebra.Ring.Associator | [
"Iff.mpr",
"instZeroAddMonoidHom",
"HMul.hMul",
"Semigroup.to_isAssociative",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddCommGroup.toAddGroup",
"SemigroupWithZero.toSemigroup",
"NonUnitalRing.toNonUnitalNonAssocRing",
"AddZeroClass.toAddZero",
"inferInstance",
"Non... | true |
CategoryTheory.ObjectProperty.IsCodetecting | Mathlib.CategoryTheory.Generator.Basic | [
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ExistsUnique",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.ObjectProperty",
"CategoryTheory.Category"
] | true |
_private.Mathlib.Data.Seq.Basic.0.Stream'.Seq.get?_set_of_not_terminatedAt._simp_1_3 | Mathlib.Data.Seq.Basic | [
"Option.some",
"Option.ne_none_iff_exists'",
"Exists",
"Ne",
"Option.none",
"propext",
"Eq.symm",
"Eq",
"Option"
] | false |
ModuleCat.hom_zsmul | Mathlib.Algebra.Category.ModuleCat.Basic | [
"instHSMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"LinearMap.addCommGroup",
"AddCommGroup.toAddGroup",
"Int",
"LinearMap",
"ModuleCat.instSMulIntHom",
"ModuleCat.isAddCommGroup",
"AddGroup.toSubNegMonoid",
"ModuleCat.moduleCateg... | true |
CategoryTheory.GradedObject.mapBifunctorRightUnitor_inv_naturality | Mathlib.CategoryTheory.GradedObject.Unitor | [
"CategoryTheory.GradedObject.ιMapBifunctorMapObj",
"CategoryTheory.GradedObject.ι_mapBifunctorMapMap",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.GradedObject.HasMap",
"CategoryTheory.GradedObject.mapBifunctorMapObj",
"Category... | true |
achart | Mathlib.Geometry.Manifold.ChartedSpace | [
"chartAt",
"Membership.mem",
"Set.Elem",
"chart_mem_atlas",
"Subtype.mk",
"TopologicalSpace",
"atlas",
"Set.instMembership",
"OpenPartialHomeomorph",
"Set",
"ChartedSpace"
] | true |
Lean.Parser.CacheableParserContext._sizeOf_inst | Lean.Parser.Types | [
"SizeOf.mk",
"SizeOf",
"Lean.Parser.CacheableParserContext._sizeOf_1",
"Lean.Parser.CacheableParserContext"
] | false |
Set.subset_fst_image_prod_snd_image | Mathlib.Data.Set.Prod | [
"Set.instSProd",
"Eq.mpr",
"SProd.sprod",
"congrArg",
"Set.mem_prod._simp_1",
"Set.mem_image._simp_1",
"Prod.exists._simp_1",
"Membership.mem",
"Exists",
"exists_and_right._simp_1",
"id",
"Prod.mk",
"_private.Mathlib.Data.Set.Prod.0.Set.subset_fst_image_prod_snd_image.match_1_1",
"HasSubse... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getKey?_union_of_contains_eq_false_left._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 |
Lean.Compiler.LCNF.casesIntToMono._unsafe_rec | Lean.Compiler.LCNF.ToMono | [
"Pure.pure",
"Lean.Compiler.LCNF.Alt.updateCode",
"Lean.Compiler.LCNF.Cases.resultType",
"Lean.Compiler.LCNF.Arg",
"Lean.Compiler.LCNF.Arg.fvar",
"Lean.Compiler.LCNF.LetDecl.mk",
"Lean.Compiler.LCNF.ToMonoM.State",
"ReaderT",
"Monad.toApplicative",
"Lean.Compiler.LCNF.Code.cases",
"Lean.Compiler... | false |
Lean.Elab.Term.elabShow._regBuiltin.Lean.Elab.Term.elabShow.declRange_3 | Lean.Elab.BuiltinNotation | [
"Lean.addBuiltinDeclarationRanges",
"Lean.DeclarationRange.mk",
"IO",
"instOfNatNat",
"Unit",
"Lean.Position.mk",
"Nat",
"OfNat.ofNat",
"Lean.DeclarationRanges.mk",
"Lean.Name.mkStr4"
] | false |
Std.HashMap.Raw.get?_inter_of_not_mem_left | Std.Data.HashMap.RawLemmas | [
"Std.HashMap.Raw.WF.out",
"Membership.mem",
"Std.HashMap.Raw.WF",
"LawfulHashable",
"Std.HashMap.Raw",
"Inter.inter",
"Option.none",
"EquivBEq",
"Std.HashMap.Raw.get?",
"Std.HashMap.Raw.inner",
