name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Meta.Context.mk.noConfusion | Lean.Meta.Basic | [
"id",
"Lean.Core.CoreM",
"Nat",
"Lean.Meta.ConfigWithKey",
"Bool",
"Lean.FVarIdSet",
"Lean.LocalInstances",
"Lean.ConstantInfo",
"Eq",
"Lean.Meta.Context.mk",
"Lean.Meta.Context.noConfusion",
"Lean.LocalContext",
"Lean.Meta.Context",
"Lean.Meta.Config",
"Lean.Meta.DefEqContext",
"Optio... | false |
Int.mul_le_mul | Init.Data.Int.Order | [
"HMul.hMul",
"Int",
"LE.le",
"Int.instMul",
"instOfNat",
"Int.le_trans",
"Int.mul_le_mul_of_nonneg_left",
"OfNat.ofNat",
"Int.instLEInt",
"Int.mul_le_mul_of_nonneg_right",
"instHMul"
] | true |
Submodule.dualCoannihilator_sup_eq | Mathlib.LinearAlgebra.Dual.Defs | [
"OrderDual.toDual",
"Submodule",
"Lattice.toSemilatticeSup",
"Semiring.toModule",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"Submodule.dualCoannihilator",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Submodule.completeLattice",
"AddMonoid.toAddZeroClass",
"Submodule.dualAnnih... | true |
instCategoryCompactum._aux_3 | Mathlib.Topology.Category.Compactum | [
"Quiver.mk",
"Quiver.Hom",
"instCategoryCompactum._aux_1",
"CategoryTheory.ofTypeMonad",
"CategoryTheory.Monad.Algebra.Hom.id",
"Ultrafilter.monad",
"CategoryTheory.types",
"Ultrafilter.lawfulMonad",
"Compactum",
"Ultrafilter"
] | false |
_private.Mathlib.RingTheory.DiscreteValuationRing.TFAE.0.IsLocalRing.finrank_CotangentSpace_eq_one_iff._simp_1_1 | Mathlib.RingTheory.DiscreteValuationRing.TFAE | [
"False",
"One",
"eq_false",
"zero_ne_one",
"One.toOfNat1",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
Std.Http.Chunk.instInhabitedExtensionName | Std.Internal.Http.Data.Chunk | [
"Std.Http.Chunk.instInhabitedExtensionName._proof_1",
"Std.Http.Chunk.ExtensionName.mk",
"Inhabited",
"Std.Http.Chunk.ExtensionName",
"Inhabited.mk"
] | true |
SimpleGraph.reachable_comm | Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected | [
"SimpleGraph.Reachable.symm",
"SimpleGraph",
"Iff",
"Iff.intro",
"SimpleGraph.Reachable"
] | true |
_private.Mathlib.GroupTheory.DivisibleHull.0.DivisibleHull.instModuleRat._simp_2 | Mathlib.GroupTheory.DivisibleHull | [
"instHSMul",
"AddMonoid.toNSMul",
"SubNegMonoid",
"Int",
"Nat.cast",
"Nat",
"HSMul.hSMul",
"instNatCastInt",
"SubNegMonoid.toAddMonoid",
"Eq.symm",
"Eq",
"natCast_zsmul",
"SubNegMonoid.toZSMul"
] | false |
StarMemClass.instStarRing._proof_1 | Mathlib.Algebra.Star.NonUnitalSubalgebra | [
"SetLike",
"AddMonoid.toAddSemigroup",
"StarAddMonoid.star_add",
"Membership.mem",
"Subtype",
"StarAddMonoid.toInvolutiveStar",
"StarMemClass.instStarAddMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"StarRing.toStarAddMonoid",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"StarRing"... | false |
ContinuousLinearMapWOT.instModule._proof_1 | Mathlib.Analysis.LocallyConvex.WeakOperatorTopology | [
"AddMonoid.toAddSemigroup",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"IsTopologicalAddGroup.toContinuousAdd",
"TopologicalSpace",
"AddSemigroup.toAdd",
"AddGroup.toSubNegMonoid",
"SubNegMonoid.toAddMonoid",
"ContinuousAdd",
"IsTopologicalAddGroup"
] | false |
CategoryTheory.Presieve.singleton.recOn | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.Presieve.singleton.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve.singleton",
"CategoryTheory.Presieve.singleton.rec",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | false |
SchwartzMap.fourierTransformCLE_apply | Mathlib.Analysis.Distribution.SchwartzSpace.Fourier | [
"FourierTransform",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"FourierTransform.fourierCLE",
"DistribSMul.toSMulZeroClass",
"ContinuousLinearEquiv.equivLike",
"FourierTransform.fourierCLE_apply",
"FourierSMul",
"AddCommMonoid",
"ContinuousFourierInv"... | true |
Aesop.Frontend.Feature.phase.noConfusion | Aesop.Frontend.RuleExpr | [
"id",
"Aesop.Frontend.Feature.noConfusion",
"Aesop.PhaseName",
"Aesop.Frontend.Feature",
"Aesop.Frontend.Feature.phase",
"Eq"
] | false |
