name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.Limits.Cowedge.ext._proof_3 | Mathlib.CategoryTheory.Limits.Shapes.End | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.WalkingMultispan",
"CategoryTheory.Limits.MultispanShape.L",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Limits.multispanIndexCoend",
"Quiver.Hom",
"CategoryTheory.Limits.multispan... | false |
_private.Mathlib.CategoryTheory.EffectiveEpi.Comp.0.CategoryTheory.effectiveEpiFamilyStructCompIso_aux._proof_1_1 | Mathlib.CategoryTheory.EffectiveEpi.Comp | [
"CategoryTheory.Category.assoc",
"False",
"eq_false",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Classical.byContradiction",
"Lean.Grind.eq_false_of_imp_eq_true",
"Eq.mp",
"id",
"True",
"CategoryTheory.CategoryStruct.comp",
"eq_true",
"Eq.refl",
"CategoryTheory.... | false |
CategoryTheory.PreGaloisCategory.autMap_comp | Mathlib.CategoryTheory.Galois.GaloisObjects | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Function.comp",
"CategoryTheory.PreGaloisCategory.comp_autMap",
"id",
"CategoryTheory.PreGaloisCategory.IsConnected",
"CategoryTheory.PreGaloisCategory.IsGalois",
"funext",
"Category... | true |
_private.Mathlib.Order.Filter.AtTopBot.Interval.0.Finset.tendsto_Icc_atBot_prod_atTop._simp_1_1 | Mathlib.Order.Filter.AtTopBot.Interval | [
"Filter.Eventually",
"Preorder.toLE",
"LE.le",
"Filter.tendsto_atTop",
"Filter.atTop",
"Filter.Tendsto",
"propext",
"Eq",
"Filter",
"Preorder"
] | false |
CategoryTheory.Limits.FormalCoproduct.eval._proof_9 | Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.FormalCoproduct.eval._proof_5",
"CategoryTheory.Functor",
"CategoryTheory.Limits.FormalCoproduct.eval._proof_2",
"CategoryTheory.Limits.FormalCoproduct",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuive... | false |
_private.Mathlib.Data.Multiset.MapFold.0.Multiset.exists_multiset_eq_map_quot_mk.match_1_1 | Mathlib.Data.Multiset.MapFold | [
"Multiset.map",
"Exists",
"Multiset",
"Exists.casesOn",
"Exists.intro",
"Quot",
"Eq",
"Quot.mk"
] | false |
instGroupLex.eq_1 | Mathlib.Algebra.Order.Group.Synonym | [
"Lex",
"Group",
"instGroupLex",
"Eq.refl",
"Eq"
] | true |
Std.TreeMap.Raw.Equiv.keyAtIdxD_eq | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.WF.out",
"Std.TreeMap.Raw.keyAtIdxD",
"Std.TreeMap.Raw.Equiv.inner",
"Ordering",
"Std.TreeMap.Raw.Equiv",
"Std.DTreeMap.Raw.Equiv.keyAtIdxD_eq",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"Nat",
"Eq"
] | true |
AlgebraicGeometry.SheafedSpace.IsOpenImmersion.ofRestrict | Mathlib.Geometry.RingedSpace.OpenImmersion | [
"AlgebraicGeometry.SheafedSpace.IsOpenImmersion",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.SheafedSpace",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.i... | true |
CategoryTheory.Functor.commShiftIso_hom_naturality | Mathlib.CategoryTheory.Shift.CommShift | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Functor.map",
"CategoryTheory.NatTrans.naturality",
"AddMonoid",
"CategoryTheory.CategoryStruct.comp",
... | true |
Lean.instBEqSourceInfo_lean | Lean.Syntax | [
"Lean.instBEqSourceInfo_lean.beq",
"Lean.SourceInfo",
"BEq.mk",
"BEq"
] | true |
Lean.ConstructorVal.cidx | Lean.Declaration | [
"Lean.ConstructorVal",
"Nat"
] | true |
_private.Lean.Meta.Basic.0.Lean.Meta.fvarsSizeLtMaxFVars.match_1 | Lean.Meta.Basic | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Nat",
"Option"
] | false |
Algebra.Generators.ofComp.eq_1 | Mathlib.RingTheory.Extension.Generators | [
"Finsupp.instAddZeroClass",
"Nat.instMulZeroClass",
"CommRing",
"Algebra.Generators.Ring",
"Algebra.Generators.comp",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra.Generators.ofComp._proof_1",
"AddMonoid.toAddZeroClass",
"MvPolynomial.X",
"Algebra",
"Nat.instAddMonoid",
"RingHom",
"... | true |
RpcEncodablePacket._@.Mathlib.Tactic.Widget.Calc.1713132172._hygCtx._hyg.1 | Mathlib.Tactic.Widget.Calc | [
"RpcEncodablePacket.mk._@.Mathlib.Tactic.Widget.Calc.1713132172._hygCtx._hyg.1"
