name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
GroupExtension.Equiv.toMulEquiv_eq_coe | Mathlib.GroupTheory.GroupExtension.Defs | [
"Monoid.toMulOneClass",
"GroupExtension.Equiv.toMulEquiv",
"GroupExtension.Equiv.instEquivLike",
"Group",
"MulOne.toMul",
"GroupExtension.Equiv.instMulEquivClass",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"GroupExtension.Equiv",
"MulEquiv",
"Eq",
"MulEquivClas... | true |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Search.0.Lean.Meta.Grind.Arith.Cutsat.processVar.match_6 | Lean.Meta.Tactic.Grind.Arith.Cutsat.Search | [
"Lean.Meta.Grind.Arith.Cutsat.FindIntValResult.found",
"Nat.hasNotBit",
"Int",
"Lean.Meta.Grind.Arith.Cutsat.FindIntValResult",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Search.0.Lean.Meta.Grind.Arith.Cutsat.processVar._sparseCasesOn_6",
"Lean.Meta.Grind.Arith.Cutsat.FindIntValResult.ctorIdx"
] | false |
AddCircle.liftIoc_eq_lift_Icc | Mathlib.Topology.Instances.AddCircle.Defs | [
"Eq.mpr",
"Preorder.toLT",
"Equiv.instEquivLike",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"AddCircle.equivIccQuot",
"Function.comp",
"SemilatticeInf.toPartialOrder",
"Fact",
"AddCommGroup",
"Set.Elem",
"DistribLattice.toLattice",
"Quot.lift",... | true |
LinearMap.exact_zero_iff_injective | Mathlib.Algebra.Exact | [
"Function.Exact",
"Submodule",
"RingHomSurjective.ids",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"LinearMap.range_zero",
"AddMonoid.toAddZeroClass",
"LinearMap.ker",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"LinearMap.range",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid... | true |
ONote.scale_opowAux | Mathlib.SetTheory.Ordinal.Notation | [
"ONote.NF",
"HMul.hMul",
"Ordinal.omega0",
"MulZeroClass.toMul",
"ONote.instZero",
"Nat.brecOn",
"ONote.scale_opowAux._f",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"ONote.repr",
"Nat",
"Ordinal.monoidWithZero",
"Zero.toOfNat0",
"instHPow",
"MulZeroOneClass.toMulZeroClass",
"ONo... | true |
_private.Mathlib.AlgebraicTopology.SimplexCategory.ToMkOne.0.SimplexCategory.toMk₁_surjective._simp_1_8 | Mathlib.AlgebraicTopology.SimplexCategory.ToMkOne | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"not_lt",
"LT.lt",
"propext",
"LinearOrder.toPartialOrder",
"Eq",
"Not"
] | false |
_private.Lean.Meta.ReduceEval.0.Lean.Meta.evalName | Lean.Meta.ReduceEval | [
"Inhabited.default",
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Meta.instInhabitedMetaM",
"Lean.Name"
] | true |
CategoryTheory.MorphismProperty.HasFunctorialFactorization.mk._flat_ctor | Mathlib.CategoryTheory.MorphismProperty.Factorization | [
"CategoryTheory.MorphismProperty.FunctorialFactorizationData",
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.HasFunctorialFactorization.mk",
"CategoryTheory.MorphismProperty.HasFunctorialFactorization",
"Nonempty",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Categor... | false |
ringChar.eq | Mathlib.Algebra.CharP.Defs | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"CharP.existsUnique",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Classical.choose_spec",
"And",
"NonAssocSemiring",
"And.right",
"ringChar",
"Nat",
"Classical.choose",
"CharP",
"Eq.symm",
"Eq"
] | true |
Set.nontrivial_of_lt | Mathlib.Data.Set.Subsingleton | [
"Preorder.toLT",
"Membership.mem",
"Exists",
"Ne",
"And",
"And.intro",
"LT.lt",
"Exists.intro",
"Set.Nontrivial",
"ne_of_lt",
"Set.instMembership",
"Preorder",
"Set"
] | true |
upperBounds_union | Mathlib.Order.Bounds.Basic | [
"Set.Subset.antisymm",
"Preorder.toLE",
"Membership.mem",
"Set.instUnion",
"upperBounds",
"LE.le",
"Set.instInter",
"Inter.inter",
"And.right",
"And.left",
"And.intro",
"Or.inl",
"Union.union",
"Or.elim",
"Eq",
"Set.instMembership",
"Or.inr",
"Preorder",
"Set"
] | true |
_private.Mathlib.Algebra.Order.Monoid.Canonical.Basic.0.Set.range_add_eq_image_Ici.match_1_3 | Mathlib.Algebra.Order.Monoid.Canonical.Basic | [
"Set.Ici",
"PartialOrder.toPreorder",
"Membership.mem",
"PartialOrder",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"Set.image",
"Eq",
"Set.instMembership",
"Set"
] | false |
