name string | module string | deps list | allowCompletion bool |
|---|---|---|---|
«term_→ₗc_» | Mathlib.RingTheory.Coalgebra.Hom | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
_private.Lean.Environment.0.Lean.VisibilityMap.const | Lean.Environment | [
"_private.Lean.Environment.0.Lean.VisibilityMap",
"_private.Lean.Environment.0.Lean.VisibilityMap.mk"
] | true |
Aesop.PhaseName.norm | Aesop.Rule.Name | [
"Aesop.PhaseName",
"Aesop.PhaseName.norm"
] | true |
_private.Mathlib.ModelTheory.Encoding.0.FirstOrder.Language.BoundedFormula.listDecode.match_1.eq_3 | Mathlib.ModelTheory.Encoding | [
"FirstOrder.Language.Term",
"Sum",
"instOfNatNat",
"Sum.inl",
"List.cons",
"List",
"Sum.inr",
"Nat",
"FirstOrder.Language.Relations",
"Eq.refl",
"FirstOrder.Language",
"Sigma.mk",
"OfNat.ofNat",
"Fin",
"Nat.succ",
"Eq",
"Sigma",
"FirstOrder.Language.BoundedFormula.listDecode.match_... | true |
Order.succ_le_iff_of_not_isMax | Mathlib.Order.SuccPred.Basic | [
"Preorder.toLT",
"Order.succ",
"Preorder.toLE",
"Order.succ_le_of_lt",
"Order.lt_succ_of_not_isMax",
"LE.le",
"Iff",
"LT.lt.trans_le",
"LT.lt",
"Iff.intro",
"SuccOrder",
"Not",
"Preorder",
"IsMax"
] | true |
CategoryTheory.ConcreteCategory.ext_iff | Mathlib.CategoryTheory.ConcreteCategory.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"HEq.refl",
"Eq.casesOn",
"CategoryTheory.ConcreteCategory.ext",
"CategoryTheory.ConcreteCategory",
"Iff",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"CategoryTheory.Category.toCategoryStruct",
"... | true |
CategoryTheory.CommSq.LiftStruct.opEquiv._proof_3 | Mathlib.CategoryTheory.CommSq | [
"Function.LeftInverse",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CommSq",
"Quiver.Hom.op",
"CategoryTheory.CommSq.LiftStruct.op",
"CategoryTheory.CommSq.LiftStruct",
"CategoryTheory.CommSq.LiftStruct.unop",
"CategoryTheory.CommSq.op",
"Opposite.op",
"... | false |
Equiv.subtypeEquiv._proof_1 | Mathlib.Logic.Equiv.Basic | [
"Iff.mpr",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"congrArg",
"Equiv.symm_apply_apply",
"Eq.rec",
"Equiv",
"Subtype",
"Subtype.mk",
"Iff",
"True",
"eq_self",
"Iff.mp",
"of_eq_true",
"congrFun'",
"Equiv.symm",
"Eq.symm",
"Subtype.val",
"Eq",
"DFunLike.coe",
"Eq.trans... | false |
Equiv.toHomeomorphOfContinuousOpen_symm_apply | Mathlib.Topology.Homeomorph.Defs | [
"Continuous",
"Equiv.instEquivLike",
"IsOpenMap",
"Equiv.toHomeomorphOfContinuousOpen",
"Equiv",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"Homeomorph.symm",
"Homeomorph",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
OrderIso.finTwoArrowIso | Mathlib.Order.Fin.Tuple | [
"RelIso.mk",
"Prod.instLE_mathlib",
"Preorder.toLE",
"OrderIso.finTwoArrowIso._proof_1",
"Equiv",
"OrderIso",
"instOfNatNat",
"LE.le",
"Pi.hasLe",
"Nat",
"OrderIso.piFinTwoIso",
"Prod",
"OfNat.ofNat",
"Fin",
"finTwoArrowEquiv",
"Preorder"
] | true |
List.drop | Init.Data.List.Basic | [
"List.drop._f",
"Nat.brecOn",
"List",
"Nat"
] | true |
Int.instCommutativeHMul | Init.Data.Int.Lemmas | [
"Std.Commutative",
"HMul.hMul",
"Int",
"Int.instMul",
"Int.mul_comm",
"Std.Commutative.mk",
"instHMul"
] | true |
_private.Lean.Elab.Tactic.Split.0.Lean.Elab.Tactic.evalSplit._regBuiltin.Lean.Elab.Tactic.evalSplit_1 | Lean.Elab.Tactic.Split | [
"Lean.Elab.Tactic.tacticElabAttribute",
"IO",
"Lean.Elab.Tactic.evalSplit",
"Unit",
"Lean.Elab.Tactic.Tactic",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
MeasureTheory.Measure.snd_prod | Mathlib.MeasureTheory.Measure.Prod | [
"Set.instSProd",
"Eq.mpr",
"MulOne.toOne",
"MeasureTheory.Measure",
"HMul.hMul",
"MeasurableSet",
"SProd.sprod",
"congrArg",
"CommSemiring.toSemiring",
"Set.univ",
"Set.univ_prod",
"MeasureTheory.IsProbabilityMeasure.measure_univ",
"id",
"MulOne.toMul",
"MeasureTheory.Measure.prod_prod",... | true |
Array.getElem_scanl_zero._proof_1 | Batteries.Data.Array.Scan | [
"Nat.zero_lt_succ._simp_1",
"congrArg",
"Array.scanl",
"instOfNatNat",
"Array",
"instHAdd",
"Array.size_scanl",
"HAdd.hAdd",
"Nat",
"LT.lt",
"True",
"of_eq_true",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Array.size",
"Eq.trans"
] | false |
DenseRange.piMap | Mathlib.Topology.NhdsWithin | [
"Eq.mpr",
"Pi.topologicalSpace",
"congrArg",
"Set.univ",
"Membership.mem",
"Dense",
"Set.range_piMap",
"id",
"Pi.map",
"DenseRange.eq_1",
"dense_pi",
"TopologicalSpace",
"DenseRange",
"Set.pi",
"Set.range",
"Eq",
"Set.instMembership",
"Set"
] | true |
_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.NormalizePattern.ParentKind.genPattern.sizeOf_spec | Lean.Meta.Tactic.Grind.EMatchTheorem | [
"instOfNatNat",
"_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.NormalizePattern.ParentKind",
"_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.NormalizePattern.ParentKind._sizeOf_inst",
"_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.NormalizePattern.ParentKin... | true |
Std.DHashMap.union_insert_right_equiv_union_insert | Std.Data.DHashMap.Lemmas | [
"Std.DHashMap.instUnion",
"Std.DHashMap.Equiv",
"Sigma.fst",
"LawfulHashable",
"EquivBEq",
"Std.DHashMap.union_insert_right_equiv_insert_union",
"Hashable",
"Union.union",
"Sigma.snd",
"BEq",
"Sigma",
"Std.DHashMap.insert",
"Std.DHashMap"
] | true |
CategoryTheory.Limits.HasBinaryBiproduct.mk'._flat_ctor | Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | [
"CategoryTheory.Limits.HasBinaryBiproduct.mk'",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.HasBinaryBiproduct",
"Nonempty",
"CategoryTheory.Limits.BinaryBiproductData",
"CategoryTheory.Category"
] | false |
LinearEquiv.rTensor_pow | