name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
PadicInt.one_le_norm_iff | Mathlib.NumberTheory.Padics.PadicIntegers | [
"Norm.norm",
"Real.partialOrder",
"Real.instLE",
"Real",
"Nat.Prime",
"PadicInt",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Fact",
"LE.le",
"iff_self",
"Real.instOne",
"And",
"Iff",
"Nat",
"Subtype.prop",
"congr",
"True",
"_private.Mathlib.NumberTheory.Padics.Pad... | true |
Lean.Parser.«command__Builtin_cbv_simproc____(_):=_» | Init.CbvSimproc | [
"Lean.Name.mkStr3",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.Parser.cbvSimprocEval",
"Lean.ParserDescr.unary",
"Lean.Parser.Tactic.simpPre",
"Lean.ParserDescr.node",
"Nat",
"Lean.Parser.Tactic.simpPost",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.const",
"Lean.P... | true |
Std.ExtHashMap.size_empty | Std.Data.ExtHashMap.Lemmas | [
"Std.ExtDHashMap.size_empty",
"instOfNatNat",
"LawfulHashable",
"Std.ExtHashMap.size",
"Std.ExtHashMap",
"Std.ExtHashMap.instEmptyCollection",
"EquivBEq",
"Nat",
"Hashable",
"EmptyCollection.emptyCollection",
"OfNat.ofNat",
"BEq",
"Eq"
] | true |
CategoryTheory.Functor.prod_δ_snd | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.OplaxMonoidal.δ",
"CategoryTheory.Functor.prod",
"Prod.fst",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.Functor.OplaxMonoidal",
"Cate... | true |
Set.unbounded_lt_of_forall_exists_le | Mathlib.Order.Bounded | [
"Preorder.toLT",
"Preorder.toLE",
"Membership.mem",
"Exists",
"LE.le",
"_private.Mathlib.Order.Bounded.0.Set.unbounded_lt_of_forall_exists_le.match_1_1",
"And",
"And.intro",
"LT.lt",
"Set.Unbounded",
"Exists.intro",
"LT.lt.not_ge",
"Set.instMembership",
"Not",
"Preorder",
"Set"
] | true |
ball_add_closedBall | Mathlib.Analysis.Normed.Module.Ball.Pointwise | [
"Eq.mpr",
"Real.instLE",
"Real",
"SeminormedAddCommGroup",
"NormedAddGroup.to_isIsometricVAdd",
"NormedSpace",
"AddMonoid.toAddSemigroup",
"instVAddOfAdd",
"Real.instZero",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Metric.vadd_ball",
"Real.instLT",
"AddComm... | true |
Std.Tactic.BVDecide.BVExpr.decEq._proof_70 | Std.Tactic.BVDecide.Bitblast.BVExpr.Basic | [
"Std.Tactic.BVDecide.BVExpr.extract",
"False",
"congrArg",
"False.elim",
"Std.Tactic.BVDecide.BVExpr.ctorIdx",
"noConfusion_of_Nat",
"Std.Tactic.BVDecide.BVExpr.arithShiftRight",
"Nat",
"True",
"of_eq_true",
"Std.Tactic.BVDecide.BVExpr",
"not_false_eq_true",
"eq_false'",
"Eq",
"Not",
"... | false |
AddCommGrpCat.noConfusion | Mathlib.Algebra.Category.Grp.Basic | [
"HEq.refl",
"AddCommGrpCat.casesOn",
"AddCommGroup",
"AddCommGrpCat",
"AddCommGrpCat.noConfusionType",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq"
] | false |
Set.finite_zero | Mathlib.Algebra.Group.Pointwise.Set.Finite | [
"Set.Finite",
"Set.zero",
"Zero.toOfNat0",
"OfNat.ofNat",
"Set.finite_singleton",
"Zero",
"Set"
] | true |
SimplexCategory.instPathConnectedSpaceCarrierObjTopCatToTop | Mathlib.AlgebraicTopology.TopologicalSimplex | [
"TopCat.instCategory",
"ULift",
"continuous_uliftUp",
"SimplexCategory.instPathConnectedSpaceCarrierObjTopCatToTop₀",
"Function.Surjective.pathConnectedSpace",
"ULift.up_surjective",
"TopCat.str",
"SimplexCategory.toTop",
"TopCat.carrier",
"SimplexCategory",
"TopCat",
"SimplexCategory.smallCat... | true |
String.Slice.Pos.Down.mk | Init.Data.String.Termination | [
"String.Slice.Pos.Down.mk",
"String.Slice",
"String.Slice.Pos",
"String.Slice.Pos.Down"
] | true |
_private.Mathlib.Data.Matrix.Cartan.0.CartanMatrix.B_transpose._proof_1_3 | Mathlib.Data.Matrix.Cartan | [
"Lean.RArray.leaf",
"False",
"Lean.Grind.CommRing.Mon.mult",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"Lean.Grind.CommRing.Stepwise.simp",
"eq_false",
"Lean.Grind.CommRing.Poly.add",
"Lean.Grind.CommRing.Expr.var",
"Lean.Grind.instIsCharPNatOfNat",
"Classical.byContradiction",
"... | false |
Lean.Grind.CommRing.Expr.toPoly_k | Init.Grind.Ring.CommSolver | [
"instPowNat",
"Lean.Grind.CommRing.Mon.mult",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"Nat.beq",