"Std.HashMap.Raw.instInterOfBEqOfHashable",
"Std.HashMap.Raw.instMembershipOfBEqOfHashable",
"Hash... | true |
AbsolutelyContinuousOnInterval.fun_neg | Mathlib.MeasureTheory.Function.AbsolutelyContinuous | [
"NegZeroClass.toNeg",
"Real",
"SeminormedAddCommGroup",
"AbsolutelyContinuousOnInterval.neg",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"AbsolutelyContinuousOnInterval",
"SeminormedAddCommGroup.toPseudoMetricSpace"... | true |
_private.Mathlib.RingTheory.Polynomial.GaussNorm.0.Polynomial.sup'_nonneg_of_ne_zero | Mathlib.RingTheory.Polynomial.GaussNorm | [
"Real.instIsOrderedRing",
"Eq.mpr",
"mul_nonneg",
"False",
"Real.partialOrder",
"Real.instLE",
"Real",
"Lattice.toSemilatticeSup",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"pow_nonneg",
"eq_false",
"IsOrderedRing.toZeroLEOneClass",
"Real.instZero",
"congrArg",
"Finset",
"Real.instS... | true |
QuotientAddGroup.norm_mk_eq_zero | Mathlib.Analysis.Normed.Group.Quotient | [
"Norm.norm",
"Eq.mpr",
"Real",
"SeminormedAddCommGroup",
"QuotientAddGroup.norm_mk_eq_zero_iff_mem_closure",
"QuotientAddGroup.instNorm",
"Real.instZero",
"congrArg",
"Iff.rfl",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"IsClosed.closure_eq",
"Membership.mem",
"Quotien... | true |
forall_eq_apply_imp_iff._simp_1 | Init.PropLemmas | [
"propext",
"forall_eq_apply_imp_iff",
"Eq"
] | false |
addIrreducible_addUnits_add | Mathlib.Algebra.Group.Irreducible.Lemmas | [
"Eq.mpr",
"AddUnits.val",
"AddMonoid.toAddSemigroup",
"congrArg",
"add_assoc",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"id",
"and_congr_right_iff",
"IsAddUnit",
"AddUnits.isAddUnit_addUnits_add",
"AddIrreducible",
"addIrreducible_iff",
"instHAdd",
"AddSemigroup.toAdd",
"A... | true |
Seminorm.finset_sup_le_sum | Mathlib.Analysis.Seminorm | [
"Iff.mpr",
"Eq.mpr",
"Seminorm.instAddCommMonoid",
"Preorder.toLT",
"congrArg",
"IsRightCancelAdd.addRightReflectLE_of_addRightReflectLT",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Finset",
"covariant_swap_add_of_covariant_add",
"AddMonoid.toAddZeroClass",
"IsCancelAdd... | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.LRATCheckerSound.0.Std.Tactic.BVDecide.LRAT.Internal.lratChecker.match_3.eq_5 | Std.Tactic.BVDecide.LRAT.Internal.LRATCheckerSound | [
"Std.Tactic.BVDecide.LRAT.Action.addEmpty",
"Std.Tactic.BVDecide.LRAT.Action",
"Std.Tactic.BVDecide.LRAT.Action.del",
"Std.Tactic.BVDecide.LRAT.Action.addRat",
"List.cons",
"Std.Tactic.BVDecide.LRAT.Internal.lratChecker.match_3",
"Array",
"List",
"Unit",
"Nat",
"Eq.refl",
"Prod",
"Std.Sat.Li... | true |
_private.Mathlib.Algebra.Module.ZLattice.Summable.0.ZLattice.exists_finsetSum_norm_rpow_le_tsum._simp_1_9 | Mathlib.Algebra.Module.ZLattice.Summable | [
"NegZeroClass.toNeg",
"abs",
"AddCommGroup.toAddCommMonoid",
"abs_le",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"SemilatticeInf.toPartialOrder",
"AddCommGroup",
"DistribLattice.toLattice",
"SubtractionMonoid.toSubNegZeroMonoid",
"LE.le",
"SubNeg... | false |
CategoryTheory.Functor.LeftExtension.mk_right | Mathlib.CategoryTheory.Functor.KanExtension.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.Functor.LeftExtension.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.discreteCategory",
"PUnit",
"CategoryTheory.Functor.whiskerin... | true |
Option.pbind | Init.Data.Option.Instances | [
"Option.pbind._proof_1",
"Option.some",