CategoryTheory.CommMon.forget₂Mon_obj_one | Mathlib.CategoryTheory.Monoidal.CommMon_ | [
"CategoryTheory.CommMon.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.BraidedCategory",
"CategoryTheory.CommMon.forget₂Mon",
"CategoryTheory.MonObj.one",
"CategoryTheory.Mon",
"CategoryTheory.Mon.X",
"CategoryTheory.Mon.in... | true |
_private.Init.Data.String.Lemmas.Pattern.String.Basic.0.String.Slice.Pattern.Model.ForwardSliceSearcher.isLongestRevMatchAt_iff_splits._simp_1_1 | Init.Data.String.Lemmas.Pattern.String.Basic | [
"String.Slice.slice",
"String.instLEPos_1",
"String",
"String.Slice",
"Exists",
"LE.le",
"String.Slice.copy",
"instAppendString",
"instHAppendOfAppend",
"And",
"propext",
"String.Slice.Pos",
"String.Slice.copy_slice_eq_iff_splits",
"Eq",
"HAppend.hAppend",
"String.Slice.Pos.Splits"
] | false |
UInt64.reduceAdd._regBuiltin.UInt64.reduceAdd.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt.4002762760._hygCtx._hyg.33 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt | [
"IO",
"UInt64.reduceAdd",
"Bool.true",
"Unit",
"Sum.inr",
"Lean.Meta.Simp.DSimproc",
"Lean.Name.mkStr2",
"Lean.Meta.Simp.addSimprocBuiltinAttr",
"Lean.Meta.Simp.Simproc"
] | false |
Metric.frontier_closedBall_subset_sphere | Mathlib.Topology.MetricSpace.Pseudo.Lemmas | [
"frontier",
"Real",
"continuous_const",
"PseudoMetricSpace.toUniformSpace",
"continuous_id'",
"Continuous.dist",
"HasSubset.Subset",
"instOrderTopologyReal",
"OrderTopology.to_orderClosedTopology",
"PseudoMetricSpace",
"frontier_le_subset_eq",
"Real.pseudoMetricSpace",
"Dist.dist",
"Pseudo... | true |
MeasureTheory.OuterMeasure.restrict._proof_1 | Mathlib.MeasureTheory.OuterMeasure.Operations | [
"CommSemiring.toSemiring",
"RingHomCompTriple",
"ENNReal.instCommSemiring",
"ENNReal",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring"
] | false |
ContT.run | Mathlib.Control.Monad.Cont | [
"ContT"
] | true |
Lean.Lsp.ClientCapabilities._sizeOf_1 | Lean.Data.Lsp.Capabilities | [
"Lean.Lsp.LeanClientCapabilities",
"Lean.Lsp.WindowClientCapabilities._sizeOf_inst",
"Option._sizeOf_inst",
"Lean.Lsp.ClientCapabilities",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Lean.Lsp.TextDocumentClientCapabilities._sizeOf_inst",
"SizeOf.sizeOf",
"instAddNat",
"Lean.Lsp.LeanClient... | false |
Filter.bot_sets_eq | Mathlib.Order.Filter.Basic | [
"Set.univ",
"Filter.sets",
"Bot.bot",
"Eq",
"Filter",
"rfl",
"Filter.instBot",
"Set"
] | true |
HahnSeries.min_orderTop_le_orderTop_add | Mathlib.RingTheory.HahnSeries.Addition | [
"HahnSeries.support",
"Iff.mpr",
"Eq.mpr",
"instReflLe",
"WithTop.instPreorder",
"congrArg",
"inf_of_le_left",
"le_top._simp_2",
"LinearOrder",
"HahnSeries.orderTop",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Classical.propDecidable",
"Preorder.toLE",
"Std.le_refl._simp_1",... | true |
Pell.IsPell.eq_1 | Mathlib.NumberTheory.PellMatiyasevic | [
"HMul.hMul",
"HSub.hSub",
"Int",
"Int.instMul",
"instHSub",
"instOfNat",
"Zsqrtd.mk",
"Eq.refl",
"Int.instSub",
"OfNat.ofNat",
"Eq",
"Pell.IsPell",
"instHMul"
] | true |
USize.not_not | Init.Data.UInt.Bitwise | [
"congrArg",
"USize.toBitVec_not",
"instComplementUSize",
"BitVec",
"BitVec.not_not",
"_private.Init.Data.UInt.Bitwise.0.USize.not_not._simp_1_1",
"System.Platform.numBits",
"USize.toBitVec",
"True",
"Complement.complement",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.trans",
"BitVe... | true |
CoxeterMatrix.I._proof_4 | Mathlib.GroupTheory.Coxeter.Matrix | [
"False",
"Equiv.instEquivLike",
"of_decide_eq_true",
"congrArg",
"Matrix",
"Matrix.of",
"instDecidableEqFin",
"Equiv",
"Ne",
"instOfNatNat",
"Decidable.not_not._simp_1",
"ite_eq_left_iff._simp_1",
"imp_self._simp_1",
"Nat.Simproc.add_eq_gt",
"Bool.true",
"instHAdd",
"HAdd.hAdd",
"i... | false |
PredOrder.prelimitRecOn_pred_of_not_isMin | Mathlib.Order.SuccPred.Limit | [
"Eq.mpr",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"PredOrder.prelimitRecOn._proof_2",
"congrArg",
"LinearOrder",
"WellFoundedGT",
"PartialOrder.toPreorder",
"PredOrder.prelimitRecOn._proof_3",
"Classical.propDecidable",
"Preorder.toLE",
"cast",
"Function.comp",
"Exists",
"Order.not_... | true |