String.Slice.toList_copy_drop | Init.Data.String.Lemmas.TakeDrop | [
"String.toList_ofList",
"congrArg",
"String",
"String.Slice.drop_eq_sliceFrom",
"String.Slice.sliceFrom",
"String.Slice",
"String.Slice.Pos.Splits.copy_sliceFrom_eq",
"String.Slice.startPos",
"String.Slice.copy",
"List",
"String.Slice.splits_nextn_startPos",
"List.drop",
"Nat",
"String.toL... | true |
InfHomClass.rec | Mathlib.Order.Hom.Lattice | [
"Min",
"InfHomClass.mk",
"InfHomClass",
"Eq",
"DFunLike.coe",
"Min.min",
"FunLike"
] | false |
ESeminormedAddCommMonoid.toAddCommMonoid | Mathlib.Analysis.Normed.Group.Defs | [
"ESeminormedAddCommMonoid",
"ESeminormedAddCommMonoid.add_comm",
"ESeminormedAddMonoid.toAddMonoid",
"AddCommMonoid",
"TopologicalSpace",
"ESeminormedAddCommMonoid.toESeminormedAddMonoid",
"AddCommMonoid.mk"
] | true |
RingHom.ker_fg_of_localizationSpan | Mathlib.RingTheory.Localization.Finiteness | [
"Eq.mpr",
"RingHom.instRingHomClass",
"IsLocalization.map",
"Semiring.toModule",
"Submonoid.le_comap_map",
"Algebra.algebraMap",
"OreLocalization.instAlgebra",
"congrArg",
"CommSemiring.toSemiring",
"Ideal.fg_of_localizationSpan",
"PartialOrder.toPreorder",
"Localization.Away",
"Preorder.toL... | true |
CategoryTheory.Sieve.inf._proof_1 | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Membership.mem",
"CategoryTheory.Sieve.downward_closed",
"CategoryTheory.Sieve.arrows",
"CategoryTheory.Sieve",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Set.instMembership",
"CategoryTheory.Category"... | false |
StieltjesFunction.rec | Mathlib.MeasureTheory.Measure.Stieltjes | [
"Real",
"ContinuousWithinAt",
"Set.Ici",
"StieltjesFunction.mk",
"LinearOrder",
"PartialOrder.toPreorder",
"Monotone",
"PseudoMetricSpace.toUniformSpace",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"TopologicalSpace",
"StieltjesFunction",
"Real.pseudoMetricSpace",
"Unifor... | false |
DerivedCategory.HomologySequence.mono_homologyMap_mor₂_iff | Mathlib.Algebra.Homology.DerivedCategory.HomologySequence | [
"CategoryTheory.Abelian.toPreadditive",
"instCategoryDerivedCategory",
"DerivedCategory.instHasZeroObject",
"DerivedCategory",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"CategoryTheory.Pretriangulated.Triangle.obj₃"... | true |
integral_gaussian | Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral | [
"instInnerProductSpaceRealComplex",
"Real.instIsOrderedRing",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Complex.instAlgebraOfReal",
"RCLike.algebraMap_eq_ofReal",
"MeasureTheory.integral_nonneg",
"Real.partialOrder",
"R... | true |
addSemiconjBy_map_iff | Mathlib.Algebra.Group.Commute.Hom | [
"AddSemiconjBy",
"AddSemiconjBy.of_map",
"AddSemiconjBy.map",
"Iff",
"Iff.intro",
"AddHomClass",
"Function.Injective",
"DFunLike.coe",
"Add",
"FunLike"
] | true |
SSet.Subcomplex.PairingCore.instIsProperPairingOfIsProper | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | [
"SSet.Subcomplex.PairingCore.isUniquelyCodimOneFace",
"SSet.Subcomplex.PairingCore.ι",
"SSet.Subcomplex.PairingCore.II",
"Eq.mpr",
"SSet.S",
"SSet.Subcomplex.PairingCore.equivII",
"Equiv.instEquivLike",
"SSet.Subcomplex.PairingCore",
"SSet.Subcomplex.PairingCore.type₂",
"congrArg",
"SSet.Subcomp... | true |
Array.toList_iterFromIdx | Std.Data.Iterators.Lemmas.Producers.Array | [
"Pure.pure",
"Std.Iterators.Types.ArrayIterator",
"congrArg",
"Monad.toApplicative",
"Array.iterFromIdx",
"Array.toList_iterFromIdxM",
"Id.run",
"Std.Iter.toIterM",
"Id",
"Applicative.toPure",
"Array.toList",
"Array",
"List",
"List.drop",
"Std.Iter.toList",
"Nat",
"True",
"eq_self"... | true |
Lean.MetavarDecl.type | Lean.MetavarContext | [
"Lean.Expr",
"Lean.MetavarDecl"
] | true |
CategoryTheory.LeftExactFunctor.whiskeringLeft._proof_5 | Mathlib.CategoryTheory.Limits.ExactFunctor | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.NatTrans.mk.congr_simp",
"CategoryTheory.leftExactFunctor",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.CategoryStruct.id",
"id",
"Categ... | false |