"Int.instNegInt",
"instOfNatNat",
"Int",
"Int.instNatPow",
"Nat.cast",
"Lean.Grind.CommRing.Poly.mul",
"Lean.Grind.CommRing.Var",
"Lean.Grind.CommRing.Poly.mulConst_k",
"Lean.Gr... | true |
String.toList_mapAux | Init.Data.String.Lemmas.Modify | [
"String.toList_singleton",
"String.Pos.Splits",
"List.append_assoc",
"congrArg",
"String.toList_push",
"String",
"List.map",
"String.Pos.Splits.exists_eq_singleton_append",
"String.mapAux.induct_unfolding",
"String.Pos.pastModify",
"String.splits_endPos_iff._simp_1",
"String.Pos.Splits.pastMod... | true |
InnerProductSpace.toDual | Mathlib.Analysis.InnerProductSpace.Dual | [
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"Semiring.toModule",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"IsSemitopologicalRing.toIsSemitopologicalSemiring",... | true |
Tropical.instGroupTropical._proof_3 | Mathlib.Algebra.Tropical.Basic | [
"instHSMul",
"Int",
"zero_zsmul",
"Tropical",
"AddGroup",
"AddGroup.toSubNegMonoid",
"instOfNat",
"Tropical.instMonoidTropical",
"One.toOfNat1",
"HSMul.hSMul",
"Monoid.toOne",
"SubNegMonoid.toAddMonoid",
"OfNat.ofNat",
"Tropical.untrop_injective",
"Eq",
"Tropical.trop",
"Tropical.unt... | false |
Std.DHashMap.Equiv.of_forall_contains_unit_eq | Std.Data.DHashMap.Lemmas | [
"Std.DHashMap.Equiv",
"Std.DHashMap.Raw",
"LawfulBEq",
"Std.DHashMap.wf",
"Std.DHashMap.Internal.Raw₀.Const.equiv_of_forall_contains_unit_eq",
"instOfNatNat",
"Std.DHashMap.Equiv.mk",
"Subtype.mk",
"Std.DHashMap.contains",
"Unit",
"Std.DHashMap.inner",
"Nat",
"Std.DHashMap.Raw.buckets",
"L... | true |
OrthonormalBasis.measurePreserving_repr | Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace | [
"LinearIsometryEquiv.instEquivLike",
"MeasureTheory.MeasurePreserving",
"Pi.Function.module",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"WithLp.instModuleFinite",
"Semiring.toModule",
"measureSpaceOfInnerProductSpace",
"fact_one_le_two_ennreal",
"Orthonorm... | true |
CategoryTheory.MonoidalCategory.Arrow.PullbackHom.isTerminalIso_hom_left | Mathlib.CategoryTheory.Monoidal.PushoutProduct | [
"CategoryTheory.Limits.IsTerminal.from",
"CategoryTheory.Functor",
"CategoryTheory.Functor.PullbackObjObj.π",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.Arrow.PullbackHom.isTerminalIso._proof_2",
"CategoryTheory.Limits.IsTerminal",
"CategoryT... | true |
AlgebraicGeometry.Scheme.Pullback.t_snd_assoc | Mathlib.AlgebraicGeometry.Pullbacks | [
"AlgebraicGeometry.Scheme.Pullback.t",
"AlgebraicGeometry.Scheme.Pullback.v._proof_1",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.pullback",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"AlgebraicGeometry.Scheme.Pullback.v",
"CategoryTheory.CategoryStruct.toQuiver",
... | true |
TrivSqZeroExt.snd_smul | Mathlib.Algebra.TrivSqZeroExt.Basic | [
"TrivSqZeroExt.snd",
"instHSMul",
"TrivSqZeroExt",
"SMul",
"HSMul.hSMul",
"Eq",
"TrivSqZeroExt.smul",
"rfl"
] | true |
Filter.NeBot.comap_of_range_mem | Mathlib.Order.Filter.Map | [
"Filter.instMembership",
"Iff.mpr",
"Filter.NeBot",
"Membership.mem",
"Filter.Frequently",
"Filter.Eventually.frequently",
"Set.range",
"Filter.comap_neBot_iff_frequently",
"Set.instMembership",
"Filter",
"Filter.comap",
"Set"
] | true |
_private.Init.Data.List.ToArray.0.Array.insertIdxIfInBounds.eq_1 | Init.Data.List.ToArray | [
"Array.insertIdxIfInBounds",
"Array.insertIdx",
"LE.le",
"instLENat",
"dite",
"Array",
"Nat",
"Eq.refl",
"Eq",
"Array.size",
"Not",
"Nat.decLe"
] | true |
_private.Mathlib.NumberTheory.Chebyshev.0.Chebyshev.integral_1_div_log_sq_le | Mathlib.NumberTheory.Chebyshev | [
"Real.instIsOrderedRing",
"Mathlib.Tactic.FieldSimp.zpow'_one",
"div_le_div₀",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"InnerProductSpace.toNormedSpace",
"instDecidableNot",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tacti... | true |
Std.Http.Internal.ChunkedBuffer._sizeOf_1 | Std.Internal.Http.Internal.ChunkedBuffer | [
"ByteArray._sizeOf_inst",
"Std.Http.Internal.ChunkedBuffer.rec",