Finset.sup_disjSum | Mathlib.Data.Finset.Lattice.Fold | [
"Finset.fold_disjSum",
"instCommutativeMax_mathlib",
"instAssociativeMax_mathlib",
"congrArg",
"Finset",
"OrderBot.toBot",
"Finset.fold",
"PartialOrder.toPreorder",
"Preorder.toLE",
"bot_sup_eq",
"OrderBot",
"SemilatticeSup.toMax",
"Sum",
"id",
"Sum.inl",
"Bot.bot",
"Sum.inr",
"Max... | true |
_private.Init.Data.List.Sort.Lemmas.0.List.mergeSort.eq_def | Init.Data.List.Sort.Lemmas | [
"instHDiv",
"List.merge",
"_private.Init.Data.List.Sort.Basic.0.List.mergeSort.match_1",
"_private.Init.Data.List.Sort.Basic.0.List.mergeSort._proof_3",
"Subtype",
"HDiv.hDiv",
"_private.Init.Data.List.Sort.Basic.0.List.mergeSort.eq_def",
"instOfNatNat",
"Prod.fst",
"List.cons",
"Subtype.mk",
... | true |
NormedAddGroupHom.norm_eq_of_isometry | Mathlib.Analysis.Normed.Group.Hom | [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Real",
"NormedAddGroupHom",
"SeminormedAddCommGroup",
"NormedAddGroupHom.funLike",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"SeminormedAddCommGroup.toNorm",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"SeminormedAddGroup.toPseudoMetricSpace",
"A... | true |
PosNum.bit0.elim | Mathlib.Data.Num.Basic | [
"PosNum.ctorIdx",
"PULift.up",
"PosNum.ctorElim",
"PosNum.bit0",
"Nat",
"PosNum",
"Eq.symm",
"Eq"
] | false |
MulAction.injective | Mathlib.Algebra.Group.Action.Basic | [
"instHSMul",
"MulAction.bijective",
"Group",
"DivInvMonoid.toMonoid",
"Function.Bijective.injective",
"Group.toDivInvMonoid",
"MulAction",
"Monoid.toSemigroup",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"Function.Injective",
"MulAction.toSemigroupAction"
] | true |
CategoryTheory.Functor.IsCartesian.mk._flat_ctor | Mathlib.CategoryTheory.FiberedCategory.Cartesian | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.IsHomLift",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Functor.IsCartesian",
"And",
"ExistsUnique",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
... | false |
Int.Linear.norm_eq_cert.eq_1 | Init.Data.Int.Linear | [
"Int.Linear.norm_eq_cert",
"Int.Linear.Poly.beq'",
"Int.Linear.Expr",
"Int.Linear.Expr.norm",
"Bool",
"Eq.refl",
"Eq",
"Int.Linear.Poly",
"Int.Linear.Expr.sub"
] | true |
_private.Mathlib.Analysis.Convex.Topology.0.diff_singleton_eventually_mem_nhds_left.match_1_1 | Mathlib.Analysis.Convex.Topology | [
"Set.Ioi",
"LinearOrder",
"PartialOrder.toPreorder",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Set.instInter",
"Inter.inter",
"And.casesOn",
"And.intro",
"Set.Iio",
"Set.instMembership",
"instDistribLatticeOfLinearOrder",
"Lattice.toSemilatticeInf",
... | false |
Finset.biUnion_nonempty | Mathlib.Data.Finset.Union | [
"Eq.mpr",
"congrArg",
"Finset",
"Finset.mem_biUnion._simp_1",
"Membership.mem",
"Exists",
"exists_and_left._simp_1",
"id",
"Finset.biUnion",
"iff_self",
"funext",
"And",
"Iff",
"exists_comm",
"Finset.instSetLike",
"True",
"propext",
"Finset.Nonempty",
"of_eq_true",
"congrFun'",... | true |
ProbabilityTheory.IsLocalizingSequence.min | Mathlib.Probability.Process.LocalProperty | [
"MeasureTheory.ae",
"OrderTopology",
"MeasureTheory.Measure",
"ProbabilityTheory.IsPreLocalizingSequence.isStoppingTime",
"WithTop.instPreorder",
"TopologicalSpace.instOrderTopologyWithTop",
"Monotone.min",
"MeasureTheory.IsStoppingTime.min",
"Pi.instMinForall_mathlib",
"LinearOrder",
"PartialOr... | true |
_private.Mathlib.Topology.Compactness.Compact.0.finite_cover_nhds_interior.match_1_1 | Mathlib.Topology.Compactness.Compact | [
"Finset",
"Set.univ",
"Membership.mem",
"Exists",
"HasSubset.Subset",
"TopologicalSpace",
"Exists.casesOn",
"Finset.instSetLike",
"interior",
"Exists.intro",
"Set.iUnion",
"SetLike.instMembership",
"Set.instHasSubset",
"Set"
] | false |
Multiset.rel_flip | Mathlib.Data.Multiset.ZeroCons | [
"Multiset",
"flip",
"_private.Mathlib.Data.Multiset.ZeroCons.0.Multiset.rel_flip_aux",
"Multiset.Rel",
"Iff",
"Iff.intro"
] | true |
IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_mem | Mathlib.RingTheory.DedekindDomain.AdicValuation | [
"Eq.mpr",
"Int.instAddCommMonoid",
"Multiplicative.linearOrder",
"Int.instIsStrictOrderedRing",