Lean.Server.Test.Runner.Client.NormalizeState.casesOn | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.NormalizeState",
"USize.instOrd",
"Ord.compare",
"Lean.Server.Test.Runner.Client.NormalizeState.mk",
"Std.TreeMap",
"USize",
"Lean.Server.Test.Runner.Client.NormalizeState.rec"
] | false |
PontryaginDual.instT2Space._proof_1 | Mathlib.Topology.Algebra.PontryaginDual | [
"Monoid",
"PontryaginDual",
"EMetricSpace.metrizableSpace",
"DivInvMonoid.toMonoid",
"instTopologicalSpaceCircle",
"Group.toDivInvMonoid",
"TopologicalSpace",
"instTopologicalSpacePontryaginDual",
"Circle",
"T2Space",
"ContinuousMonoidHom.instT2Space",
"Circle.instCommGroup",
"TopologicalSpa... | false |
HasFDerivWithinAt.iterate | Mathlib.Analysis.Calculus.FDeriv.Comp | [
"Pure.pure",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"ContinuousLinearMap.semiring",
"NormedSpace",
"SProd.sprod",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Filter.map",
"nhdsWithin",
"NormedSpace.toModule",
"AddM... | true |
CategoryTheory.MorphismProperty.Over.w | Mathlib.CategoryTheory.MorphismProperty.Comma | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.MorphismProperty.IsMultiplicative.instTop",
"congrArg",
"CategoryTheory.MorphismProperty.Comma.instCate... | true |
_private.Mathlib.Topology.Algebra.InfiniteSum.Defs.0.hasSum_sum_support_of_ne_finset_zero._proof_1_3 | Mathlib.Topology.Algebra.InfiniteSum.Defs | [
"False",
"eq_false",
"Lean.Grind.iff_eq",
"Finset",
"AddMonoid.toAddZeroClass",
"Classical.byContradiction",
"SummationFilter",
"setOf",
"Membership.mem",
"AddZeroClass.toAddZero",
"Eq.mp",
"id",
"Set.mem_setOf_eq",
"Set.instInter",
"Set.toFinset",
"FinsetCoe.fintype",
"Set.fintypeIn... | false |
ordinaryHypergeometricSeries_symm | Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric | [
"Polynomial.eval",
"Semigroup.toMul",
"Algebra.to_smulCommClass",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Ring.toNonAssocRing",
"congrArg",
"FormalMultilinearSeries",
"DistribMulAction.toDistribSMul",
"IsSemitopologi... | true |
CommRingCat.Colimits.Relation.neg_add_cancel | Mathlib.Algebra.Category.Ring.Colimits | [
"CategoryTheory.Functor",
"CommRingCat",
"CommRingCat.instCategory",
"CategoryTheory.SmallCategory",
"CommRingCat.Colimits.Relation",
"CommRingCat.Colimits.Prequotient.add",
"CommRingCat.Colimits.Relation.neg_add_cancel",
"CommRingCat.Colimits.Prequotient",
"CommRingCat.Colimits.Prequotient.zero",
... | true |
_private.Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic.0._proof_101 | Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic | [
"Eq.mpr",
"CategoryTheory.Limits.FormalCoproduct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Function.Pullback",
"id",
"CategoryTheory.Limits.FormalCoproduct.Hom.f",
"Prod.fst",
"CategoryTheory.Limits.FormalCoproduct.obj",
"Eq.refl",
"CategoryTheory.Category.toCatego... | false |
_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity.0.SimpleGraph.isBridge_iff_adj_and_not_isEdgeConnected_two.match_1_1 | Mathlib.Combinatorics.SimpleGraph.Connectivity.EdgeConnectivity | [
"SimpleGraph.IsEdgeReachable",
"SimpleGraph.Adj",
"instOfNatNat",
"And.casesOn",
"SimpleGraph",
"And",
"Nat",
"And.intro",
"OfNat.ofNat",
"Not"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getKey!_eq_getKeyD_default._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 |
FreeMagma.instMonad.eq_1 | Mathlib.Algebra.Free | [
"MulHom",
"FreeMagma.lift",
"Unit.unit",
"Equiv.instEquivLike",
"Seq.mk",
"SeqLeft.mk",
"Function.comp",
"Equiv",
"SeqRight.mk",
"Pure.mk",
"Functor.mk",
"FreeMagma.of",
"Applicative.mk",
"Unit",
"MulHom.funLike",
"Function.const",
"Eq.refl",
"Monad.mk",
"FreeMagma.instMul",
"F... | true |
Lean.Parser.Tactic.quot._regBuiltin.Lean.Parser.Tactic.quot_1 | Lean.Parser.Term | [
"IO",
"Unit",
"Lean.Parser.addBuiltinLeadingParser",
"Lean.Parser.Tactic.quot",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | false |
PFunctor.M.bisim_equiv | Mathlib.Data.PFunctor.Univariate.M | [