"Option.pbind.match_1",
"Option.none",
"Eq",
"Option"
] | true |
DifferentiableAt.prodMk._simp_1 | Mathlib.Analysis.Calculus.FDeriv.Prod | [
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"DifferentiableAt",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceProd",
"NormedField.toField",
"Prod.mk",
"Field.toSemifield",
"DifferentiableAt.prodMk",
"Semifield.toDivisionSemiring",
"SeminormedAddCommGroup.t... | false |
instTwoUniqueSumsOfModuleRat | Mathlib.Algebra.Group.UniqueProds.VectorSpace | [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Semiring.toModule",
"Finsupp.module",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"AddCommGroup.toAddCommMonoid",
"instIsLeftCancelAddOfAddLeftReflectLE",
"covariant_swap_add_of_covariant_add",
"AddMonoid.toAddZeroClass",
"Rat",
"PartialOrder... | true |
ExteriorAlgebra.ιMulti._proof_1 | Mathlib.LinearAlgebra.ExteriorAlgebra.Basic | [
"Iff.mpr",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instNeZeroNatHAdd_1",
"lt_of_le_of_lt",
"CommRing",
"Nat.recAux",
"Preorder.toLT",
"Semiring.toModule",
"HMul.hMul",
"QuadraticMap.instZero",
"outParam",
"Ring.toNonAssocRing",
"ExteriorAlgebra",
"MulZeroClass.toMul",
"Fi... | false |
NonUnitalStarSubalgebra.map_toNonUnitalSubalgebra | Mathlib.Algebra.Star.NonUnitalSubalgebra | [
"NonUnitalSubalgebra",
"CommSemiring.toSemiring",
"NonUnitalSubalgebra.map",
"StarHomClass",
"SetLike.coe_injective",
"NonUnitalStarSubalgebra.map",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"SetLike.coe",
"Star",
"NonUnitalSubalgebra.instSetLike",
"Semiring.toMonoid",
"No... | true |
Batteries.RBMap.forM | Batteries.Data.RBMap.Basic | [
"Batteries.RBNode.WF",
"Batteries.RBNode",
"Ordering.byKey",
"Batteries.RBMap",
"Ordering",
"Prod.fst",
"PUnit",
"Batteries.RBNode.forM",
"Prod",
"Monad",
"Subtype.val",
"Batteries.RBMap.foldl.match_1"
] | true |
UniformEquiv.setCongr._proof_1 | Mathlib.Topology.UniformSpace.Equiv | [
"Equiv.instEquivLike",
"Equiv.subtypeEquiv._proof_3",
"Membership.mem",
"Equiv.subtypeEquivProp._proof_1",
"Equiv",
"Subtype",
"Equiv.setCongr._proof_1",
"Subtype.val",
"Equiv.refl",
"Eq",
"Set.instMembership",
"DFunLike.coe",
"EquivLike.toFunLike",
"Set"
] | false |
Ideal.Quotient.instUniqueQuotientTop._proof_1 | Mathlib.RingTheory.Ideal.Quotient.Basic | [
"Iff.mpr",
"Inhabited.default",
"Submodule.Quotient.instZeroQuotient",
"Semiring.toModule",
"Ideal.Quotient.mk",
"Quot.ind",
"RingHom",
"Membership.mem",
"Submodule.instTop",
"Ideal",
"Ideal.Quotient.eq_zero_iff_mem",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"HasQuotient.Quotient",
"Id... | false |
_private.Mathlib.Algebra.MvPolynomial.Variables.0.MvPolynomial.vars_rename._simp_1_2 | Mathlib.Algebra.MvPolynomial.Variables | [
"Finset.mem_image",
"Finset",
"Membership.mem",
"Exists",
"And",
"Finset.instSetLike",
"propext",
"Eq",
"Finset.image",
"SetLike.instMembership",
"DecidableEq"
] | false |
MeasureTheory.eLpNorm_mono_nnnorm | Mathlib.MeasureTheory.Function.LpSeminorm.Basic | [
"MeasureTheory.ae",
"MeasureTheory.eLpNorm_mono_nnnorm_ae",
"MeasureTheory.Measure",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"Preorder.toLE",
"SeminormedAddGroup.toContinuousENorm",
"Filter.Eventually.of_forall",
"NNReal",
... | true |
DiffeologicalSpace.CorePlotsOn.rec | Mathlib.Geometry.Diffeology.Basic | [
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"PiLp.normedSpace",
"fact_one_le_two_ennreal",
"Real.denselyNormedField",
"instTopENat",
"Real.instRCLike",
"TopologicalSpace.IsOpen",
"Set.univ",
"PseudoMetricSpace.toUniformSpace",
"ContDiffOn",
"Diffeologica... | false |
commandUnsuppress_compilationIn_ | Mathlib.Tactic.SuppressCompilation | [
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
partialOrderOfSO._proof_7 | Mathlib.Order.RelClasses | [
"False",
"irrefl",
"congrArg",
"Eq.mp",
"IsStrictOrder",
"Eq",
"IsStrictOrder.toIrrefl"
] | false |
Int8.toInt.inj | Init.Data.SInt.Lemmas | [
"Int8",
"Int8.toInt",
"instOfNatNat",
"Int",
"BitVec.eq_of_toInt_eq",
"Nat",
"Int8.toBitVec",
"Int8.toBitVec.inj",
"OfNat.ofNat",
"Eq"
] | true |
_private.Lean.Elab.LetRec.0.Lean.Elab.Term.withAuxLocalDecls.loop._unsafe_rec | Lean.Elab.LetRec | [
"Lean.Elab.Term.LetRecDeclView.type",
"Array.push",
"Lean.Elab.Term.instMonadTermElabM",
"instMonadControlTOfPure",
"Lean.Meta.State",
"_private.Lean.Elab.LetRec.0.Lean.Elab.Term.withAuxLocalDecls.loop._unsafe_rec",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instOfNatNat",
"Applicative.toP... | false |
Finset.mul_inf_le_inf_mul_of_nonneg | Mathlib.Algebra.Order.GroupWithZero.Finset | [
"HMul.hMul",
"MulZeroClass.toMul",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"LE.le",
"OrderTop",
"MulPosMono",
"SemilatticeInf",
"MonoidWithZero",
"PosMulMono",
"MonoidWithZero.toMulZeroOneClass",
"Finset.instSetLike",
"mu... | true |
Fin.castSucc_eq_zero_iff | Init.Data.Fin.Lemmas | [
"instNeZeroNatHAdd_1",
"congrArg",
"Zero.ofOfNat0",
"_private.Init.Data.Fin.Lemmas.0.Fin.castSucc_eq_zero_iff._simp_1_1",
"Fin.instOfNat",
"instOfNatNat",
"Fin.val",
"iff_self",
"instHAdd",
"Iff",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"congr",
"True",
"of_eq_true",
"instAddNat",
... | true |
ContinuousMulEquiv.rec | Mathlib.Topology.Algebra.ContinuousMonoidHom | [
"Continuous",
"Mul",
"ContinuousMulEquiv.mk",
"MulEquiv.toEquiv",
"Equiv.toFun",
"TopologicalSpace",
"MulEquiv",
"ContinuousMulEquiv",
"Equiv.invFun"
] | false |
ESeminormedMonoid.recOn | Mathlib.Analysis.Normed.Group.Defs | [
"Monoid",
"ESeminormedMonoid",
"ENNReal.instAdd",
"Semigroup.toMul",
"HMul.hMul",
"ESeminormedMonoid.mk",
"ESeminormedMonoid.rec",
"LE.le",
"ContinuousENorm",
"TopologicalSpace",
"instHAdd",
"ENorm.enorm",
"ContinuousENorm.toENorm",
"HAdd.hAdd",
"ENNReal.instLE",
"ENNReal",
"Monoid.t... | false |
MeasureTheory.SimpleFunc.instMul | Mathlib.MeasureTheory.Function.SimpleFunc | [
"Mul.mk",
"HMul.hMul",
"MeasureTheory.SimpleFunc.seq",
"Mul",
"MeasureTheory.SimpleFunc",
"MeasurableSpace",
"instHMul",
"MeasureTheory.SimpleFunc.map"
] | true |
Stream'.cycle._proof_1 | Mathlib.Data.Stream.Defs | [
"List",
"Eq",
"rfl",
"List.nil"
] | false |
_private.Mathlib.Topology.Algebra.Support.0.LocallyFinite.exists_finset_nhds_mulSupport_subset._simp_1_1 | Mathlib.Topology.Algebra.Support | [
"Finset",
"Membership.mem",
"And",
"Finset.instSetLike",
"DecidablePred",
"propext",
"Finset.mem_filter",
"Finset.filter",
"Eq",
"SetLike.instMembership"
] | false |
Lean.initFn._@.Lean.Util.PPExt.3629515885._hygCtx._hyg.4 | Lean.Util.PPExt | [
"Lean.Option",
"IO",
"Lean.Name.mkStr3",
"Lean.Option.Decl.mk",
"Lean.KVMap.instValueBool",
"Lean.Option.register",
"Bool",
"Lean.Name.mkStr2",
"Bool.false"
] | false |
Diffeomorph.sumEmpty_apply_inl | Mathlib.Geometry.Manifold.Diffeomorph | [
"ChartedSpace.sum",
"NormedSpace",
"Diffeomorph.sumEmpty",
"Sum",
"Diffeomorph",
"Sum.inl",
"IsEmpty",
"instTopologicalSpaceSum",
"TopologicalSpace",
"ModelWithCorners",
"Diffeomorph.instEquivLike",
"ENat",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"NormedAddCom... | true |
Std.DHashMap.Raw.emptyWithCapacity | Std.Data.DHashMap.Raw | [
"Std.DHashMap.Raw",
"instOfNatNat",
"Std.DHashMap.Internal.Raw₀.emptyWithCapacity",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"Std.DHashMap.Internal.AssocList",
"instLTNat",
"optParam",
"OfNat.ofNat",
"Subtype.val",
"Array.size"
] | true |
_private.Mathlib.Util.Notation3.0.Mathlib.Notation3.isType'.match_1 | Mathlib.Util.Notation3 | [
"Lean.Expr",
"Nat.hasNotBit",
"Lean.Expr.sort",
"Lean.Level",
"Lean.Expr.ctorIdx",
"_private.Mathlib.Util.Notation3.0.Mathlib.Notation3.isType'._sparseCasesOn_1"
] | false |
CategoryTheory.monoidalOfHasFiniteCoproducts.associator_hom | Mathlib.CategoryTheory.Monoidal.OfHasFiniteProducts | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.coprod.desc",
"CategoryTheory.monoidalOfHasFiniteCoproducts",
"CategoryTheory.Limits.coprod.inl",
"CategoryTheory.monoidalOfHasFiniteCoproducts._proof_3",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.C... | true |
CategoryTheory.MorphismProperty.Arrow.w | Mathlib.CategoryTheory.MorphismProperty.Comma | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.Comma.instCategory",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"CategoryTheory.Comma.hom",
"CategoryTheory.CommaMorphism.w",
"Ca... | true |
_private.Mathlib.MeasureTheory.Measure.Typeclasses.SFinite.0.MeasureTheory.Measure.add_right_inj._simp_1_1 | Mathlib.MeasureTheory.Measure.Typeclasses.SFinite | [
"MeasureTheory.Measure",
"MeasurableSpace",
"ENNReal",
"propext",
"MeasureTheory.Measure.ext_iff'",
"Eq",
"DFunLike.coe",
"MeasureTheory.Measure.instFunLike",
"Set"
] | false |
CategoryTheory.Limits.piConstAdj._proof_4 | Mathlib.CategoryTheory.Limits.Shapes.Products | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.Fan.mk",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Limits.HasProducts",
"CategoryTheory.Functor.category",
"C... | false |
Lean.Meta.Grind.Arith.Cutsat.Search.Kind.rat | Lean.Meta.Tactic.Grind.Arith.Cutsat.SearchM | [
"Lean.Meta.Grind.Arith.Cutsat.Search.Kind",
"Lean.Meta.Grind.Arith.Cutsat.Search.Kind.rat"
] | true |
_private.Mathlib.Tactic.GRewrite.Core.0.Lean.MVarId.grewrite.match_8 | Mathlib.Tactic.GRewrite.Core | [
"Lean.Expr",
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
_private.Mathlib.Analysis.Analytic.OfScalars.0.FormalMultilinearSeries.ofScalarsSum_zero._simp_1_1 | Mathlib.Analysis.Analytic.OfScalars | [
"instHSMul",
"Ring.toNonAssocRing",
"FormalMultilinearSeries.ofScalars_apply_eq",
"Algebra",
"ContinuousMultilinearMap",
"Algebra.toSMul",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"ContinuousMultilinearMap.funLike",
"Field.toSemifield",
"NonAssocRing.toNonUnitalNo... | false |
EReal.induction₂_symm_neg | Mathlib.Data.EReal.Operations | [
"Real.partialOrder",
"Real",
"Real.instZero",
"instIsLeftCancelAddOfAddLeftReflectLE",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"EReal.instNeg",
"EReal",
"Real.instLT",
"Preorder.toLE",
"Eq.rec",
"AddZeroClass.toAddZero",
"neg_pos_of_neg",
"instTopEReal",
"neg_neg",
"AddG... | true |
MonCat.instConcreteCategoryMonoidHomCarrier.eq_1 | Mathlib.Algebra.Category.MonCat.Basic | [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"MonCat.instConcreteCategoryMonoidHomCarrier._proof_4",
"CategoryTheory.ConcreteCategory.mk",
"_private.Mathlib.Algebra.Category.MonCat.Basic.0.MonCat.Hom.mk",
"MonCat",
"MonCat.instConcreteCategoryMonoidHomCarrier._proof_3",
"MonCat.inst... | true |
Std.ExtDHashMap.Const.getKeyD_unitOfList_of_mem | Std.Data.ExtDHashMap.Lemmas | [
"List.Pairwise",
"Membership.mem",
"LawfulHashable",
"Bool.true",
"List",
"BEq.beq",
"Unit",
"EquivBEq",
"List.instMembership",
"Std.ExtDHashMap.Const.unitOfList",
"Bool",
"Hashable",
"Std.ExtDHashMap.getKeyD",
"Bool.false",
"BEq",
"Eq",
"Std.DHashMap.Const.getKeyD_unitOfList_of_mem"... | true |
_private.Mathlib.Data.Nat.PrimeFin.0.Nat.disjoint_primeFactors._simp_1_2 | Mathlib.Data.Nat.PrimeFin | [
"Nat.gcd",
"Nat.Coprime",
"instOfNatNat",
"Nat.coprime_iff_gcd_eq_one",
"Nat",
"propext",
"OfNat.ofNat",
"Eq"
] | false |
Lean.Lsp.ChangeAnnotationSupport.mk.noConfusion | Lean.Data.Lsp.Capabilities | [
"Lean.Lsp.ChangeAnnotationSupport",
"id",
"Bool",
"Lean.Lsp.ChangeAnnotationSupport.noConfusion",
"Eq",
"Lean.Lsp.ChangeAnnotationSupport.mk",
"Option"
] | false |
Matroid.IsCircuit.subset_closure_diff_singleton | Mathlib.Combinatorics.Matroid.Circuit | [
"Eq.mpr",
"Matroid.IsCircuit.closure_diff_singleton_eq",
"congrArg",
"Set.instSingletonSet",
"id",
"Matroid.subset_closure",
"HasSubset.Subset",
"SDiff.sdiff",
"Matroid.IsCircuit.subset_ground",
"Matroid.IsCircuit",
"Matroid.closure",
"Singleton.singleton",
"Eq",
"Matroid",
"Set.instSDif... | true |
R1Space.mk | Mathlib.Topology.Separation.Basic | [
"Specializes",
"R1Space",
"Filter.instCompleteLatticeFilter",
"PartialOrder.toPreorder",
"R1Space.mk",
"Preorder.toLE",
"Disjoint",
"nhds",
"CompleteLattice.toBoundedOrder",
"TopologicalSpace",
"BoundedOrder.toOrderBot",
"Or",
"Filter",
"Filter.instPartialOrder"
] | true |
_private.Init.Data.Range.Polymorphic.RangeIterator.0.Std.Rxi.Iterator.instIteratorLoop.loop.wf._unary.induct_unfolding | Init.Data.Range.Polymorphic.RangeIterator | [
"Pure.pure",
"PSigma.snd",
"Eq.mpr",
"_private.Init.Data.Range.Polymorphic.RangeIterator.0.Std.Rxc.Iterator.instIteratorLoop.loop.wf.match_1",
"Std.PRange.UpwardEnumerable",
"congrArg",
"Std.Rxi.Iterator.mk",
"Monad.toApplicative",
"invImage",
"_private.Init.Data.Range.Polymorphic.RangeIterator.0.... | false |
List.unattach_flatten | Init.Data.List.Attach | [
"List.unattach",
"Eq.mpr",
"congrArg",
"List.map",
"Eq.mp",
"id",
"Subtype",
"List.map_subtype",
"List.rec",
"List.cons",
"Subtype.mk",
"funext",
"instHAppendOfAppend",
"List.map_id_fun'",
"List",
"congrFun",
"congr",
"True",
"eq_self",
"of_eq_true",
"Eq.refl",
"congrFun'",... | true |
_private.Lean.DocString.Parser.0.Lean.Doc.Parser.numbering.go | Lean.DocString.Parser | [
"List.brecOn",
"Lean.Doc.Parser.OrderedListType",
"List",
"_private.Lean.DocString.Parser.0.Lean.Doc.Parser.numbering.go._f",
"Lean.Parser.ParserFn"
] | true |
_private.Std.Internal.Http.Data.Body.Full.0.Std.Http.Body.Full.mk.sizeOf_spec | Std.Internal.Http.Data.Body.Full | [
"_private.Std.Internal.Http.Data.Body.Full.0.Std.Http.Body.Full.mk",
"Option._sizeOf_inst",
"ByteArray._sizeOf_inst",
"instOfNatNat",
"Std.Http.Body.Full._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Std.Mutex",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"Std.Mutex._sizeOf_inst",
"ByteArr... | true |