"CommRing",
"Preorder.toLT",
"Dvd.dvd",
"Semiring.toModule",
"IsScalarTower.right",
"congrArg",
"CommSemiring.toSemiring",
"Int.instLinearOrder",
"Submodule.instNonUnitalSemiring",
"Iff.rfl",
... | true |
SemimoduleCat.comp_apply | Mathlib.Algebra.Category.ModuleCat.Semi | [
"SemimoduleCat.isModule",
"SemimoduleCat.moduleCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"SemimoduleCat.isAddCommMonoid",
"CategoryTheory.ConcreteCategory.hom",
"LinearMap.instFunLike",
"SemimoduleCat",
"LinearMap",
"SemimoduleCat.carrier",
"SemimoduleCat.instConcreteCat... | true |
Lean.KVMap.findCore._f | Lean.Data.KVMap | [
"Option.some",
"instDecidableEqBool",
"Prod.mk",
"List.cons",
"_private.Lean.Data.KVMap.0.Lean.KVMap.findCore.match_1",
"Bool.true",
"Option.none",
"List",
"BEq.beq",
"Bool",
"List.below",
"Lean.Name",
"Lean.DataValue",
"Prod",
"Eq",
"Lean.Name.instBEq",
"List.nil",
"Option",
"it... | false |
Std.TreeSet.Raw.Equiv.getLED_eq | Std.Data.TreeSet.Raw.Lemmas | [
"Std.TreeSet.Raw.WF.out",
"Ordering",
"Std.TreeSet.Raw.getLED",
"Std.TransCmp",
"Std.TreeSet.Raw",
"Unit",
"Std.TreeSet.Raw.Equiv.inner",
"Std.TreeSet.Raw.Equiv",
"Std.TreeMap.Raw.Equiv.getKeyLED_eq",
"Std.TreeSet.Raw.inner",
"Eq",
"Std.TreeSet.Raw.WF"
] | true |
ContinuousMap.curry._proof_3 | Mathlib.Topology.CompactOpen | [
"Continuous",
"ContinuousMap.continuous_postcomp",
"ContinuousMap",
"Continuous.comp",
"instTopologicalSpaceProd",
"ContinuousMap.comp",
"Function.comp",
"ContinuousMap.continuous_coev",
"TopologicalSpace",
"ContinuousMap.coev",
"Prod",
"ContinuousMap.compactOpen"
] | false |
CategoryTheory.Abelian.SpectralObject.δ_toCycles_assoc | Mathlib.Algebra.Homology.SpectralObject.Cycles | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Abelian.SpectralObject.cycles",
"CategoryTheory.Abelian.SpectralObject.δ_toCycles",
"CategoryTheory.Abelian.SpectralObject.δToCycles",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Abelian.SpectralObject.H",
"Part... | true |
toMeromorphicNFOn_eqOn_codiscrete | Mathlib.Analysis.Meromorphic.NormalForm | [
"Filter.instMembership",
"dite_cond_eq_true",
"Iff.mpr",
"NormedCommRing.toSeminormedCommRing",
"NormedSpace",
"congrArg",
"ite_self",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"Classical.propDecidable",
"Membership.mem",
"MeromorphicOn.analyticAt_mem_codiscreteWithin",
"Filter.mp_mem",
... | true |
_private.Lean.Meta.Tactic.Grind.Arith.Linear.OfNatModule.0.Lean.Meta.Grind.Arith.Linear.isZeroInst | Lean.Meta.Tactic.Grind.Arith.Linear.OfNatModule | [
"Lean.Meta.Sym.isSameExpr",
"Lean.Expr.appArg!",
"Lean.Expr",
"Lean.Meta.Grind.Arith.Linear.NatStruct",
"Bool",
"Lean.Meta.Grind.Arith.Linear.NatStruct.zero"
] | true |
_private.Mathlib.Tactic.Translate.Core.0.Mathlib.Tactic.Translate.applyReplacementFun.visitApp._sparseCasesOn_5 | Mathlib.Tactic.Translate.Core | [
"Lean.Name.rec",
"Nat.ne_of_beq_eq_false",
"String",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Name.num",
"Lean.Name.ctorIdx",
"Lean.Name.str",
"Lean.Name.anonymous",
"Nat.land",
"Nat",
"Bool",
"Lean.Name",
"Eq.refl",
"OfNat.ofNat",
"Bool.false"
] | false |
CategoryTheory.CoreSmallCategoryOfSet.recOn | Mathlib.CategoryTheory.SmallRepresentatives | [
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Set.Elem",
"Equiv",
"CategoryTheory.CoreSmallCategoryOfSet",
"CategoryTheory.CoreSmallCategoryOfSet.mk",
"CategoryTheory.Category.toCategoryStruct",
"DFunLike.coe",
"EquivLike.toFunLike",
"CategoryTheory.Category",
... | false |
IsLocalization.atOne._proof_1 | Mathlib.RingTheory.Localization.Away.Basic | [
"MulOne.toOne",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"IsUnit",
"CommSemiring",
"MulOneClass.toMulOne",
"isUnit_one",
"Semiring.toMonoid",
"One.toOfNat1",
"OfNat.ofNat"
] | false |
Eq.subst | Init.Prelude | [
"Eq.ndrec",
"Eq"
] | true |
Std.HashMap.getElem!_union_of_not_mem_left | Std.Data.HashMap.Lemmas | [
"Std.DHashMap.Const.get!_union_of_not_mem_left",
"Membership.mem",
"Std.HashMap",
"Std.HashMap.instUnion",
"LawfulHashable",
"EquivBEq",
"Inhabited",
"Hashable",
"Union.union",
"Std.HashMap.instGetElem?Mem",
"Std.HashMap.inner",
"BEq",
"Eq",