"_private.Mathlib.Data.PFunctor.Univariate.M.0.PFunctor.M.bisim_equiv.match_1_1",
"PFunctor",
"PFunctor.A",
"PFunctor.Obj",
"PFunctor.M.bisim'",
"PFunctor.M",
"PFunctor.B",
"Exists",
"Prod.mk",
"Prod.fst",
"And",
"And.intro",
"Exists.intro",
"PFunctor.M.dest",
"Sigma.mk",
"Prod",
"Eq... | true |
NumberField.mixedEmbedding.convexBodyLTFactor._proof_1 | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
mfderiv_sub | Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions | [
"NormedCommRing.toNormedRing",
"mfderiv",
"NormedRing.toRing",
"chartedSpaceSelf",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"instAddCommGroupTangentSpace",
"instIsTopologicalAddGroupTangentSpace",
"NormedSpace.toModule",
"HasMFDerivAt.mfderiv",
"MDifferentiableAt.hasMFDerivAt",
"HSub.hSu... | true |
_private.Mathlib.Algebra.Category.ModuleCat.Stalk.0.CategoryTheory.Limits.filteredColimitsModule._simp_1 | Mathlib.Algebra.Category.ModuleCat.Stalk | [
"outParam",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.comp_apply",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.ConcreteCategory",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq.symm",
"Eq",
"DFunLike... | false |
Std.Internal.List.getValue?_cons_of_true | Std.Data.Internal.List.Associative | [
"cond",
"congrArg",
"Option.some",
"List.cons",
"Bool.true",
"List",
"BEq.beq",
"Std.Internal.List.getValue?",
"True",
"eq_self",
"Bool",
"of_eq_true",
"congrFun'",
"Sigma.mk",
"BEq",
"Eq",
"Sigma",
"Eq.trans",
"Option"
] | true |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.getEntry._proof_1 | Std.Data.Internal.List.Associative | [
"Bool.true",
"List",
"Std.Internal.List.containsKey",
"Bool",
"Std.Internal.List.getEntry?",
"Option.isSome",
"Eq.symm",
"BEq",
"Eq",
"Std.Internal.List.containsKey_eq_isSome_getEntry?",
"Sigma",
"Eq.trans"
] | false |
AntitoneOn.add | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"add_le_add",
"AddLeftMono",
"Preorder.toLE",
"Membership.mem",
"AddRightMono",
"LE.le",
"instHAdd",
"HAdd.hAdd",
"AntitoneOn",
"Set.instMembership",
"Add",
"Preorder",
"Set"
] | true |
_private.Init.Internal.Order.Basic.0.Lean.Order.coind_monotone_and.match_1_1 | Init.Internal.Order.Basic | [
"And.casesOn",
"And",
"And.intro"
] | false |
ContDiffPointwiseHolderAt.of_exponent_le | Mathlib.Analysis.Calculus.ContDiffHolder.Pointwise | [
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real.instPow",
"Real.partialOrder",
"Real.instLE",
"Real",
"ContDiffPointwiseHolderAt.isBigO",
"ContDiffPointwiseHolderAt",
"Set.Ici",
"NormedSpace",
"ContinuousMultilinearMap.instSub",
"Real.denselyNormedField",
"Real.instZero",
"AddCom... | true |
UniformFun.uniformSpace | Mathlib.Topology.UniformSpace.UniformConvergenceTopology | [
"UniformSpace",
"UniformSpace.ofCore",
"UniformFun",
"UniformFun.uniformCore"
] | true |
_private.Lean.Meta.Tactic.Grind.Theorems.0.Lean.Meta.Grind.Theorems.origins._default | Lean.Meta.Tactic.Grind.Theorems | [
"id",
"Lean.PHashSet",
"Lean.Meta.Grind.instBEqOrigin",
"Lean.Meta.Grind.Origin",
"Lean.Meta.Grind.instHashableOrigin",
"Lean.PersistentHashSet.instEmptyCollection",
"EmptyCollection.emptyCollection"
] | false |
Manifold.IsSmoothEmbedding | Mathlib.Geometry.Manifold.SmoothEmbedding | [
"NormedSpace",
"TopologicalSpace",
"ModelWithCorners",
"ENat",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Manifold.IsSmoothEmbedding.mk",
"NormedAddCommGroup",
"WithTop",
"ChartedSpace"
] | true |
Bundle.Pretrivialization.restrictPreimage_toFun | Mathlib.Topology.FiberBundle.Trivialization | [
"Set.restrictPreimage",
"Bundle.Pretrivialization.restrictPreimage'._proof_1",
"Membership.mem",
"Set.Elem",
"Prod.mk",
"Set.instInter",
"Bundle.Pretrivialization.toFun'",
"Subtype.mk",
"Inter.inter",
"Bundle.Pretrivialization",
"TopologicalSpace",
"Set.Nonempty",
"Set.preimage",
"Bundle.P... | true |
CategoryTheory.PreGaloisCategory.evaluationEquivOfIsGalois_symm_fiber | Mathlib.CategoryTheory.Galois.GaloisObjects | [
"CategoryTheory.GaloisCategory.toPreGaloisCategory",