"instOfNatNat",
"Array._sizeOf_inst",
"Array",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"instSizeOfNat",
"ByteArray",
"Std.Http.Internal.ChunkedBuffer",
"OfNat.ofNat"
] | false |
Set.Finite.isOpen_sInter | Mathlib.Topology.Basic | [
"Eq.mpr",
"Set.sInter_empty",
"congrArg",
"Set.univ",
"Set.sInter_insert",
"Set.Finite",
"Membership.mem",
"Eq.mp",
"id",
"Insert.insert",
"Set.instInter",
"isOpen_univ",
"Inter.inter",
"TopologicalSpace",
"And",
"Set.Finite.induction_on",
"Set.instInsert",
"And.right",
"And.left... | true |
FourierTransform.«term𝓕⁻» | Mathlib.Analysis.Fourier.Notation | [
"instOfNatNat",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"OfNat.ofNat"
] | true |
Lean.Lsp.DocumentSymbolParams.recOn | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.TextDocumentIdentifier",
"Lean.Lsp.DocumentSymbolParams.mk",
"Lean.Lsp.DocumentSymbolParams.rec",
"Lean.Lsp.DocumentSymbolParams"
] | false |
Lean.Elab.Term.ToDepElimPattern.TopSort.State.mk | Lean.Elab.Match | [
"Lean.Elab.Term.ToDepElimPattern.TopSort.State.mk",
"Lean.Expr",
"Lean.MVarIdSet",
"Array",
"Lean.FVarIdSet",
"Lean.Elab.Term.ToDepElimPattern.TopSort.State"
] | true |
Turing.ListBlank.head | Mathlib.Computability.TuringMachine.Tape | [
"Turing.ListBlank.head._proof_1",
"Turing.ListBlank",
"Inhabited",
"List.headI",
"Turing.ListBlank.liftOn"
] | true |
Derivation.couple._proof_12 | Mathlib.RingTheory.Derivation.Lie | [
"CommRing",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.toModule",
"smulCommClass_self",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"CommRing.toCommSemiring",
"CommMonoid.toMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"CommSemiring.toCommMonoid",
"Monoid.toSemigroup",
"Module.... | false |
ENNReal.tsum_condensed_le | Mathlib.Analysis.PSeries | [
"Eq.mpr",
"ENNReal.instIsOrderedRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"ENNReal.instAdd",
"le_refl",
"Nat.instMulZeroClass",
"instHSMul",
"HMul.hMul",
"Finset.sum_condensed_le",
"ENNReal.instAddCommMonoid",
"Nat.ble",
"Nat.instNontrivial",
"congrArg",
"CommSemiring.toSemiring",
... | true |
Set.infsep_eq_iInf | Mathlib.Topology.MetricSpace.Infsep | [
"Iff.mpr",
"Eq.mpr",
"_private.Mathlib.Topology.MetricSpace.Infsep.0.Set.infsep_eq_iInf._simp_1_6",
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Real.partialOrder",
"Real.instLE",
"Set.offDiag_nonempty",
"Real",
"iInf",
"Real.instZero",
"lowerBounds",
"congrArg",
"_private.Mathlib.Topolog... | true |
QuadraticMap.IsOrtho.polar_eq_zero | Mathlib.LinearAlgebra.QuadraticForm.Basic | [
"Iff.mpr",
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"LinearMap.IsOrtho",
"QuadraticMap.polar",
"SubtractionMonoid.toSubNegZeroMonoid",
"QuadraticMap.isOrtho_polarBilin",
"QuadraticMap.instFunLike",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCom... | true |
_private.Init.Data.Array.Lemmas.0.Array.shrink.loop.eq_1 | Init.Data.Array.Lemmas | [
"_private.Init.Data.Array.Basic.0.Array.shrink.loop",
"instOfNatNat",
"Array",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
MonoidHom.CompTriple.instRootCompTriple | Mathlib.Algebra.Group.Hom.CompTypeclasses | [
"Monoid",
"Eq.mpr",
"MonoidHom.instFunLike",
"MonoidHom.coe_comp",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"Function.comp",
"MonoidHom.CompTriple.comp_eq",
"id",
"MonoidHom.CompTriple",
"MonoidHom.comp",
"MulOneClass.toMulOne",
"CompTriple",
"Eq.refl",
"CompTriple.mk",
"Eq.s... | true |
IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers.mem_units_iff_valued_eq_one | Mathlib.RingTheory.DedekindDomain.AdicValuation | [
"Int.instAddCommGroup",
"WithZero.instNontrivial",
"Multiplicative.group",
"Units.val",
"Eq.mpr",
"Int.instAddCommMonoid",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"SetLike.mem_coe._simp_1",
"_private.Mathlib.RingTheory.DedekindDomain.Ad... | true |
IsZLattice.mk._flat_ctor | Mathlib.Algebra.Module.ZLattice.Basic | [
"Submodule",
"IsZLattice.mk",
"NormedSpace",
"IsZLattice",
"AddCommGroup.toAddCommMonoid",