"GetElem?.getElem!",
"Not",
"Std.HashMap.ins... | true |
_private.Mathlib.AlgebraicTopology.SimplicialSet.Horn.0.SSet.horn_obj_zero._simp_1_2 | Mathlib.AlgebraicTopology.SimplicialSet.Horn | [
"Membership.mem",
"Set.instSingletonSet",
"Set.mem_singleton_iff",
"propext",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Set"
] | false |
LinearIsometry.id | Mathlib.Analysis.Normed.Operator.LinearIsometry | [
"LinearIsometry",
"LinearMap.id",
"LinearIsometry.id._proof_1",
"SeminormedAddCommGroup",
"AddCommGroup.toAddCommMonoid",
"LinearIsometry.mk",
"SeminormedAddCommGroup.toAddCommGroup",
"Semiring",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | true |
_private.Mathlib.Data.List.Sym.0.List.map_mk_disjoint_sym2._simp_1_1 | Mathlib.Data.List.Sym | [
"Sym2.mk",
"Membership.mem",
"List.mk_mem_sym2_iff",
"List",
"And",
"List.sym2",
"List.instMembership",
"propext",
"Eq",
"Sym2"
] | false |
_private.Lean.Util.CollectAxioms.0.Lean.CollectAxioms.State | Lean.Util.CollectAxioms | [
"_private.Lean.Util.CollectAxioms.0.Lean.CollectAxioms.State.mk"
] | true |
CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.hasLiftingProperty_mk_isInitial_isTerminal_iff | Mathlib.CategoryTheory.LiftingProperties.PushoutProduct | [
"CategoryTheory.HasLiftingProperty",
"Eq.mpr",
"CategoryTheory.Limits.IsTerminal.from",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.PreservesLimitsOfShape.preservesLimit",
"CategoryTheory.MonoidalCategory.Arrow.pushoutProduct",... | true |
Real.dist_le_of_mem_Icc | Mathlib.Topology.MetricSpace.Pseudo.Real | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Real.instLE",
"Real",
"neg_sub",
"Real.lattice",
"abs",
"congrArg",
"Set.Icc_subset_uIcc",
"Real.instSub",
"covariant_swap_add_of_covariant_add",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"Membership.mem",... | true |
_private.Mathlib.SetTheory.Cardinal.SchroederBernstein.0.Function.Embedding.total.match_1_5 | Mathlib.SetTheory.Cardinal.SchroederBernstein | [
"cond",
"ULift",
"Exists",
"Nonempty.intro",
"Function.Embedding",
"Bool.true",
"Bool.casesOn",
"Exists.casesOn",
"Nonempty.casesOn",
"Exists.intro",
"Bool",
"Nonempty",
"Bool.false"
] | false |
CategoryTheory.Limits.biproduct.map_matrix_assoc | Mathlib.CategoryTheory.Preadditive.Biproducts | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.biproduct.map",
"Finite",
"CategoryTheory.Limits.HasFiniteBiproducts",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.Preadditive",
"CategoryTheory.... | true |
CategoryTheory.Grp.rightUnitor_hom_hom | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.Grp.instMonoidalCategoryStruct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Grp.rightUnitor_hom_hom_hom",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"CategoryTheory.Mon.Hom.hom",
"CategoryTheory.Grp.instCategory",
"CategoryTheory.SemiCartesianMono... | true |
_private.Lean.Meta.Tactic.Grind.Arith.Linear.Search.0.Lean.Meta.Grind.Arith.Linear.getBestLower?.match_6 | Lean.Meta.Tactic.Grind.Arith.Linear.Search | [
"Lean.Grind.Linarith.Poly.ctorIdx",
"Nat.hasNotBit",
"Int",
"Lean.Grind.Linarith.Var",
"_private.Lean.Meta.Tactic.Grind.Arith.Linear.Search.0.Lean.Meta.Grind.Arith.Linear.getBestLower?._sparseCasesOn_6",
"Lean.Grind.Linarith.Poly.add",
"Lean.Grind.Linarith.Poly"
] | false |
Fin.univ_castSuccEmb | Mathlib.Data.Fintype.Basic | [
"Finset.insert_compl_self",
"Finset.univ",
"Finset.cons",
"congrArg",
"Compl.compl",
"Finset",
"instDecidableEqFin",
"Finset.map",
"Membership.mem",
"BooleanAlgebra.toCompl",
"Insert.insert",
"instOfNatNat",
"Finset.cons.congr_simp",
"Finset.instInsert",
"Fin.fintype",
"Function.Embedd... | true |
_private.Batteries.CodeAction.Misc.0.Batteries.CodeAction.addSubgoalsActionCore.match_5 | Batteries.CodeAction.Misc | [
"Option.ctorIdx",
"Option.some",
"Lean.Syntax",
"Nat.hasNotBit",
"_private.Batteries.CodeAction.Misc.0.Batteries.CodeAction.instanceStub.collectFields._sparseCasesOn_1",
"Option"
] | false |
LT.lt.ne_zero | Mathlib.Algebra.Order.IsBotOne | [
"Preorder.toLT",
"ne_zero_of_lt",
"Preorder.toLE",
"Ne",
"IsBotZeroClass",
"LT.lt",
"Zero.toOfNat0",
"OfNat.ofNat",