] | false |
CategoryTheory.Iso.app._proof_4 | Mathlib.CategoryTheory.NatIso | [
"CategoryTheory.Functor",
"_private.Mathlib.CategoryTheory.NatIso.0.CategoryTheory.Iso.app._proof_3",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso",
"CategoryTheory.CategoryStruct.comp",
"CategoryTh... | false |
KaehlerDifferential.polynomialEquiv._proof_5 | Mathlib.RingTheory.Kaehler.Polynomial | [
"CommRing",
"CommSemiring.toSemiring",
"Polynomial",
"RingHomInvPair",
"CommRing.toCommSemiring",
"Polynomial.semiring",
"RingHomInvPair.ids",
"RingHom.id",
"Semiring.toNonAssocSemiring"
] | false |
Lean.Elab.Tactic.simpOnlyBuiltins | Lean.Elab.Tactic.Simp | [
"List.cons",
"List",
"Lean.Name",
"Lean.Name.mkStr1",
"List.nil"
] | true |
Option.attachWith.match_1 | Init.Data.Option.Attach | [
"Option.casesOn",
"Option.some",
"Option.none",
"Eq",
"Option"
] | false |
_private.Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic.0.DomMulAct.dist_smul_Lp._simp_1_1 | Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic | [
"DomMulAct",
"instHSMul",
"MeasureTheory.Measure",
"SMul",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddSubgroup.neg",
"Subtype",
"DomMulAct.smul_Lp_neg",
"MeasureTheory.Lp",
"MeasureTheory.AEEqFun",
"AddSubgroup",
"MeasurableSpace",
"MeasureTheory... | false |
SimpleGraph.neighborFinset_def | Mathlib.Combinatorics.SimpleGraph.Finite | [
"Finset",
"SimpleGraph.neighborFinset",
"SimpleGraph.neighborSet",
"Set.Elem",
"Set.toFinset",
"SimpleGraph",
"Fintype",
"Eq",
"rfl"
] | true |
Std.Internal.List.minKeyD_insertEntryIfNew_le_minKeyD | Std.Data.Internal.List.Associative | [
"Std.Internal.List.DistinctKeys",
"Ord",
"congrArg",
"Std.TransOrd",
"Std.Internal.List.insertEntryIfNew",
"Ordering",
"Eq.mp",
"Std.Internal.List.minKey_eq_minKeyD",
"Std.Internal.List.minKeyD",
"Ord.compare",
"Bool.true",
"List",
"List.isEmpty",
"congr",
"Bool",
"Std.LawfulBEqOrd",
... | true |
extDeriv_apply_vectorField | Mathlib.Analysis.Calculus.DifferentialForm.VectorField | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"ContinuousAlternatingMap.instAddCommGroup._proof_7",
"instHSMul",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"Finset.univ",
"NormedSpace",
"Fin.succ",
... | true |
NonUnitalSubsemiring.mem_iInf._simp_1 | Mathlib.RingTheory.NonUnitalSubsemiring.Basic | [
"iInf",
"NonUnitalSubsemiring.mem_iInf",
"Membership.mem",
"propext",
"NonUnitalSubsemiring.instSetLike",
"NonUnitalSubsemiring",
"NonUnitalSubsemiring.instInfSet",
"NonUnitalNonAssocSemiring",
"Eq",
"SetLike.instMembership"
] | false |
AlgebraicGeometry.Scheme.Hom.stalkMap_hom_inv | Mathlib.AlgebraicGeometry.Scheme | [
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"TopCat.instCategory",
"ContinuousMap",
"Inseparable.of_eq",
"CommRingCat.instCategory",
"CategoryTheory.Iso",
... | true |
Std.Internal.List.getValueCast? | Std.Data.Internal.List.Associative | [
"List.brecOn",
"LawfulBEq",
"List",
"Std.Internal.List.getValueCast?._f",
"BEq",
"Sigma",
"Option"
] | true |
KStar.rec | Mathlib.Algebra.Order.Kleene | [
"KStar.mk",
"KStar"
] | false |
ProfiniteGrp.ofProfinite | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic | [
"Profinite.instTotallyDisconnectedSpaceCarrierToTop",
"ProfiniteGrp.of",
"Group",
"ProfiniteGrp",
"TotallyDisconnectedSpace",
"TopCat.str",
"Profinite",
"TopCat.carrier",
"IsTopologicalGroup",
"TopCat",
"CompHausLike.toTop",
"ProfiniteGrp.ofProfinite._proof_1"
] | true |
MonoidWithZeroHom.instCommGroupWithZeroValueGroup₀._proof_1 | Mathlib.Algebra.GroupWithZero.Range | [
"GroupWithZero.div_eq_mul_inv",
"GroupWithZero.toMonoidWithZero",
"Semigroup.toMul",
"instHDiv",
"GroupWithZero.toInv",
"HMul.hMul",
"Membership.mem",
"Units",
"GroupWithZero.toDiv",
"Subtype",
"HDiv.hDiv",
"Subgroup",
"Units.instGroup",
"MonoidWithZeroHomClass",
"MonoidWithZero",
"Inv... | false |
MeasureTheory.LevyProkhorov.instPseudoEMetricSpaceMeasure | Mathlib.MeasureTheory.Measure.LevyProkhorovMetric | [