"DiscreteTopology",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField",
"Subtype",
"Int",
"Submodule.instTop",
"Field.toSemifield",
"NormedField",
... | false |
CategoryTheory.Functor.Monoidal.noConfusionType | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Monoidal.casesOn",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.LaxMonoidal.ε",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Functor.OplaxMonoidal.δ",
"CategoryTheory.Functo... | false |
IsGLB.ciInf_set_eq | Mathlib.Order.ConditionallyCompleteLattice.Indexed | [
"Lattice.toSemilatticeSup",
"iInf",
"PartialOrder.toPreorder",
"ConditionallyCompleteLattice",
"Preorder.toLE",
"Membership.mem",
"Eq.rec",
"Set.Elem",
"Set.image_eq_range",
"IsGLB.csInf_eq",
"Set.Nonempty",
"Set.Nonempty.image",
"IsGLB",
"Set.image",
"ConditionallyCompletePartialOrderSu... | true |
Algebra.SubmersivePresentation.exists_sum_eq_σ_jacobian_mul_σ_jacobian_inv_sub_one | Mathlib.RingTheory.Extension.Presentation.Core | [
"Algebra.Generators.ker",
"Finsupp.instAddZeroClass",
"Units.val",
"MulOne.toOne",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Algebra.Extension.commRing",
"MonoidHom.instFunLike",
"NonUnitalAlgSemiHomClass.toDistribMulActionSemiHomClass",
"Algebra.Generators.Ring",
"Semi... | true |
_private.Mathlib.Topology.Algebra.Valued.LocallyCompact.0.Valued.integer.norm_coe_unit._simp_1_1 | Mathlib.Topology.Algebra.Valued.LocallyCompact | [
"Real",
"NNReal",
"propext",
"Eq.symm",
"Eq",
"NNReal.toReal",
"NNReal.coe_inj"
] | false |
Vector.getElem?_insertIdx | Init.Data.Vector.InsertIdx | [
"instGetElem?OfGetElemOfDecidable",
"Vector.insertIdx_mk._proof_3",
"Array.insertIdx",
"Vector",
"congrArg",
"Vector.instGetElemNatLt",
"HSub.hSub",
"Option.some",
"Vector.casesOn",
"Eq.rec",
"instSubNat",
"instOfNatNat",
"Vector.getElem?_mk",
"LE.le",
"instLENat",
"Array",
"Option.n... | true |
CategoryTheory.IsFiltered.SmallFilteredIntermediate._proof_1 | Mathlib.CategoryTheory.Filtered.Small | [
"CategoryTheory.Functor",
"CategoryTheory.IsFiltered.instEssentiallySmallFullSubcategoryFilteredClosure",
"CategoryTheory.EssentiallySmall",
"CategoryTheory.IsFiltered.filteredClosure",
"CategoryTheory.ObjectProperty.FullSubcategory",
"CategoryTheory.ObjectProperty.FullSubcategory.category",
"CategoryTh... | false |
Std.TreeMap.toList_rii | Std.Data.TreeMap.Slice | [
"Pure.pure",
"Std.Slice.toList",
"Std.TreeMap.toList_rii._auto_1",
"Std.DTreeMap.Internal.Const.RiiSliceData",
"Monad.toApplicative",
"Std.Iterators.Types.Map.instIterator",
"MonadLiftT.monadLift",
"instMonadLiftT",
"Std.TreeMap.inner",
"Ordering",
"Std.Rii.mk",
"Prod.mk",
"Std.DTreeMap.inne... | true |
ValuationSubring.decompositionSubgroupMulSemiringAction._proof_5 | Mathlib.RingTheory.Valuation.RamificationGroup | [
"SubMulAction.mulAction",
"ValuationSubring.decompositionSubgroup",
"SubMulAction.instSetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"HMul.hMul",
"CommSemiring.toSemiring",
"Algebra",
"Membership.mem",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"AddCommMonoidWithOne.t... | false |
Congruent.comp_right_iff | Mathlib.Topology.MetricSpace.Congruence | [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"Function.comp",
"id",
"Congruent",
"PseudoEMetricSpace",
"Iff",
"congruent_comm",
"propext",
"Eq",
"Congruent.comp_left_iff",
"Isometry"
] | true |
Int.Linear.Poly.div._unsafe_rec | Init.Data.Int.Linear | [
"Int.instDiv",
"instHDiv",
"HDiv.hDiv",
"Int",
"Int.Linear.Var",
"Int.Linear.Poly.div._unsafe_rec",
"Int.Linear.Poly.num",
"Int.Linear.Poly.add",
"Int.Linear.cdiv",
"Int.Linear.Poly.denote.match_1",
"Int.Linear.Poly"
] | false |
CategoryTheory.Limits.reflectsLimitsOfShape_op | Mathlib.CategoryTheory.Limits.Preserves.Opposites | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.ReflectsColimitsOfShape",
"CategoryTheory.Limits.ReflectsLimitsOfShape",
"CategoryTheory.Category.opposite",
"CategoryTheory.Functor.leftOp",
"CategoryTheory.Limits.ReflectsLimitsOfShape.mk",