"Preorder",
"Zero"
] | true |
_private.Lean.Meta.Tactic.Backtrack.0.Lean.Meta.Tactic.Backtrack.Backtrack.run.match_5.eq_1 | Lean.Meta.Tactic.Backtrack | [
"_private.Lean.Meta.Tactic.Backtrack.0.Lean.Meta.Tactic.Backtrack.Backtrack.run.match_5",
"Option.some",
"Lean.MVarId",
"Option.none",
"List",
"Unit",
"Eq.refl",
"Eq",
"Option"
] | true |
CategoryTheory.ShortComplex.LeftHomologyMapData.add_φH | Mathlib.Algebra.Homology.ShortComplex.Preadditive | [
"CategoryTheory.ShortComplex.LeftHomologyMapData.add",
"CategoryTheory.ShortComplex.LeftHomologyMapData",
"CategoryTheory.ShortComplex.instAddHom",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Sh... | true |
Differential.ext | Mathlib.RingTheory.Derivation.DifferentialRing | [
"Derivation",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"HEq.refl",
"Differential",
"Eq.casesOn",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Int",
"NonUnitalNonAssocSemiring.toAddCommM... | true |
ContinuousLinearEquiv.continuousAlternatingMapCongrRight._proof_6 | Mathlib.Topology.Algebra.Module.Alternating.Topology | [
"NormedCommRing.toNormedRing",
"ContinuousLinearMap.compContinuousAlternatingMapCLM",
"Continuous",
"NormedRing.toRing",
"ContinuousLinearMap.topologicalSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"ContinuousAlternatingMap.instContinuousCo... | false |
MeasureTheory.definition._@.Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic.3112114093._hygCtx._hyg.44 | Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic | [
"Real",
"MeasureTheory.Measure",
"MeasurableSpace.instLE",
"NormedSpace",
"MeasureTheory.AEEqFun.cast",
"MeasureTheory.SigmaFinite",
"MeasureTheory.Measure.trim",
"PseudoMetricSpace.toUniformSpace",
"MeasureTheory.condExpL1",
"MeasureTheory.aestronglyMeasurable_condExpL1",
"Classical.propDecidab... | false |
Aesop.RuleTacOutput.mk.injEq | Aesop.RuleTac.Basic | [
"Eq.propIntro",
"Aesop.RuleTacOutput.mk",
"Array",
"Aesop.RuleTacOutput.mk.inj",
"Aesop.RuleApplication",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Aesop.RuleTacOutput"
] | true |
CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_snd | Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.BinaryFan.fst",
"CategoryTheory.IsIso",
"CategoryTheory.Limits.BinaryFan",
"CategoryTheory.Limits.IsTerminal",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingPair.right",
"CategoryTheory.Limits.BinaryFan.mk",
"Nonempty.some",
"Cate... | true |
Mathlib.Tactic.BicategoryLike.MkEvalComp.mk | Mathlib.Tactic.CategoryTheory.Coherence.Normalize | [
"Mathlib.Tactic.BicategoryLike.NormalExpr",
"Lean.Expr",
"Mathlib.Tactic.BicategoryLike.Structural",
"Mathlib.Tactic.BicategoryLike.MkEvalComp.mk",
"Mathlib.Tactic.BicategoryLike.WhiskerLeft",
"Mathlib.Tactic.BicategoryLike.MkEvalComp"
] | true |
one_add_one_eq_two | Mathlib.Data.Nat.Cast.Defs | [
"Eq.mpr",
"of_decide_eq_true",
"AddMonoid.toAddSemigroup",
"congrArg",
"Nat.instAtLeastTwoHAddOfNat",
"id",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"Nat.cast",
"Nat.cast_add",
"AddMonoidWithOne.toOne",
"Bool.true",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Nat.instNeZeroSuc... | true |
List.foldlRecOn.match_1 | Init.Data.List.Lemmas | [
"Membership.mem",
"List.cons",
"List",
"List.instMembership",
"List.casesOn",
"List.nil"
] | false |
Lean.Meta.Grind.Arith.CommRing.isSubInst | Lean.Meta.Tactic.Grind.Arith.CommRing.Reify | [
"Pure.pure",
"Monad.toApplicative",
"Lean.Meta.Sym.isSameExpr",
"Lean.Expr.appArg!",
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Meta.Grind.Arith.CommRing.getSubFn",
"MonadLiftT",
"Applicative.toPure",
"Lean.MonadError",
"Bool",
"Monad.toBind",
"Bind.bind",
"Lean.Meta.Grind.Arith.CommRing.MonadR... | true |
instIsAdicCompleteMaximalIdealOfIsArtinianRing | Mathlib.RingTheory.AdicCompletion.Noetherian | [
"SModEq.bot",
"Eq.mpr",
"Submodule",
"CommRing",
"instHSMul",
"Semiring.toModule",
"IsArtinianRing",
"IsScalarTower.right",
"instIsNoetherianRingOfIsArtinianRing",
"congrArg",
"CommSemiring.toSemiring",
"SMulWithZero.toSMulZeroClass",
"AddCommGroup.toAddCommMonoid",
"IsAdicComplete.mk",
... | true |