"MeasureTheory.LevyProkhorov.instPseudoEMetricSpaceMeasure._proof_3",
"MeasureTheory.Measure",
"MeasureTheory.LevyProkhorov",
"PseudoEMetricSpace",
"MeasurableSpace",
"PseudoEMetricSpace.mk",
"PseudoEMetricSpace.toUniformSpace",
"OpensMeasurableSpace",
"MeasureTheory.LevyProkhorov.instPseudoEMetricS... | true |
Finsupp.support_nonempty_iff._simp_1 | Mathlib.Data.Finsupp.Defs | [
"Finsupp.support",
"Ne",
"Finsupp.support_nonempty_iff",
"propext",
"Finset.Nonempty",
"Zero.toOfNat0",
"Finsupp.instZero",
"OfNat.ofNat",
"Eq",
"Finsupp",
"Zero"
] | false |
Submonoid.saturation | Mathlib.Algebra.Group.Submonoid.Saturation | [
"SaturatedSubmonoid",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"LE.le",
"SaturatedSubmonoid.toSubmonoid",
"SaturatedSubmonoid.instInfSet",
"Submonoid.instPartialOrder",
"MulOneClass",
"InfSet.sInf",
"Submonoid"
] | true |
Equiv.monoid.eq_1 | Mathlib.Algebra.Group.TransferInstance | [
"Monoid",
"Function.Injective.monoid",
"MulOne.toOne",
"Equiv.instEquivLike",
"Monoid.toMulOneClass",
"Equiv.monoid",
"Equiv.monoid._proof_3",
"Equiv",
"MulOne.toMul",
"Equiv.monoid._proof_2",
"Monoid.toPow",
"MulOneClass.toMulOne",
"Equiv.mul",
"Nat",
"Eq.refl",
"Equiv.monoid._proof_1... | true |
CategoryTheory.Limits.WalkingParallelPairHom | Mathlib.CategoryTheory.Limits.Shapes.Equalizers | [
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.WalkingParallelPairHom.right",
"CategoryTheory.Limits.WalkingParallelPairHom.id",
"CategoryTheory.Limits.WalkingParallelPairHom.left"
] | true |
Lean.SCC.Data._sizeOf_1 | Lean.Util.SCC | [
"Lean.SCC.Data.rec",
"Option._sizeOf_inst",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Bool",
"instAddNat",
"instSizeOfNat",
"Lean.SCC.Data",
"OfNat.ofNat",
"Bool._sizeOf_inst",
"Option"
] | false |
AddSubgroup.comap_inf | Mathlib.Algebra.Group.Subgroup.Map | [
"AddSubgroup.comap",
"AddSubgroup.instCompleteLattice",
"CompleteLattice.toLattice",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddSubgroup",
"AddGroup",
"AddSubgroup.gc_map_comap",
"GaloisConnection.u_inf",
"AddGroup.toSubNegMonoid",
"AddSubgroup.instMin",
"SubNegMonoid.toAddMonoi... | true |
CategoryTheory.SmallObject.SuccStruct.extendToSucc.obj_succ_eq | Mathlib.CategoryTheory.SmallObject.Iteration.ExtendToSucc | [
"Eq.mpr",
"CategoryTheory.Functor",
"Order.succ",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"LinearOrder.toDecidableLE",
"Set.Elem",
"DistribLattice.toLattice",
"id",
"Preorder.smallCategory",
"LE.le",
"dif... | true |
AlgebraNorm.restriction._proof_3 | Mathlib.Analysis.Normed.Unbundled.AlgebraNorm | [
"Subalgebra.instSetLike",
"AlgebraNorm.instFunLikeReal",
"Real.partialOrder",
"Real.instLE",
"Real",
"Subring.instSetLike",
"AddMonoid.toAddSemigroup",
"SeminormedCommRing",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"SeminormedCommRing.toCommRing",
"Algebra",
"Algebra.toSMul",
"... | false |
AddSubmonoid.IsLocalizationMap.exists_of_eq | Mathlib.GroupTheory.MonoidLocalization.Basic | [
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Exists",
"Subtype",
"AddSubmonoid",
"AddCommMonoid",
"instHAdd",
"HAdd.hAdd",
"AddSubmonoid.IsLocalizationMap",
"AddCommMonoid.toAddMonoid",
"AddCommSemigroup.toAddCommMagma",
"AddCommMonoid.toAddCommSemigroup",
"Subtype.val",
"AddSubmonoid.in... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.getD_filterMap_of_getKey?_eq_some._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 |
NumberField.hermiteTheorem.finite_of_discr_bdd_of_isComplex | Mathlib.NumberTheory.NumberField.Discriminant.Basic | [
"Int.instAddCommGroup",
"Multiset.toFinset",
"le_max_right",
"Iff.mpr",
"zero_le",
"NormedCommRing.toNormedRing",
"IntermediateField.lift",
"Real.instIsOrderedRing",
"Norm.norm",
"Int.cast",
"NumberField.InfinitePlace.instFunLikeReal",
"Eq.mpr",
"NegZeroClass.toNeg",
"mul_nonneg",
"NonAs... | true |
OmegaCompletePartialOrder.ωScottContinuous_iff_monotone_map_ωSup | Mathlib.Order.OmegaCompletePartialOrder | [