"CategoryTheory.Functor",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Finite",
"FintypeCat",
"TypeCat.instFunLikeFun",
"CategoryTheory.ObjectProperty.FullSubcategory.concreteCategory",
"... | true |
AddSubmonoid.coe_finset_sum | Mathlib.Algebra.Group.Submonoid.BigOperators | [
"Finset",
"AddSubmonoid.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Subtype",
"AddSubmonoid",
"AddCommMonoid",
"AddCommMonoid.toAddMonoid",
"Subtype.val",
"AddSubmonoid.instSetLike",
"Eq",
"SetLike.instMembership",
"Finset.sum",
"AddSubmonoid.coe_finsetSum"
] | true |
CategoryTheory.GrothendieckTopology.OneHypercover.inter._proof_2 | Mathlib.CategoryTheory.Sites.Hypercover.One | [
"CategoryTheory.Presieve.instHasPullbacksOfArrowsOfHasPullback",
"CategoryTheory.Limits.hasPullbackVertPaste",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Is... | false |
_private.Init.Grind.ToInt.0.Lean.Grind.instBEqIntInterval.beq.match_1.eq_4 | Init.Grind.ToInt | [
"Unit.unit",
"_private.Init.Grind.ToInt.0.Lean.Grind.instBEqIntInterval.beq.match_1",
"Int",
"Lean.Grind.IntInterval.co",
"Lean.Grind.IntInterval.ii",
"Lean.Grind.IntInterval.ci",
"Unit",
"Lean.Grind.IntInterval.io",
"Eq.refl",
"Eq",
"Lean.Grind.IntInterval"
] | true |
CategoryTheory.Pretriangulated.isoTriangleOfIso₁₃_hom_hom₁ | Mathlib.CategoryTheory.Triangulated.Pretriangulated | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"CategoryTheory.Pretriangulated.Triangle.obj₃",
"CategoryTheory.shiftFunctor",
"Membership.mem",
"CategoryTheory.Iso",
"Int",
"Int.instAddMonoid",
"CategoryT... | true |
Std.TreeMap.valuesIter | Std.Data.TreeMap.Iterator | [
"Pure.pure",
"Monad.toApplicative",
"MonadLiftT.monadLift",
"instMonadLiftT",
"Std.TreeMap.inner",
"Ordering",
"Std.DTreeMap.Internal.Zipper",
"Id",
"Applicative.toPure",
"Std.Iterators.instMonadPostconditionT",
"Std.Iter",
"Std.Iterators.Types.Map",
"Std.DTreeMap.valuesIter",
"Applicative... | true |
Affine.Simplex.signedInfDist_affineCombination | Mathlib.Geometry.Euclidean.SignedDist | [
"NormedCommRing.toNormedRing",
"Norm.norm",
"Eq.mpr",
"Pi.Function.module",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Submodule",
"Finset.affineCombination_apply_eq_lineMap_sum",
"instNeZeroNatHAdd_1",
"Set.instNonemptyRange",
"Affine.Simplex.points",
"Nat.inst... | true |
SSet.instIsStableUnderRetractsInnerFibrations._proof_1 | Mathlib.AlgebraicTopology.Quasicategory.InnerFibration | [
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.MorphismProperty.IsStableUnderRetracts",
"SSet",
"SSet.innerFibrations",
"CategoryTheory.types",
"SimplexCategory",
"CategoryTheory.Category.opposite",
"CategoryTheory.MorphismProperty.rlp_isStableUnderRetracts",
"SimplexCategory.small... | false |
Std.Ric.mk.sizeOf_spec | Init.Data.Range.Polymorphic.PRange | [
"instOfNatNat",
"Std.Ric.mk",
"Std.Ric",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"Std.Ric._sizeOf_inst",
"SizeOf",
"OfNat.ofNat",
"Eq"
] | true |
Subgroup.hasDetOne_adjoinNegOne_iff | Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | [
"one_pow",
"Units.val",
"Eq.mpr",
"NegZeroClass.toNeg",
"MulOne.toOne",
"CommRing",
"Subgroup.HasDetOne",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Ring.toNonAssocRing",
"MonoidHom",
"Monoid.toMulOneClass",
"co... | true |
CategoryTheory.Limits.isColimitOfIsColimitCoforkMap | Mathlib.CategoryTheory.Limits.Preserves.Shapes.Equalizers | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.mapCocone",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"CategoryTheory.Limits.IsCo... | true |
_private.Mathlib.LinearAlgebra.Eigenspace.Basic.0.Module.End.genEigenspace_inf_le_add._simp_1_1 | Mathlib.LinearAlgebra.Eigenspace.Basic | [
"Submodule",
"Membership.mem",
"Submodule.mem_inf",
"AddCommMonoid",
"And",
"Submodule.instMin",
"Submodule.setLike",
"propext",
"Semiring",
"Module",
"Eq",
"SetLike.instMembership",
"Min.min"
] | false |
TopCat.Presheaf.generateEquivalenceOpensLe_inverse'._proof_1 | Mathlib.Topology.Sheaves.SheafCondition.OpensLeCover | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"CategoryTheory.Over",