fderivWithin_comp_of_eq' | Mathlib.Analysis.Calculus.FDeriv.Comp | [
"ContinuousLinearMap.comp",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"UniqueDiffWithinAt",
"NormedField.toField",
"Field.toSemifield",
"ContinuousLinearMap",
"fderivWithin",
"Semifield.toDivisionSemiring",
"SeminormedAddCommGrou... | true |
Polynomial.definition._@.Mathlib.Algebra.Polynomial.Smeval.3997496041._hygCtx._hyg.2 | Mathlib.Algebra.Polynomial.Smeval | [
"Pow",
"AddMonoid.toAddZeroClass",
"Polynomial.sum",
"AddZeroClass.toAddZero",
"MulActionWithZero",
"Polynomial.smul_pow",
"Polynomial",
"AddCommMonoid",
"AddZero.toZero",
"Nat",
"Semiring",
"AddCommMonoid.toAddMonoid",
"Semiring.toMonoidWithZero"
] | false |
le_neg_add_of_add_le | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"AddMonoid.toAddZeroClass",
"AddLeftMono",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"LE.le",
"SubNegZeroMonoid.toNegZeroClass",
"LE",
"instHAdd",
"AddGroup",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
... | true |
Std.ExtDTreeMap.contains_alter_of_not_compare_eq | Std.Data.ExtDTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.ExtDTreeMap.alter",
"Ordering",
"Ordering.eq",
"Std.TransCmp",
"Std.ExtDTreeMap.contains",
"Std.DTreeMap.contains_alter_of_not_compare_eq",
"Std.LawfulEqCmp",
"Std.ExtDTreeMap.inductionOn",
"Std.ExtDTreeMap",
"Bool",
"Eq",
"Not",
"Option"
] | true |
CochainComplex.HomComplex.Cochain.rightUnshift_neg | Mathlib.Algebra.Homology.HomotopyCategory.HomComplexShift | [
"AddEquivClass.instAddMonoidHomClass",
"NegZeroClass.toNeg",
"HomologicalComplex.instCategory",
"CochainComplex.HomComplex.instAddCommGroupCochain",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"CochainCom... | true |
pow_mul_le_of_le_of_pow_mul_le | Mathlib.Analysis.Distribution.TemperateGrowth | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"zpow_natCast",
"AddGroup.toSubtractionMonoid",
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"mul_nonneg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Real.one_le_r... | true |
MulOpposite.instNonAssocRing._proof_6 | Mathlib.Algebra.Ring.Opposite | [
"MulOpposite.instAddCommGroupWithOne",
"MulOpposite",
"IntCast.intCast",
"AddCommGroup.toAddGroup",
"instOfNatNat",
"NonAssocRing",
"AddCommGroupWithOne.intCast_negSucc",
"Nat.cast",
"NonAssocRing.toAddCommGroupWithOne",
"instHAdd",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"Nat",
"SubNegMon... | false |
Aesop.UnionFind.merge | Aesop.Util.UnionFind | [
"Aesop.UnionFind",
"Inhabited.default",
"Aesop.instInhabitedUnionFind",
"Pi.instInhabited",
"Hashable",
"BEq"
] | true |
Topology.WithUpper.isOpen_preimage_ofUpper | Mathlib.Topology.Order.LowerUpperTopology | [
"Topology.WithUpper.instTopologicalSpace",
"Equiv.instEquivLike",
"TopologicalSpace.IsOpen",
"Iff.rfl",
"Topology.WithUpper",
"Equiv",
"Topology.upper",
"Iff",
"Set.preimage",
"IsOpen",
"DFunLike.coe",
"Topology.WithUpper.ofUpper",
"Preorder",
"EquivLike.toFunLike",
"Set"
] | true |
Plausible.PrintableProp.ctorIdx | Plausible.Testable | [
"Nat",
"Plausible.PrintableProp"
] | false |
_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.Clz.0.Std.Tactic.BVDecide.BVExpr.bitblast.blastClz.go_denote_eq._simp_1_2 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.Clz | [
"instOfNatNat",
"instHAdd",
"And",
"HAdd.hAdd",
"Nat",
"propext",
"instAddNat",
"OfNat.ofNat",
"Eq",
"Nat.add_eq_zero_iff"
] | false |
WeierstrassCurve.Jacobian.Point.mk.inj | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Point | [
"CommRing",
"WeierstrassCurve.Jacobian.Point.mk.noConfusion",
"WeierstrassCurve.Jacobian.NonsingularLift",
"WeierstrassCurve.Jacobian.Point.mk",
"WeierstrassCurve.Jacobian",
"WeierstrassCurve.Jacobian.Point",
"WeierstrassCurve.Jacobian.PointClass",
"eq_of_heq",
"HEq",
"Eq"
] | true |
Lean.Widget.RpcEncodablePacket.mk.injEq._@.Lean.Server.FileWorker.WidgetRequests.2734021171._hygCtx._hyg.1 | Lean.Server.FileWorker.WidgetRequests | [
"Lean.Json",
"Lean.Widget.RpcEncodablePacket.mk.inj._@.Lean.Server.FileWorker.WidgetRequests.2734021171._hygCtx._hyg.1",
"Eq.propIntro",
"Lean.Widget.RpcEncodablePacket._@.Lean.Server.FileWorker.WidgetRequests.2734021171._hygCtx._hyg.1",