"Set.range_comp",
"Eq.mpr",
"congrArg",
"HEq.refl",
"PartialOrder.toPreorder",
"Monotone",
"Preorder.toLE",
"DirectedOn",
"Function.comp",
"Membership.mem",
"Exists",
"Eq.mp",
"Eq.casesOn",
"id",
"OmegaCompletePartialOrder.ωScottContinuous.map_ωSup",
"LE.le",
"LE",
"OmegaCompletePa... | true |
SNum.bit_zero | Mathlib.Data.Num.Bitwise | [
"SNum",
"Bool.true",
"Bool.casesOn",
"Bool",
"Eq.ndrec",
"Eq.refl",
"SNum.zero",
"Eq.symm",
"Bool.false",
"Eq",
"SNum.bit"
] | true |
NonarchAddGroupSeminorm._sizeOf_1 | Mathlib.Analysis.Normed.Group.Seminorm | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Real.instLE",
"Real",
"AddMonoid.toAddSemigroup",
"Real.instZero",
"ZeroHom.toFun",
"NonarchAddGroupSeminorm",
"SubtractionMonoid.toSubNegZeroMonoid",
"instOfNatNat",
"LE.le",
"SubNegZeroMonoid.toNegZeroClass",
"ZeroHom",
"instHAdd",
... | false |
CategoryTheory.ShortComplex.Homotopy.compRight_h₃ | Mathlib.Algebra.Homology.ShortComplex.Preadditive | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.Homotopy",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.ShortComplex.Homotopy.compRight",
"CategoryTheory.Preadditive",
"CategoryTheory.ShortComplex.Homotopy.h₃",
"Categ... | true |
_private.Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup.0.IsCoprime.mulVecSL._simp_1_1 | Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | [
"Matrix",
"Matrix.vecMul",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"NonUnitalCommSemiring.toNonUnitalSemiring",
"Fintype",
"Matrix.transpose",
"NonUnitalCommSemiring",
"Matrix.vecMul_transpose",
"Eq.symm",
"Matrix.mulVec",
"Eq"
] | false |
_private.Mathlib.Data.Set.NAry.0.Set.image2_subset_iff_right._simp_1_1 | Mathlib.Data.Set.NAry | [
"HasSubset.Subset",
"Set.preimage",
"propext",
"Set.image",
"Set.image_subset_iff",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
_private.Mathlib.CategoryTheory.Abelian.SerreClass.Localization.0.CategoryTheory.ObjectProperty.SerreClassLocalization.isZero_obj_iff._simp_1_1 | Mathlib.CategoryTheory.Abelian.SerreClass.Localization | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"propext",
"CategoryTheory.Limits.IsZero",
"Zero.toOfNat0",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheo... | false |
Mathlib.Tactic.Bicategory.eval_of | Mathlib.Tactic.CategoryTheory.Bicategory.Normalize | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso.refl",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Category.comp_id",
"CategoryTheory.Bicategory",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp"... | true |
CategoryTheory.FinCategory.asTypeEquivObjAsType._proof_6 | Mathlib.CategoryTheory.FinCategory.AsType | [
"CategoryTheory.FinCategory.asTypeEquivObjAsType._proof_2",
"CategoryTheory.Functor",
"CategoryTheory.FinCategory.categoryAsType",
"Equiv.instEquivLike",
"CategoryTheory.FinCategory.objAsTypeToAsType",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Equiv.symm_apply_apply",
"C... | false |
AEMeasurable.mono_ac | Mathlib.MeasureTheory.Measure.AEMeasurable | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"AEMeasurable",
"Measurable",
"setOf",
"MeasureTheory.Measure.AbsolutelyContinuous",
"AEMeasurable.mk",
"Filter.EventuallyEq",
"MeasurableSpace",
"And",
"MeasureTheory.Measure.AbsolutelyContinuous.ae_le",
"And.intro",
"Exists.intro",
"AEMeasurab... | true |
LSeries.abscissaOfAbsConv_le_of_le_const | Mathlib.NumberTheory.LSeries.Convergence | [
"Norm.norm",
"Eq.mpr",
"Real.instPow",
"Real.instLE",
"Real",
"HMul.hMul",
"Real.instZero",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"EReal",
"Preorder.toLE",
"Real.rpow_zero",
"Exists",
"Complex.instNorm",
"Real.semiring",
"Eq.mp",
"id",
"Ne",
"instOf... | true |
Ideal.ofRel | Mathlib.RingTheory.Ideal.Span | [
"Semiring.toModule",
"setOf",
"Exists",
"Distrib.toAdd",
"Ideal",
"instDistribOfSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"instHAdd",
"And",