"CategoryTheory.Li... | true |
MulSemiringActionHom.ext | Mathlib.GroupTheory.GroupAction.Hom | [
"Monoid",
"MonoidHom",
"Monoid.toMulOneClass",
"DFunLike.ext",
"MulSemiringActionHom",
"MulOneClass.toMulOne",
"MulSemiringActionHom.instFunLike",
"MulSemiringAction",
"Semiring",
"Eq",
"DFunLike.coe"
] | true |
MeasureTheory.FiniteMeasure.testAgainstNN | Mathlib.MeasureTheory.Measure.FiniteMeasure | [
"MeasureTheory.FiniteMeasure",
"ENNReal.ofNNReal",
"BoundedContinuousFunction.instFunLike",
"NNReal",
"ENNReal.toNNReal",
"instPseudoMetricSpaceNNReal",
"MeasurableSpace",
"TopologicalSpace",
"MeasureTheory.FiniteMeasure.toMeasure",
"DFunLike.coe",
"BoundedContinuousFunction",
"MeasureTheory.l... | true |
NormedCommRing.toNonUnitalNormedCommRing._proof_11 | Mathlib.Analysis.Normed.Ring.Basic | [
"NormedCommRing.toNormedRing",
"Semigroup.toMul",
"Semigroup.mul_assoc",
"NormedRing.toRing",
"HMul.hMul",
"NormedCommRing",
"Semiring.toMonoid",
"Monoid.toSemigroup",
"Ring.toSemiring",
"Eq",
"instHMul"
] | false |
Ideal.map_eq_bot_iff_of_injective | Mathlib.RingTheory.Ideal.Maps | [
"Submodule.span_eq_bot._simp_1",
"Submodule",
"SetLike.mem_coe._simp_1",
"Semiring.toModule",
"congrArg",
"AddMonoid.toAddZeroClass",
"Set.mem_image._simp_1",
"Function.Injective.eq_iff",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"map_zero",
"Ideal.map",
"RingHomClass.toMonoidW... | true |
lt_mul_of_one_le_of_lt | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"MulOne.toOne",
"Trans.trans",
"Preorder.toLT",
"HMul.hMul",
"instTransLTLE",
"Preorder.toLE",
"MulOne.toMul",
"MulRightMono",
"LE.le",
"MulOneClass.toMulOne",
"LT.lt",
"mul_le_mul_left",
"One.toOfNat1",
"instTransEq_1",
"MulOneClass",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"one_mul",
... | true |
EquicontinuousAt.comp | Mathlib.Topology.UniformSpace.Equicontinuity | [
"Filter.instMembership",
"UniformSpace",
"uniformity",
"Function.comp",
"Membership.mem",
"nhds",
"Prod.mk",
"Filter.Eventually.mono",
"TopologicalSpace",
"EquicontinuousAt",
"Prod",
"Set.instMembership",
"Filter",
"Set"
] | true |
Matrix.instLieRingToLieAlgebra._aux_24 | Mathlib.Algebra.Lie.SerreConstruction | [
"LieAlgebra.toModule",
"CommRing",
"FreeLieAlgebra.instLieRing",
"LieRing.toAddCommGroup",
"LieSubmodule.Quotient.mk",
"Matrix",
"Bracket.bracket",
"LieSubmodule.toSubmodule",
"LieSubmodule",
"LieRingModule.toBracket",
"LieSubmodule.instHasQuotient",
"Int",
"CartanMatrix.Relations.toIdeal",
... | false |
UInt32.toUInt16_ofNat | Init.Data.UInt.Lemmas | [
"UInt32.toUInt16_ofNat'",
"UInt32.toUInt16",
"UInt16",
"Nat",
"UInt32",
"OfNat.ofNat",
"Eq",
"UInt32.instOfNat",
"UInt16.instOfNat"
] | true |
TensorProduct.range_mapIncl_mono | Mathlib.LinearAlgebra.TensorProduct.Map | [
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"TensorProduct.mapIncl",
"congrArg",
"CommSemiring.toSemiring",
"Submodule.addCommMonoid",
"TensorProduct.addCommMonoid",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"LinearMap.range",
"id",
"Subtype",
"Submodule.instParti... | true |
MeasureTheory.integrable_llr_tilted_right | Mathlib.MeasureTheory.Measure.LogLikelihoodRatio | [
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"MeasureTheory.integrable_congr",
"Real",
"MeasureTheory.Measure",
"Pi.instNeg",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"congrArg",
"IsSemitopologicalRing.toIsSemitopologicalSemiring",
"MeasureTheory.Integrable.neg"... | true |
CategoryTheory.Functor.OneHypercoverDenseData.essSurj.presheafObjObjIso.inv | Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | [
"CategoryTheory.Functor.PreOneHypercoverDenseData.multicospanIndex",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"Cate... | true |
ContinuousAlgEquiv.ext | Mathlib.Topology.Algebra.Algebra.Equiv | [
"Algebra",
"ContinuousAlgEquiv.equivLike",
"CommSemiring",
"TopologicalSpace",
"ContinuousAlgEquiv.toAlgEquiv_injective",
"AlgEquiv",
"AlgEquiv.ext",
"Semiring",
"ContinuousAlgEquiv",
"congr_fun",
"ContinuousAlgEquiv.toAlgEquiv",
"Eq",