_private.Std.Data.DHashMap.Internal.AssocList.Lemmas.0.Std.DHashMap.Internal.AssocList.get.eq_def | Std.Data.DHashMap.Internal.AssocList.Lemmas | [
"Eq.mpr",
"Std.DHashMap.Internal.AssocList.below",
"Std.DHashMap.Internal.AssocList.get._f",
"congrArg",
"Std.DHashMap.Internal.AssocList.brecOn.eq",
"HEq.refl",
"_private.Std.Data.DHashMap.Internal.AssocList.Lemmas.0.Std.DHashMap.Internal.AssocList.get.match_1.splitter",
"Std.DHashMap.Internal.AssocL... | true |
OpenPartialHomeomorph.lift_openEmbedding_trans_apply | Mathlib.Topology.OpenPartialHomeomorph.Constructions | [
"Topology.IsOpenEmbedding.toIsEmbedding",
"congrArg",
"OpenPartialHomeomorph.trans",
"OpenPartialHomeomorph.toFun'",
"Function.Injective.extend_apply",
"TopologicalSpace",
"Topology.IsOpenEmbedding",
"True",
"Topology.IsEmbedding.injective",
"eq_self",
"Classical.arbitrary",
"of_eq_true",
"N... | true |
Lean.Lsp.ClientInfo.mk._flat_ctor | Lean.Data.Lsp.InitShutdown | [
"String",
"Lean.Lsp.ClientInfo",
"Lean.Lsp.ClientInfo.mk",
"Option"
] | false |
Orientation.inner_rightAngleRotation_right | Mathlib.Analysis.InnerProductSpace.TwoDim | [
"LinearIsometryEquiv.instEquivLike",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Orientation",
"Real.partialOrder",
"Real",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Inner.inner",
"Real.instRCLike",
"congrArg",
"CommSemiring.toSemiring",
"Orientation.rightAngleRotation_def",
"Add... | true |
AlgebraicGeometry.Scheme.Pullback.t'_fst_fst_snd_assoc | Mathlib.AlgebraicGeometry.Pullbacks | [
"AlgebraicGeometry.Scheme.Pullback.v._proof_1",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"AlgebraicGeometry.Scheme.Pullback.v",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Algebraic... | true |
mem_generatePiSystem_iUnion_elim' | Mathlib.MeasureTheory.PiSystem | [
"Finset.set_biInter_finset_image",
"_private.Mathlib.MeasureTheory.PiSystem.0.mem_generatePiSystem_iUnion_elim'._simp_1_6",
"Iff.mpr",
"Set.ext",
"Eq.mpr",
"mem_generatePiSystem_iUnion_elim",
"Iff.of_eq",
"congrArg",
"Subtype.val_injective",
"Set.iInter",
"Finset",
"Set.univ",
"Iff.rfl",
"... | true |
upperCentralSeries.card_image_eq_of_le_nilpotencyClass | Mathlib.GroupTheory.Nilpotent | [
"Subgroup.upperCentralSeries",
"Group",
"Subgroup.upperCentralSeries.card_image_eq_of_le_nilpotencyClass",
"Subgroup",
"instOfNatNat",
"LE.le",
"Group.nilpotencyClass",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"Nat.instPreorder",
"Nat",
"instAddNat",
"Set.image",
"Set.Iic",
"Set.ncard",
... | true |
_private.Mathlib.RingTheory.Valuation.LocalSubring.0.LocalSubring.exists_le_valuationSubring_of_isIntegrallyClosedIn.match_1_1 | Mathlib.RingTheory.Valuation.LocalSubring | [
"LocalSubring.isLocalRing",
"GroupWithZero.toMonoidWithZero",
"Semiring.toModule",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"Subring.instSetLike",
"DivInvOneMonoid.toInvOneClass",
"MulZeroClass.toMul",
"AddGroupWithOne.toAddGroup",
"CommSemiri... | false |
_private.Mathlib.Data.Set.Image.0.Set.Nonempty.preimage.match_1_3 | Mathlib.Data.Set.Image | [
"Membership.mem",
"Set.Nonempty",
"Exists.casesOn",
"Exists.intro",
"Set.instMembership",
"Set"
] | false |
Fin.hIterateFrom.congr_simp | Init.Data.Fin.Iterate | [
"Fin.hIterateFrom",
"Eq.rec",
"instOfNatNat",
"LE.le",
"instLENat",
"Fin.val",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Fin",
"Eq"
] | true |