"Lean.injEq_helper",
"And",
"Eq.ndrec",
"Eq.refl",
"Lean.Widge... | false |
SheafOfModules.GeneratingSections.IsFiniteType.rec | Mathlib.Algebra.Category.ModuleCat.Sheaf.Generators | [
"AddCommGrpCat.instCategory",
"Finite",
"AddMonoid.toAddZeroClass",
"RingCat.ring",
"AddCommGroup.toAddGroup",
"RingHom",
"AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier",
"SheafOfModules.GeneratingSections",
"AddZeroClass.toAddZero",
"RingCat.instConcreteCategoryRingHomCarrier",
"AddComm... | false |
SemigroupIdeal.mem_closure' | Mathlib.Algebra.Group.Ideal | [
"Semigroup",
"SubMulAction.instSetLike",
"SemigroupIdeal",
"Eq.mpr",
"_private.Mathlib.Algebra.Group.Ideal.0.SemigroupIdeal.mem_closure'._simp_1_1",
"Semigroup.toMul",
"instSMulOfMul",
"HMul.hMul",
"congrArg",
"Set.mem_univ._simp_1",
"Set.univ",
"SemigroupIdeal.coe_closure",
"Membership.mem"... | true |
_private.Mathlib.Analysis.Complex.Hadamard.0.Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStrip₀₁'._simp_1_8 | Mathlib.Analysis.Complex.Hadamard | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
SymmetricAlgebra.algHom_surjective | Mathlib.LinearAlgebra.SymmetricAlgebra.Basic | [
"TensorAlgebra.SymRel",
"RingQuot.mkAlgHom_surjective",
"SymmetricAlgebra",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"RingQuot.instSemiring",
"SymmetricAlgebra.algHom._proof_1",
"Algebra.id",
"SymmetricAlgebra.algHom",
"TensorAlgebra",
"instSemiringTensorAlgebra",
"IsScalarTowe... | true |
Lean.Lsp.TextDocumentRegistrationOptions.documentSelector?._default | Lean.Data.Lsp.Basic | [
"Lean.Lsp.DocumentSelector",
"id",
"Option.none",
"Option"
] | false |
Std.Ric.forIn'_eq_forIn'_toArray | Init.Data.Range.Polymorphic.Lemmas | [
"Std.Iter.forIn'_eq_forIn'_toArray",
"Std.Iter.instForIn'",
"Std.Rxc.Iterator",
"Std.Rxc.Iterator.instLawfulIteratorLoop",
"Std.Ric.Internal.isPlausibleIndirectOutput_iter_iff",
"Std.PRange.UpwardEnumerable",
"Array.forIn'_congr",
"congrArg",
"Std.Rxc.Iterator.instIteratorLoop",
"_private.Init.Dat... | true |
CategoryTheory.Limits.HasBiproductsOfShape.has_biproduct | Mathlib.CategoryTheory.Limits.Shapes.Biproducts | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.HasBiproduct",
"CategoryTheory.Limits.HasBiproductsOfShape",
"CategoryTheory.Category"
] | true |
Homeomorph.piEquivPiSubtypeProd | Mathlib.Topology.Homeomorph.Lemmas | [
"Homeomorph.mk",
"Pi.topologicalSpace",
"instTopologicalSpaceProd",
"Equiv",
"Subtype",
"Homeomorph.piEquivPiSubtypeProd._proof_1",
"TopologicalSpace",
"DecidablePred",
"Homeomorph",
"Equiv.piEquivPiSubtypeProd",
"Prod",
"Subtype.val",
"Homeomorph.piEquivPiSubtypeProd._proof_3",
"Not"
] | true |
ContinuousLinearMap.coe_mk' | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic | [
"Continuous",
"ContinuousLinearMap.mk",
"ContinuousLinearMap.funLike",
"LinearMap.instFunLike",
"RingHom",
"LinearMap.toAddHom",
"LinearMap",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"Semiring",
"AddCommSemigroup.toAddCommMagma",
"Module",
"AddCommMonoid.toAddCommSemigro... | true |
tendsto_prod_uniformity_fst | Mathlib.Topology.UniformSpace.Basic | [
"UniformSpace",
"instUniformSpaceProd",
"Filter.map_mono",
"Filter.map",
"Filter.instCompleteLatticeFilter",
"uniformity",
"PartialOrder.toPreorder",
"CompleteLattice.toConditionallyCompleteLattice",
"Prod.mk",
"Prod.fst",
"Filter.Tendsto",
"inf_le_left",
"UniformSpace.comap",
"Conditional... | true |
BiheytingAlgebra.mk.noConfusion | Mathlib.Order.Heyting.Basic | [
"BiheytingAlgebra",
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"id",
"LE.le",
"HNot.hnot",
"GeneralizedHeytingAlgebra.toOrderTop",
"SDiff.sdiff",
"heq_of_eq",
"Iff",
"BiheytingAlgebra.mk",
"OrderTop.toTop",
"HNot",
"Max.max",
"Gene... | false |
Polynomial.fiberEquivQuotient._simp_1 | Mathlib.RingTheory.LocalRing.ResidueField.Polynomial | [
"RingHom.instRingHomClass",
"RingHom.comap_ker",
"RingHom",
"Ideal",
"RingHom.comp",
"RingHom.instFunLike",
"Ideal.comap",
"Semiring",
"Eq.symm",
"Semiring.toNonAssocSemiring",
"Eq",
"RingHom.ker"
] | false |
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