"DFunLike.coe",
"AlgEquiv.instFunLike",
"EquivLike.t... | true |
Module.Free.shrink | Mathlib.LinearAlgebra.FreeModule.Basic | [
"LinearEquiv.symm",
"Shrink.instAddCommMonoid",
"AddCommMonoid",
"Module.Free",
"RingHomInvPair.ids",
"Module.Free.of_equiv",
"Shrink.linearEquiv",
"Semiring",
"Shrink",
"Module",
"Shrink.instModule",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Small"
] | true |
CategoryTheory.Functor.OplaxLeftLinear.δₗ_associativity_assoc | Mathlib.CategoryTheory.Monoidal.Action.LinearFunctor | [
"CategoryTheory.Functor.OplaxLeftLinear",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionAssocIso",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Monoi... | true |
Nonneg.mk_nnratCast | Mathlib.Algebra.Order.Nonneg.Field | [
"LinearOrder",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"NNRat.cast_nonneg",
"DistribLattice.toLattice",
"Semifield",
"Subtype",
"NNRat",
"LE.le",
"DivisionSemiring.toNNRatCast",
"Subtype.mk",
"Semifield.toDivisionSemiring",
"Non... | true |
_private.Mathlib.SetTheory.ZFC.Basic.0.ZFSet.map_isFunc.match_1_1 | Mathlib.SetTheory.ZFC.Basic | [
"ZFSet",
"Membership.mem",
"ZFSet.Definable₁",
"And.casesOn",
"And",
"ZFSet.pair",
"Exists.casesOn",
"ExistsUnique",
"And.intro",
"Exists.intro",
"Eq",
"ZFSet.instSetLike",
"SetLike.instMembership",
"ZFSet.map"
] | false |
MeasureTheory.Measure.add_left_inj | Mathlib.MeasureTheory.Measure.Typeclasses.SFinite | [
"Eq.mpr",
"MeasureTheory.Measure",
"congrArg",
"MeasureTheory.Measure.add_right_inj",
"MeasureTheory.SigmaFinite",
"Iff.rfl",
"id",
"add_comm",
"MeasurableSpace",
"MeasureTheory.Measure.instAddCommMonoid",
"instHAdd",
"Iff",
"HAdd.hAdd",
"MeasureTheory.Measure.instAdd",
"propext",
"Add... | true |
Std.ExtTreeSet.max! | Std.Data.ExtTreeSet.Basic | [
"Std.ExtTreeMap.maxKey!",
"Ordering",
"Std.ExtTreeSet.inner",
"Std.TransCmp",
"Unit",
"Std.ExtTreeSet",
"Inhabited"
] | true |
Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux | Mathlib.RingTheory.Etale.QuasiFinite | [
"_private.Mathlib.RingTheory.Etale.QuasiFinite.0.Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux._simp_1_8",
"Prime.irreducible",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Subalgebra.instSetLike",
"Iff.mpr",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"eq_sub_... | true |
Asymptotics.IsLittleOTVS.fst | Mathlib.Analysis.Asymptotics.TVS | [
"NormedCommRing.toSeminormedCommRing",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"AddMonoid.toAddZeroClass",
"Prod.instSMul",
"Asymptotics.IsLittleOTVS",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceProd",
"AddCommGroup.toAddGroup"... | true |
symmDiff.«term_∆_» | Mathlib.Order.SymmDiff | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
_private.Mathlib.Dynamics.Ergodic.Extreme.0.Ergodic.of_mem_extremePoints_measure_univ_eq._simp_1_4 | Mathlib.Dynamics.Ergodic.Extreme | [
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"mul_assoc",
"Eq.symm",
"Eq",
"instHMul"
] | false |
Int64.reduceBEq._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt.4041591762._hygCtx._hyg.3 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt | [
"Int64",
"instOfNatNat",
"instBEqOfDecidableEq",
"BEq.beq",
"Nat",
"Lean.Meta.Simp.DSimproc",
"instDecidableEqInt64",
"Lean.Name.mkStr2",
"OfNat.ofNat",
"Int64.reduceBoolPred._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.SInt.4041591762._hygCtx._hyg.3"
] | false |
CategoryTheory.Limits.diagonalObjPullbackFstIso._proof_10 | Mathlib.CategoryTheory.Limits.Shapes.Diagonal | [
"CategoryTheory.Limits.hasPullbackVertPaste",
"CategoryTheory.Limits.pullback",
"CategoryTheory.Limits.hasPullback_symmetry",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsPullback.instHasPullbackFst",
"CategoryTheory.Limits.pullback.snd",
"CategoryTheory.Limits.diagonalObj... | false |
AddGrpCat.Forget₂.createsLimit.eq_1 | Mathlib.Algebra.Category.Grp.Limits | [
"CategoryTheory.Limits.IsLimit.ofFaithful",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"AddGrpCat.Forget₂.createsLimit",