"HAdd.hAdd",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Submodule.span",
"Semiring",
"Semiring.toNonAssocSemiring",
"Eq"
] | true |
Std.ExtDTreeMap.getKey?_eq_some_getKeyD_of_contains | Std.Data.ExtDTreeMap.Lemmas | [
"Std.ExtDTreeMap.getKey?",
"Std.DTreeMap",
"Std.DTreeMap.getKey?_eq_some_getKeyD_of_contains",
"Option.some",
"Ordering",
"Std.ExtDTreeMap.getKeyD",
"Std.TransCmp",
"Std.ExtDTreeMap.contains",
"Bool.true",
"Std.ExtDTreeMap.inductionOn",
"Std.ExtDTreeMap",
"Bool",
"Eq",
"Option"
] | true |
CategoryTheory.Functor.pointwiseRightKanExtensionCompIsoOfPreserves._proof_2 | Mathlib.CategoryTheory.Functor.KanExtension.Preserves | [
"CategoryTheory.Functor.pointwiseRightKanExtensionCounit",
"CategoryTheory.Functor",
"CategoryTheory.Functor.hasPointwiseRightKanExtension_of_preserves",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.PreservesPointwiseRightKanExtension",
"CategoryTheory.Functor.IsRightKanExtension",
"CategoryTh... | false |
_private.Mathlib.Order.Filter.Bases.Basic.0.Filter.inf_neBot_iff_frequently_left._simp_1_1 | Mathlib.Order.Filter.Bases.Basic | [
"Filter.instMembership",
"Filter.NeBot",
"Membership.mem",
"Set.instInter",
"Filter.instInf",
"Inter.inter",
"Set.Nonempty",
"propext",
"Filter.inf_neBot_iff",
"Eq",
"Filter",
"Min.min",
"Set"
] | false |
InformationTheory.continuous_klFun | Mathlib.InformationTheory.KullbackLeibler.KLFun | [
"Real",
"Real.continuous_mul_log",
"Continuous",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSeparatelyContinuousAddOfContinuousAdd",
"HMul.hMul",
"IsSemitopologicalRing.toIsSemitopologicalSemiring",
"Real.instSub",
"PseudoMetricSpace.toUniformSpace",
"continuous_id'",
"IsTopologicalAd... | true |
UniformContinuous.exists_contDiff_dist_le | Mathlib.Analysis.Calculus.BumpFunction.SmoothApprox | [
"half_lt_self",
"UniformContinuous",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHDiv",
"CompleteSpace",
"Continuous.exists_contDiff_dist_le_of_forall_mem_ball_dist_le",
"NormedSpace",
"MulZeroClass.toMul",
"Real.denselyNormedField",
"Real.inst... | true |
CategoryTheory.MorphismProperty.HasLocalization.L | Mathlib.CategoryTheory.Localization.HasLocalization | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.MorphismProperty.HasLocalization.hD",
"CategoryTheory.MorphismProperty.HasLocalization.D",
"CategoryTheory.MorphismProperty.HasLocalization",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
Polynomial.Chebyshev.chebyshevTsequence | Mathlib.RingTheory.Polynomial.Chebyshev | [
"Polynomial.Chebyshev.T._proof_7",
"IsDomain",
"Polynomial.Chebyshev.chebyshevTsequence._proof_1",
"CommRing",
"Polynomial.Chebyshev.T",
"CommSemiring.toSemiring",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toNatCast",
"Polynomial.Sequence.mk",
"instOf... | true |
CompactIccSpace.mk'' | Mathlib.Topology.Order.Compact | [
"Set.Icc_self",
"LE.le.eq_or_lt",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.Finite",
"PartialOrder",
"Set.instSingletonSet",
"Set.finite_singleton._simp_1",
"LE.le",
"CompactIccSpace.mk'",
"TopologicalSpace",
"Set.Icc",
"LT.lt",
"True",
"of_eq_true... | true |
WittVector.frobeniusEquiv._proof_4 | Mathlib.RingTheory.WittVector.Frobenius | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"Nat.Prime",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"ExpChar",
"Fact",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"CommRing.toCommSemiring",
"Nat",
"CharP",
"CommRing.toRing",
"Semiring.toNonAssocSemiring",
"R... | false |
sInfHom.dual | Mathlib.Order.Hom.CompleteLattice | [
"sInfHom.dual._proof_1",
"OrderDual.toDual",
"sInfHom.mk",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"Function.comp",
"sInfHom.dual._proof_2",
"sInfHom.instFunLike",
"Equiv.mk",
"InfSet",
"Equiv",
"sSupHom.instFunLike",
"OrderDual.supSet",
"sInfHom.dual._proof_3",
"sInfHom",
"sSupHom"... | true |
_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Expr.0.Std.Tactic.BVDecide.BVExpr.bitblast.go.match_17.splitter | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Expr | [