MeasureTheory.Measure.InnerRegularWRT.measure_eq_iSup | Mathlib.MeasureTheory.Measure.Regular | [
"Eq.mpr",
"iSup₂_le",
"MeasureTheory.Measure",
"Preorder.toLT",
"Iff.of_eq",
"congrArg",
"iSup",
"CompletelyDistribLattice.toCompleteLattice",
"MeasureTheory.OuterMeasure.mono",
"PartialOrder.toPreorder",
"Exists",
"id",
"HasSubset.Subset",
"ConditionallyCompleteLinearOrder.toConditionally... | true |
AffineSubspace.subtypeₐᵢ | Mathlib.Analysis.Normed.Affine.Isometry | [
"NormedCommRing.toNormedRing",
"Submodule",
"SeminormedAddCommGroup",
"instSMulOfMul",
"NormedRing.toRing",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AffineSubspace.subtypeₐᵢ._proof_2",
"Membership.mem",
"NormedField.toField",
"Submodule.normedSpace",
"Subtype",... | true |
QuotientAddGroup.equivIocMod | Mathlib.Algebra.Order.ToIntervalMod | [
"toIocMod_periodic",
"Set.Ioc",
"Preorder.toLT",
"QuotientAddGroup.equivIocMod._proof_2",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"AddCommGroup.toAddGroup",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Equiv.mk",
"AddCommGroup",
"Set.Elem",
"Distrib... | true |
CategoryTheory.ChosenPullbacksAlong.hasPullbacks | Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong | [
"CategoryTheory.ChosenPullbacksAlong.hasPullbackAlong",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasPullbacks",
"CategoryTheory.ChosenPullbacks",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.hasPullbacks_of_hasLimit_cospan",
"CategoryTheory.C... | true |
PNat.XgcdType.flip_a | Mathlib.Data.PNat.Xgcd | [
"PNat.XgcdType.flip",
"PNat.XgcdType",
"PNat.XgcdType.a",
"Eq",
"rfl",
"PNat.XgcdType.b",
"PNat"
] | true |
Lean.Meta.Grind.EMatch.State.thms | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.EMatch.State",
"Lean.PArray",
"Lean.Meta.Grind.EMatchTheorem"
] | true |
mfderivWithin_projIcc_one | Mathlib.Geometry.Manifold.Instances.Icc | [
"instOneTangentSpaceRealModelWithCornersSelf",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"PiLp.normedSpace",
"fact_one_le_two_ennreal",
"chartedSpaceSelf",
"definition._proof_2._@.Mathlib.Geometry.Manifold.Instances.Icc.2712988316._hygCtx._hyg.2",
... | true |
Homotopy.ofEq | Mathlib.Algebra.Homology.Homotopy | [
"HomologicalComplex.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Homotopy.ofEq._proof_2",
"HomologicalComplex",
"Homotopy.mk",
"Pi.instZero",
"ComplexShape",
"Homotopy.ofEq._proof_1",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"CategoryTheory.Preadditive",
"Categ... | true |
Lean.Lsp.Range.mk.inj | Lean.Data.Lsp.BasicAux | [
"Lean.Lsp.Range.mk",
"And",
"And.intro",
"Lean.Lsp.Range.mk.noConfusion",
"Lean.Lsp.Position",
"Lean.Lsp.Range",
"Eq"
] | true |
Lean.Parser.Command.initGrindNorm._regBuiltin.Lean.Parser.Command.initGrindNorm.formatter_5 | Lean.Meta.Tactic.Grind.Parser | [
"Lean.PrettyPrinter.Formatter",
"Lean.Name.mkStr5",
"IO",
"Lean.Parser.Command.initGrindNorm.formatter",
"Unit",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
ContinuousLinearEquiv.arrowCongrSL._proof_2 | Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap | [
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"ContinuousLinearEquiv.arrowCongrEquivₛₗ",
"ContinuousLinearMap.addCommMonoid",
"AddCommGroup.toAddGroup",
"RingHom",
"ContinuousLinearMap.precomp._proof_3",
"NormedField.toField",
"AddZeroClass.toAddZero... | false |
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