"CategoryTheory.Limits.Cone",
"AddMonCat.instConcreteCategoryAddMonoidHomCarrier",
"CategoryTheory.LiftsToLimit.mk",
"Equiv.instEquivLike",
"CategoryTheory.Limits.T... | true |
Polynomial.card_support_eq' | Mathlib.Algebra.Polynomial.EraseLead | [
"Finset.mem_univ",
"Eq.mpr",
"Polynomial.C",
"Finset.exists_ne_zero_of_sum_ne_zero",
"Finset.sum_eq_single_of_mem",
"_private.Mathlib.Algebra.Polynomial.EraseLead.0.Polynomial.card_support_eq'._simp_1_4",
"HMul.hMul",
"Finset.univ",
"congrArg",
"HEq.refl",
"Finset",
"AddMonoid.toAddZeroClass",... | true |
Set.iUnion_le_nat | Mathlib.Data.Set.Lattice | [
"Iff.mpr",
"le_refl",
"Set.subset_univ",
"Set.univ",
"setOf",
"Membership.mem",
"subset_antisymm",
"LE.le",
"instLENat",
"Set.instAntisymmSubset",
"Set.mem_setOf",
"Nat.instPreorder",
"Nat",
"Set.mem_iUnion_of_mem",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set.instHasSubset",
"... | true |
Std.DTreeMap.le_minKey | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.isEmpty",
"Ord.mk",
"Membership.mem",
"Ordering",
"Std.DTreeMap.minKey",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Std.DTreeMap.instMembership",
"Bool.true",
"Iff",
"Std.DTreeMap.wf",
"Bool",
"Std.DTreeMap.Internal.Impl.le_minKey",
"Ordering.isLE",
"Bool.fals... | true |
Submodule.localizedEquiv._proof_3 | Mathlib.Algebra.Module.LocalizedModule.Submodule | [
"Submodule",
"Submodule.module._proof_1",
"Semiring.toModule",
"instSMulOfMul",
"IsScalarTower.right",
"IsLocalization",
"LocalizedModule",
"OreLocalization.instAlgebra",
"Submodule.localized._proof_2",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"Submodule.... | false |
Std.DHashMap.Internal.IsHashSelf.casesOn | Std.Data.DHashMap.Internal.Defs | [
"Std.DHashMap.Internal.AssocList.toList",
"Std.DHashMap.Internal.IsHashSelf.rec",
"Array",
"GetElem.getElem",
"Array.instGetElemNatLtSize",
"Std.DHashMap.Internal.IsHashSelf.mk",
"Nat",
"LT.lt",
"Std.DHashMap.Internal.AssocList",
"Hashable",
"instLTNat",
"BEq",
"Std.DHashMap.Internal.IsHashS... | false |
CategoryTheory.GrpObj.ofIso_one | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.GrpObj.toMonObj",
"CategoryTheory.Iso",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.MonObj.one",
"CategoryTheory.GrpObj",
"CategoryTheory.Categor... | true |
Function.Periodic.lift._proof_1 | Mathlib.Algebra.Ring.Periodic | [
"QuotientAddGroup.leftRel_apply",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"instHSMul",
"add_eq_of_eq_neg_add",
"AddMonoid.toAddSemigroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Eq.mp",
"SubtractionMonoid.toSubNegZeroMonoid",
"Int",... | false |
Lean.Meta.Simp.Context.noConfusion | Lean.Meta.Tactic.Simp.Types | [
"Lean.Meta.SimpCongrTheorems",
"Lean.Meta.Simp.Config",
"Lean.Expr",
"Nat",
"Lean.Meta.ConfigWithKey",
"Bool",
"Eq.ndrec",
"Lean.Meta.Simp.Context",
"UInt32",
"Eq.refl",
"Lean.FVarIdSet",
"Eq",
"Lean.Meta.SimpTheoremsArray",
"Lean.Meta.Simp.Context.casesOn",
"Option",
"Lean.Meta.Simp.C... | false |
instIsWellFoundedTransGen | Mathlib.Order.RelClasses | [
"IsWellFounded.mk",
"IsWellFounded.wf",
"WellFounded.transGen",
"Relation.TransGen",
"IsWellFounded"
] | true |
CategoryTheory.ShortComplex.LeftHomologyData.IsPreservedBy.hf' | Mathlib.Algebra.Homology.ShortComplex.PreservesHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.ShortComplex.LeftHomologyData.f'",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.ShortComplex.LeftH... | true |
Int.Linear.Poly.getConst._unsafe_rec | Init.Data.Int.Linear | [
"Int",
"Int.Linear.Var",
"Int.Linear.Poly.getConst._unsafe_rec",
"Int.Linear.Poly.denote.match_1",
"Int.Linear.Poly"
] | false |
TopCat.isColimitCoconeOfForget._proof_1 | Mathlib.Topology.Category.TopCat.Limits.Basic | [
"ContinuousMap.continuous",
"Eq.mpr",
"CategoryTheory.Limits.IsColimit.fac",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Functor.mapCocone",
"Continuous",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"i... | false |