"Exists.choose_spec",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instCompleteLattice",
"TopologicalSpace.Opens.instPartialOrder",
"iSup",
"PartialOrder.toPreorder",
"CategoryTheory.Objec... | false |
intrinsicClosure_diff_intrinsicFrontier | Mathlib.Analysis.Convex.Intrinsic | [
"Eq.mpr",
"frontier",
"intrinsicFrontier",
"intrinsicClosure",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"intrinsicInterior",
"Set.image_diff",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddCommGroup",
"id",
"Subtype",
"Subtype.coe_injective",
"AffineSubspace.instSetLike",
"Topolo... | true |
OrderIso.tendsto_atBot_iff._simp_1 | Mathlib.Order.Filter.AtTopBot.Map | [
"Preorder.toLE",
"OrderIso",
"instFunLikeOrderIso",
"Filter.Tendsto",
"OrderIso.tendsto_atBot_iff",
"propext",
"Filter.atBot",
"Eq",
"DFunLike.coe",
"Filter",
"Preorder"
] | false |
RootPairing.restrictScalars_toLinearMap_apply_apply | Mathlib.LinearAlgebra.RootSystem.BaseChange | [
"Submodule",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"AddMon... | true |
Lean.Elab.Tactic.NormCast.elabNormCastConfig | Lean.Elab.Tactic.NormCast | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.instMonadEnvOfMonadLift",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Term.instAddErrorMessageContextTermElabM",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.indentD",
"Lean.Meta.Simp.Nor... | true |
_private.Mathlib.Order.Atoms.0.isAtom_iff_le_of_ge._simp_1_1 | Mathlib.Order.Atoms | [
"And",
"Classical.not_imp",
"propext",
"Eq",
"Not"
] | false |
Polynomial.toFinsupp_ofNat | Mathlib.Algebra.Polynomial.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Polynomial.toFinsupp",
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"AddMonoidWithOne.toNatCast",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Polynomial",
"Nat",
"Semiring",
"AddMonoidAlgebra.nonAssocSemiring",
"AddMonoidAlgebra",
"OfNat.ofNat",
... | true |
_private.Mathlib.Data.List.TakeDrop.0.List.dropLast_drop_eq_drop_dropLast._proof_1_18 | Mathlib.Data.List.TakeDrop | [
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"getElem?_neg",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Int.Linear.norm_le",
"eq_false",
"Lean.Grind.CommRing.Expr.var",
"Int.Linear.Expr.eq_of_norm_eq",
"Option.ctorIdx",
... | false |
CategoryTheory.CosimplicialObject.δ_comp_δ' | Mathlib.AlgebraicTopology.SimplicialObject.Basic | [
"SimplexCategory.δ_comp_δ'",
"SimplexCategory.instOfNatToTypeOrderHomFinHAddNatLenOfNat._proof_1",
"instNeZeroNatHAdd_1",
"CategoryTheory.CosimplicialObject",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Fin.pred",
"congrArg",
"PartialOrder.toPreorder",
"CategoryTheory.CosimplicialObje... | true |
Aesop.VariableMap.erasePatSubst | Aesop.Forward.State | [
"Aesop.InstMap",
"Aesop.instBEqPremiseIndex",
"Aesop.InstMap.erasePatSubst",
"Lean.PersistentHashMap.map",
"Aesop.PremiseIndex",
"Aesop.SlotIndex",
"Aesop.Substitution",
"Aesop.VariableMap.map",
"Aesop.VariableMap",
"Aesop.instHashablePremiseIndex",
"Aesop.VariableMap.mk"
] | true |
CategoryTheory.Limits.PullbackCone.isLimitAux'._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limits.PullbackCone.fst",
"Subtype",
"CategoryTheory.Limits.Cone.pt",
"CategoryTheory.Limits.WalkingPair",
"And",
"And.left",
"CategoryTheory.Limits.cospan",
"CategoryTheor... | false |
CategoryTheory.FreeBicategory.Rel.below.rec | Mathlib.CategoryTheory.Bicategory.Free | [
"CategoryTheory.FreeBicategory.Hom.comp",
"CategoryTheory.FreeBicategory.Rel.below.id_whisker_left",
"CategoryTheory.FreeBicategory.Rel.below.whisker_right",
"CategoryTheory.FreeBicategory.Hom₂.vcomp",
"CategoryTheory.FreeBicategory.Rel.below.comp_id",
"CategoryTheory.FreeBicategory.Rel.below.associator_i... | false |
_private.Mathlib.Algebra.Group.Conj.0.isConj_iff.match_1_3 | Mathlib.Algebra.Group.Conj | [
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"Exists",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Inv.inv",
"Exists.casesOn",
"Exists.intro",
"In... | false |
approxAddOrderOf | Mathlib.NumberTheory.WellApproximable | [
"Real",
"SeminormedAddGroup.toAddGroup",
"SeminormedAddGroup",
"addOrderOf",
"setOf",
"Metric.thickening",
"AddGroup.toSubNegMonoid",
"SeminormedAddGroup.toPseudoMetricSpace",
"Nat",
"SubNegMonoid.toAddMonoid",
"Eq",
"PseudoMetricSpace.toPseudoEMetricSpace",
"Set"
] | true |
InformationTheory.klFun_nonneg | Mathlib.InformationTheory.KullbackLeibler.KLFun | [
"Real.instLE",
"Real",
"Real.instZero",
"Eq.rec",
"LE.le",
"Real.instOne",
"InformationTheory.isMinOn_klFun",
"InformationTheory.klFun_one",
"One.toOfNat1",
"Zero.toOfNat0",
"InformationTheory.klFun",
"OfNat.ofNat",
"Eq"
] | true |
MeasureTheory.SimpleFunc.setToSimpleFunc_sub | Mathlib.MeasureTheory.Integral.FinMeasAdditive | [
"MeasureTheory.SimpleFunc.instAdd",
"MeasureTheory.SimpleFunc.instAddGroup",
"Eq.mpr",
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"False",
"Real",
"MeasureTheory.Measure",
"Preorder.toLT",
"Pi.instNeg",
"NormedSpace",
"eq_false",
"congrArg",
"AddCommGroup.toAddCommMonoid",
... | true |
RingHomSurjective.ids | Mathlib.Algebra.Ring.CompTypeclasses | [
"RingHomSurjective.invPair",
"RingHomSurjective.mk",
"RingHomInvPair.ids",
"Semiring",
"RingHomSurjective",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"RingHomSurjective.is_surjective"
] | true |
_private.Mathlib.CategoryTheory.WithTerminal.Cone.0.CategoryTheory.WithInitial.coconeBack._proof_2 | Mathlib.CategoryTheory.WithTerminal.Cone | [
"Eq.mpr",
"CategoryTheory.instCategoryUnder",
"CategoryTheory.Functor",
"CategoryTheory.WithInitial.liftFromUnder",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.WithInitial.of",
"congrArg",
"CategoryTheory.Under.homMk",
"CategoryTheory.W... | false |
setOf_isOpen_sup | Mathlib.Topology.Order | [
"Lattice.toSemilatticeSup",
"setOf",
"CompleteLattice.toConditionallyCompleteLattice",
"TopologicalSpace.instCompleteLattice",
"SemilatticeSup.toMax",
"Set.instInter",
"Inter.inter",
"TopologicalSpace",
"Max.max",
"IsOpen",
"ConditionallyCompleteLattice.toLattice",
"Eq",
"rfl",
"Set"
] | true |
CategoryTheory.Mon.instCreatesLimitsForget | Mathlib.CategoryTheory.Monoidal.Internal.Limits | [
"CategoryTheory.CreatesLimitsOfSize.mk",
"CategoryTheory.CreatesLimitsOfShape",
"CategoryTheory.MonoidalCategory",
"inferInstance",
"CategoryTheory.CreatesLimits",
"CategoryTheory.Mon.forget",
"CategoryTheory.Mon",
"CategoryTheory.Mon.instCategory",
"CategoryTheory.Mon.instCreatesLimitsOfShapeForget... | true |
Ideal.relNorm_eq_bot_iff._simp_1 | Mathlib.RingTheory.Ideal.Norm.RelNorm | [
"IsDomain",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Module.IsTorsionFree",
"MonoidWithZeroHom.funLike",
"Algebra",
"Algebra.toModule",
"Algebra.id",
"NonUnitalNonAssocRing.toNonUnitalNonAssocS... | false |
Cardinal.cantorFunctionAux_nonneg | Mathlib.Analysis.Real.Cardinality | [
"Real.instIsOrderedRing",
"Eq.mpr",
"Real.partialOrder",
"Real.instLE",
"Real",
"IsOrderedRing.toPosMulMono",
"pow_nonneg",
"Real.instZero",
"Real.instZeroLEOneClass",
"instReflLe",
"congrArg",
"Cardinal.cantorFunctionAux_false",
"Std.le_refl._simp_1",
"Real.semiring",
"id",
"Real.inst... | true |
_private.Mathlib.Analysis.Normed.Group.Ultra.0.IsUltrametricDist.nnnorm_sum_eq_sup_of_pairwise_ne._proof_1_2 | Mathlib.Analysis.Normed.Group.Ultra | [
"False",
"Lean.Grind.nestedProof",
"eq_false",
"Lean.Grind.iff_eq",
"Finset.cons",
"Finset",
"Classical.byContradiction",
"Membership.mem",
"Eq.mp",
"id",
"Lean.Grind.eq_false_of_or_eq_false_right",
"Iff",
"SetLike.coe",
"Finset.instSetLike",
"True",
"eq_true",
"Or",
"Eq.symm",
"... | false |
_private.Batteries.Data.Char.AsciiCasing.0.Char.toUpper_toLower_eq_toUpper._simp_1_3 | Batteries.Data.Char.AsciiCasing | [
"ge_iff_le",
"GE.ge",
"LE.le",
"LE",
"propext",
"Eq"
] | false |
WithTop.top_pos | Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | [
"WithTop.coe_lt_top",
"WithTop.top",