"Std.Tactic.BVDecide.BVExpr.extract",
"HMul.hMul",
"Std.Tactic.BVDecide.BVExpr.bin",
"Std.Tactic.BVDecide.BVBinOp",
"Std.Tactic.BVDecide.BVUnOp",
"BitVec",
"instMulNat",
"Std.Tactic.BVDecide.BVExpr.shiftLeft",
"instHAdd",
"Std.Tactic.BVDecide.BVExpr.arithShiftRight",
"Std.Tactic.BVDecide.BVExpr.... | true |
CategoryTheory.WithTerminal.opEquiv_unitIso_hom_app | Mathlib.CategoryTheory.WithTerminal.Basic | [
"CategoryTheory.Limits.IsTerminal.from",
"CategoryTheory.Functor",
"CategoryTheory.Equivalence.unitIso",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.WithInitial.of",
"CategoryTheory.CategoryStruct.opposite",
"CategoryTheory.WithTerminal.id.match_1",
"Quiver.... | true |
isOpen_univ._simp_1 | Mathlib.Topology.Defs.Basic | [
"Set.univ",
"isOpen_univ",
"TopologicalSpace",
"True",
"eq_true",
"IsOpen",
"Eq"
] | false |
MvPolynomial.prod_X_pow | Mathlib.Algebra.MvPolynomial.Basic | [
"Finsupp.mem_support_iff",
"Finsupp.instAddZeroClass",
"Finsupp.instFunLike",
"Finsupp.indicator",
"Eq.mpr",
"instDecidableNot",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Semiring.toModule",
"HMul.hMul",
"Finset.univ",
... | true |
Fin.zero_le | Init.Data.Fin.Lemmas | [
"Nat.zero_le",
"Zero.ofOfNat0",
"Fin.instOfNat",
"instOfNatNat",
"LE.le",
"Fin.val",
"instLEFin",
"Nat",
"NeZero",
"OfNat.ofNat",
"Fin"
] | true |
CategoryTheory.Limits.coconeLeftOpOfConeEquiv | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Limits.ConeMorphism.mk",
"CategoryTheory.Limits.coconeLeftOpOfConeEquiv._proof_3",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.Cone",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"CategoryTheory.Functor.mk... | true |
AddCommGrpCat.enoughInjectives | Mathlib.Algebra.Category.Grp.EnoughInjectives | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"Rat.instOfNat",
"Eq.mpr",
"ULift.addZeroClass",
"AddCommGrpCat.injective_of_divisible",
"AddMonoidHom.instAddMonoidHomClass",
"CategoryTheory.Mono",
"ULift.addCommGroup",
"SemilinearMapClass.distribMulActionSemiHomClass",
"AddCommGrpCat.instCategory",
... | true |
Equiv.Perm.applyMulAction | Mathlib.Algebra.Group.Action.End | [
"Equiv.instEquivLike",
"DivInvMonoid.toMonoid",
"SMul.mk",
"Equiv.Perm.applyMulAction._proof_2",
"SemigroupAction.mk",
"Group.toDivInvMonoid",
"Equiv.Perm.permGroup",
"Equiv.Perm",
"MulAction",
"Monoid.toSemigroup",
"MulAction.mk",
"Equiv.Perm.applyMulAction._proof_1",
"DFunLike.coe",
"Equ... | true |
_private.Mathlib.Topology.Instances.CantorSet.0.ofDigits_zero_two_sequence_mem_cantorSet._simp_1_2 | Mathlib.Topology.Instances.CantorSet | [
"Set.iInter",
"Membership.mem",
"Set.mem_iInter",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
OrdinalApprox.lfpApprox_mono_left | Mathlib.SetTheory.Ordinal.FixedPointApproximants | [
"Eq.mpr",
"sup_le_sup_left",
"Pi.preorder",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"ChainCompletePartialOrder.instOfCompleteLattice",
"iSup₂_mono",
"Ordinal.partialOrder",
"CompleteLattice.toLattice",
"congrArg",
"iSup",
"PartialOrder.toPreorder",
"Monotone",
"Preorder.toLE",
"Comp... | true |
MagmaCat.Hom.ext_iff | Mathlib.Algebra.Category.Semigrp.Basic | [
"MulHom",
"HEq.refl",
"MagmaCat.Hom.ext",
"Eq.casesOn",
"Iff",
"MagmaCat.Hom.hom'",
"Iff.intro",
"MagmaCat.carrier",
"MagmaCat.str",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"MagmaCat",
"MagmaCat.Hom"
] | true |
GromovHausdorff.eq_toGHSpace_iff | Mathlib.Topology.MetricSpace.GromovHausdorff | [
"Isometry.comp",
"NormedCommRing.toNormedRing",
"TopologicalSpace.NonemptyCompacts.instSetLike",
"Eq.mpr",
"kuratowskiEmbedding._proof_1",
"NormedCommRing.toSeminormedCommRing",
"IsometryEquiv.range_eq_univ",
"Set.image_univ",
"GromovHausdorff.toGHSpace",
"Real",
"TopologicalSpace.NonemptyCompac... | true |
ChevalleyThm.MvPolynomialC.degBound_le_degBound | Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | [
"LE.le",
"instLENat",
"PSum.inl",