Std.DTreeMap.Raw.Const.minEntryD | Std.Data.DTreeMap.Raw.Basic | [
"Ordering",
"Std.DTreeMap.Raw.inner",
"Std.DTreeMap.Internal.Impl.Const.minEntryD",
"Prod",
"Std.DTreeMap.Raw"
] | true |
toDegLex | Mathlib.Data.Finsupp.MonomialOrder.DegLex | [
"Equiv",
"DegLex",
"Equiv.refl"
] | true |
Multiset.pi._proof_2 | Mathlib.Data.Multiset.Pi | [
"Eq.mpr",
"Multiset.bind_hcongr",
"Multiset.bind_bind",
"Multiset.map",
"Multiset.cons_swap",
"Multiset.Pi.cons_swap",
"congrArg",
"Multiset.map_bind",
"Function.comp",
"Membership.mem",
"Multiset",
"Multiset.cons",
"id",
"HEq.rfl",
"Multiset.map_hcongr",
"dite",
"Multiset.instMember... | false |
_private.Std.Time.DateTime.PlainDateTime.0.Std.Time.PlainDateTime.ofTimestampAssumingUTC._proof_17 | Std.Time.DateTime.PlainDateTime | [
"of_decide_eq_true",
"Int.decLe",
"id",
"instDecidableEqBool",
"Int.ofNat",
"instOfNatNat",
"Int",
"LE.le",
"Bool.true",
"instOfNat",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Decidable.decide",
"Eq",
"Int.instLEInt",
"ite"
] | false |
Finset.cons_subset_cons._simp_1 | Mathlib.Data.Finset.Insert | [
"Finset.cons_subset_cons",
"Finset.cons",
"Finset",
"Membership.mem",
"HasSubset.Subset",
"Finset.instSetLike",
"propext",
"Finset.instHasSubset",
"Eq",
"Not",
"SetLike.instMembership"
] | false |
_private.Mathlib.Util.Qq.0.Qq.findLocalDeclWithTypeQ?.match_1 | Mathlib.Util.Qq | [
"Option.ctorIdx",
"Option.some",
"_private.Mathlib.Util.Qq.0.Qq.getLevelQ'._sparseCasesOn_1",
"Lean.FVarId",
"Nat.hasNotBit",
"Option"
] | false |
LatticeCon.ker_r | Mathlib.Order.Lattice.Congruence | [
"Lattice",
"Function.onFun",
"LatticeHomClass",
"LatticeCon.ker",
"Eq.refl",
"LatticeCon.toSetoid",
"Eq",
"DFunLike.coe",
"Setoid.r",
"FunLike"
] | true |
HomologicalComplex.extend.hasHomology | Mathlib.Algebra.Homology.Embedding.ExtendHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.extend.homologyData'",
"HomologicalComplex.HasHomology",
"HomologicalComplex",
"ComplexShape.prev",
"HomologicalComplex.extend",
"ComplexShape",
"HomologicalComplex.sc",
"CategoryTheory.ShortComplex.HasHomology.mk'",
"ComplexShape.next"... | true |
RootPairing.Hom.coweightMap | Mathlib.LinearAlgebra.RootSystem.Hom | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"LinearMap",
"RootPairing.Hom",
"CommRing.toCommSemiring",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"RootPairing"
] | true |
_private.Mathlib.Analysis.Calculus.FDeriv.Equiv.0.hasFDerivWithinAt_comp_smul_iff_smul._simp_1_1 | Mathlib.Analysis.Calculus.FDeriv.Equiv | [
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"IsBoundedSMul.toUniformConti... | false |
_private.Std.Time.Format.Basic.0.Std.Time.formatWith.match_29 | Std.Time.Format.Basic | [
"Std.Time.TypeFormat",
"Std.Time.Fraction",
"Std.Time.Modifier.V",
"Std.Time.ZoneName",
"Std.Time.Modifier.F",
"Std.Time.Modifier.m",
"Std.Time.Modifier.O",
"Std.Time.Modifier.Qorq",
"Std.Time.Modifier.E",
"Std.Time.Modifier.d",
"Std.Time.Year",
"Std.Time.Modifier.N",
"Std.Time.Modifier.w",
... | false |
MonoidHom.commute_noncommPiCoprod | Mathlib.GroupTheory.NoncommPiCoprod | [
"Monoid",
"MonoidHom.noncommPiCoprod._proof_3",
"Commute.mul_right",
"MonoidHom.instFunLike",
"Finset.univ",
"MonoidHom",
"Monoid.toMulOneClass",
"Finset",
"Commute",
"Membership.mem",
"Finset.noncommProd_induction",
"id",
"MulOne.toMul",
"Pi.mulOneClass",
"MulOneClass.toMulOne",
"Fint... | true |
CategoryTheory.Oplax.OplaxTrans.Hom.of._flat_ctor | Mathlib.CategoryTheory.Bicategory.Modification.Oplax | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Oplax.OplaxTrans.Hom",
"CategoryTheory.Oplax.OplaxTrans.Hom.of",
"CategoryTheory.Bicategory",
"CategoryTheory.Oplax.OplaxTrans.categoryStruct",
"CategoryTheory.OplaxFunctor",
"CategoryTheory.Oplax.OplaxTrans.Modification"
] | false |
Int.natCast_nonneg._simp_1 | Init.Data.Int.Order | [
"Int",
"LE.le",
"Nat.cast",
"instOfNat",
"Nat",
"True",
"eq_true",
"instNatCastInt",
"OfNat.ofNat",
"Eq",
"Int.instLEInt",
"Int.natCast_nonneg"
] | false |
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