"WithTop.instLT",
"LT.lt",
"Zero.toOfNat0",
"WithTop.zero",
"Top.top",
"OfNat.ofNat",
"LT",
"WithTop",
"Zero"
] | true |
_private.Init.Data.SInt.Lemmas.0.Int8.toInt64_ofNat._proof_1_1 | Init.Data.SInt.Lemmas | [
"instPowNat",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"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.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
... | false |
selfZPow_of_neg | Mathlib.RingTheory.Localization.Away.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"selfZPow",
"IsLocalization.Away",
"Algebra",
"Int.decLe",
"Preorder.toLE",
"RingHom",
"SemilatticeInf.toPartialOrder",
"Int",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"... | true |
CategoryTheory.ObjectProperty.instIsStableUnderFiniteProductsTrWOfIsTriangulated | Mathlib.CategoryTheory.Triangulated.Subcategory | [
"CategoryTheory.ObjectProperty.instIsTriangulatedIsoClosure",
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"Exists.choose_spec",
"CategoryTheory.Limits.HasProduct",
"CategoryTheory.Functor.preservesFiniteBiproductsOfAdditive",
"CategoryTheory.Limits.PreservesBiproductsOfShape.preserves",
"CategoryTheo... | true |
fixedPoints_addSubmonoid_sup | Mathlib.GroupTheory.GroupAction.FixingSubgroup | [
"OrderDual.toDual",
"Lattice.toSemilatticeSup",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"AddSubmonoid.toAddMonoid",
"CompleteLattice.toLattice",
"AddSubmonoid.instCompleteLattice",
"AddSubmonoid.addAction",
"AddMonoid.toAddZeroClass",
"fixingAddSubmonoid_fixedPoints_gc",
"Function.comp",
"M... | true |
Lean.OpaqueVal.noConfusionType | Lean.Declaration | [
"Lean.ConstantVal",
"Lean.Expr",
"List",
"Lean.OpaqueVal",
"Bool",
"Lean.Name",
"Lean.OpaqueVal.casesOn",
"Eq"
] | false |
Submonoid.groupPowers._proof_4 | Mathlib.Algebra.Group.Submonoid.Membership | [
"Monoid",
"MulOne.toOne",
"Semigroup.toMul",
"HMul.hMul",
"Monoid.toMulOneClass",
"SubmonoidClass.instPow",
"Membership.mem",
"Submonoid.groupPowers._proof_2",
"Submonoid.instSubmonoidClass",
"Subtype",
"Submonoid.toMonoid",
"Int",
"Nat.cast",
"Monoid.toPow",
"Submonoid.groupPowers._proo... | false |
StateT.run_monadMap | Init.Control.Lawful.Instances | [
"StateT.run",
"StateT.instMonadFunctor",
"MonadFunctorT",
"MonadFunctorT.monadMap",
"instMonadFunctorTOfMonadFunctor",
"StateT",
"Prod",
"Eq",
"rfl"
] | true |
AddSubsemigroup.inclusion.eq_1 | Mathlib.Algebra.Group.Subsemigroup.Operations | [
"AddSubsemigroup.instSetLike",
"AddHom",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddSubsemigroup.inclusion._proof_1",
"Membership.mem",
"AddSubsemigroup.instAddMemClass",
"Subtype",
"LE.le",
"AddSubsemigroup.inclusion",
"AddSubsemigroup.instPartialOrder",
"AddMemClass.add",
"AddSubsemig... | true |
Lean.Grind.CutsatConfig.reducible._inherited_default | Init.Grind.Config | [
"id",
"Bool.true",
"Bool"
] | false |
SimplexCategory.δ_σ₀Iter | Mathlib.AlgebraicTopology.SimplexCategory.DeltaZeroIter | [
"Fin.succAbove_of_le_castSucc",
"Fin.succAbove",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"SimplexCategory.coe_δ",
"Nat.instOrderedSub",
"Preorder.toLT",
"of_decide_eq_true",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Fin.succ",
"CategoryTheory.ConcreteCategory.comp_apply",
"... | true |
_private.Mathlib.Analysis.InnerProductSpace.Projection.Basic.0.Submodule.starProjection_comp_starProjection_eq_zero_iff._simp_1_1 | Mathlib.Analysis.InnerProductSpace.Projection.Basic | [
"ContinuousLinearMap.funLike",
"RingHom",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"ContinuousLinearMap.ext_iff",
"propext",
"Semiring",
"Module",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe"
] | false |
Submodule.involutivePointwiseNeg | Mathlib.Algebra.Module.Submodule.Pointwise | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"Submodule.pointwiseNeg",
"AddCommGroup",
"InvolutiveNeg",
"InvolutiveNeg.mk",
"Semiring",
"Module",
"Submodule.involutivePointwiseNeg._proof_1"
] | true |
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