"Nat",
"LT.lt",
"PSigma.mk",
"ChevalleyThm.MvPolynomialC.degBound_le_degBound._mutual",
"instLTNat",
"PSigma",
"ChevalleyThm.MvPolynomialC.degBound"
] | true |
Finsupp.sumFinsuppEquivProdFinsupp.eq_1 | Mathlib.RingTheory.Extension.Generators | [
"Finsupp.sumFinsuppEquivProdFinsupp._proof_4",
"Equiv.mk",
"Finsupp.sumFinsuppEquivProdFinsupp._proof_3",
"Sum",
"Equiv",
"Prod.mk",
"Sum.inl",
"Prod.fst",
"Sum.inr",
"Finsupp.sumFinsuppEquivProdFinsupp._proof_1",
"Eq.refl",
"Finsupp.sumFinsuppEquivProdFinsupp._proof_2",
"Finsupp.sumFinsuppE... | true |
Lean.Grind.NoopConfig.lia._default | Init.Grind.Config | [
"id",
"Bool",
"Bool.false"
] | false |
SetRel.isCover_id._simp_1 | Mathlib.Data.Rel.Cover | [
"SetRel.id",
"HasSubset.Subset",
"SetRel.isCover_id",
"SetRel.IsCover",
"propext",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
_private.Mathlib.SetTheory.ZFC.VonNeumann.0.ZFSet.mem_vonNeumann._simp_1_1 | Mathlib.SetTheory.ZFC.VonNeumann | [
"Preorder.toLT",
"Ordinal.partialOrder",
"ZFSet",
"PartialOrder.toPreorder",
"Membership.mem",
"Exists",
"ZFSet.mem_vonNeumann'",
"HasSubset.Subset",
"ZFSet.vonNeumann",
"And",
"LT.lt",
"propext",
"ZFSet.instHasSubset",
"Eq",
"ZFSet.instSetLike",
"SetLike.instMembership",
"Ordinal"
] | false |
CategoryTheory.Adjunction.ofCat_unit | Mathlib.CategoryTheory.Bicategory.Adjunction.Cat | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Cat.str",
"CategoryTheory.Adjunction.unit",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Cat.instQuiver",
"CategoryTheory.Bicategory.toCategoryStruct",
"Categ... | true |
SimpleGraph.cliqueNum | Mathlib.Combinatorics.SimpleGraph.Clique | [
"SimpleGraph.IsNClique",
"Finset",
"setOf",
"Exists",
"SimpleGraph",
"Nat",
"Nat.instSupSet",
"SupSet.sSup"
] | true |
_private.Mathlib.Analysis.SpecialFunctions.Complex.Log.0.Complex.exp_eq_exp_iff_exists_int._simp_1_3 | Mathlib.Analysis.SpecialFunctions.Complex.Log | [
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"SubNegMonoid.toSub",
"instHAdd",
"instHSub",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"propext",
"AddZero.toAdd",
"SubNegMonoid.toAddMonoid",
"Eq",
"sub_eq_iff_eq_add'"
] | false |
Lean.Grind.Linarith.Poly.denoteN_mul' | Init.Grind.Module.NatModuleNorm | [
"Eq.mpr",
"Int.toNat_natCast",
"instHSMul",
"Lean.Grind.Linarith.Poly.add.noConfusion",
"HMul.hMul",
"Int.toNat_mul",
"Lean.Grind.NatModule.nsmul_zero",
"Lean.Grind.Linarith.Poly.denoteN",
"congrArg",
"Lean.Grind.Linarith.Context",
"HEq.refl",
"False.elim",
"Lean.Grind.Linarith.Poly.ctorIdx"... | true |
ModuleCat.adj._proof_3 | Mathlib.Algebra.Category.ModuleCat.Adjunctions | [
"Equiv.instEquivLike",
"ModuleCat.freeHomEquiv",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"id",
"Equiv",
"ModuleCat.instConcreteCategoryLinearMapIdCarrier",
"LinearMap",
"CategoryTheory.Functor.map",
"Module... | false |
_private.Mathlib.Topology.MetricSpace.Antilipschitz.0.antilipschitzWith_iff_le_mul_dist._simp_1_1 | Mathlib.Topology.MetricSpace.Antilipschitz | [
"NNDist.nndist",
"HMul.hMul",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toNNDist",
"Preorder.toLE",
"antilipschitzWith_iff_le_mul_nndist",
"NNReal",
"LE.le",
"instDistribOfSemiring",
"NNReal.instPartialOrder",
"PseudoMetricSpace",
"Distrib.toMul",
"propext",
"NNReal.instSemiring",
"E... | false |
Prod.instCompleteAtomicBooleanAlgebra | Mathlib.Order.CompleteBooleanAlgebra | [
"BooleanAlgebra",
"Lattice.toSemilatticeSup",
"Prod.instBooleanAlgebra",
"Prod.instCompleteAtomicBooleanAlgebra._proof_3",
"Prod.instCompleteAtomicBooleanAlgebra._proof_12",
"Prod.instCompletelyDistribLattice",
"CompletelyDistribLattice.toCompleteLattice",
"Prod.instCompleteAtomicBooleanAlgebra._proof... | true |
Set.Finite.ecard_strictMonoOn | Mathlib.Data.Finite.Card | [
"ChainCompletePartialOrder.instOfCompleteLattice",
"PartialOrder.toPreorder",
"setOf",
"Set.Finite",
"Function.comp",
"Membership.mem",
"Set.Elem",
"instPreorderENat",
"ChainCompletePartialOrder.toPartialOrder",
"ENat",
"CompleteBooleanAlgebra.toCompleteLattice",
"Set.Finite.ecard_lt_ecard",
... | true |
CategoryTheory.Over.sections._proof_2 | Mathlib.CategoryTheory.LocallyCartesianClosed.Sections | [
"CategoryTheory.Over",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.instCategoryOver",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.Category.comp_id",
"C... | false |
SSet.horn₃₂.desc | Mathlib.AlgebraicTopology.SimplicialSet.HornColimits | [
"SSet.Subcomplex.toSSet",
"CompleteLattice.MulticoequalizerDiagram.multispanIndex",
"Opposite",
"CategoryTheory.Limits.WalkingMultispan",
"SimplexCategory.instFintypeToTypeOrderHomFinHAddNatLenOfNat",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Compl.compl",
"Finset",
"CategoryTheory.... | true |
OrdinalApprox.exists_lfpApprox_eq_lfpApprox | Mathlib.SetTheory.Ordinal.FixedPointApproximants | [
"_private.Mathlib.SetTheory.Ordinal.FixedPointApproximants.0.OrdinalApprox.exists_lfpApprox_eq_lfpApprox.match_1_1",
"Preorder.toLT",
"Order.succ",
"ChainCompletePartialOrder.instOfCompleteLattice",
"SuccOrder.succ",
"Ordinal.partialOrder",
"Cardinal",
"congrArg",
"PartialOrder.toPreorder",
"Subty... | true |
GroupFilterBasis.rec | Mathlib.Topology.Algebra.FilterBasis | [
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"GroupFilterBasis",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Exists",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"HasSubset.Subset",
"Group.toDivInvMono... | false |
Std.LawfulEqCmp.recOn | Init.Data.Order.Ord | [
"Ordering",
"Ordering.eq",
"Std.LawfulEqCmp",
"Eq",
"Std.ReflCmp",
"Std.LawfulEqCmp.mk",
"Std.LawfulEqCmp.rec"
] | false |
TensorAlgebra.toDirectSum.eq_1 | Mathlib.LinearAlgebra.TensorAlgebra.ToTensorPower | [
"PiTensorProduct.instModule",
"LinearEquiv.symm",
"Equiv.instEquivLike",
"CommSemiring.toSemiring",
"AlgHom",
"TensorAlgebra.toDirectSum",
"Nat.instAddMonoid",
"Algebra.toModule",
"Algebra.id",
"TensorPower.galgebra",
"Fin.instOfNat",
"Equiv",
"TensorAlgebra",
"instOfNatNat",
"PiTensorPr... | true |
CategoryTheory.Pretriangulated.rotateRotateRotateIso._proof_3 | Mathlib.CategoryTheory.Triangulated.TriangleShift | [
"Int.instAddCommMonoid",
"NegZeroClass.toNeg",
"CategoryTheory.Functor",
"Units.instMulAction",
"CategoryTheory.shiftFunctorComm_eq_refl",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrA... | false |
Std.HashMap.Raw.getKey | Std.Data.HashMap.Raw | [
"Membership.mem",
"Std.HashMap.Raw",
"Std.DHashMap.Raw.getKey",
"Std.HashMap.Raw.inner",
"Std.HashMap.Raw.instMembershipOfBEqOfHashable",
"Hashable",
"BEq"
] | true |
CategoryTheory.Limits.isColimitSigmaConstCokernelCofork._proof_4 | Mathlib.CategoryTheory.Limits.Preserves.SigmaConst | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.isColimitSigmaConstCokernelCofork.match_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"congrArg",
"Compl.compl",
"Subtype.casesOn",
"Membership.mem",
"CategoryThe... | false |
Std.DTreeMap.Internal.Impl.mem_keys | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.mem_keys._simp_1_1",
"Ord",
"Std.instLawfulBEqOrd",
"congrArg",
"beqOfOrd",
"Std.TransOrd",
"List.contains",
"Membership.mem",
"id",
"Std.DTreeMap.Internal.Impl.WF",
"Bool.true",
"List",
"Iff",
"List.instM... | true |
Turing.TM1to0.trAux.eq_3 | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Turing.TM1to0.Λ'",
"Turing.TM1to0.trAux",
"Eq.refl",
"Turing.TM1.Stmt.load",
"Prod",
"Eq",
"Turing.TM0.Stmt",
"Turing.TM1.Stmt"
] | true |
ContinuousMap.isometryEquivBoundedOfCompact._proof_1 | Mathlib.Topology.ContinuousMap.Compact | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"ContinuousMap.equivBoundedOfCompact",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"BoundedContinuousFunction.instPseudoMetricSpace",
"Equiv.toFun",
"CompactSpace",
"TopologicalSpace",
"PseudoMetricSpace",
"WeakPseudoEMetricSpace.toEDist",
... | false |
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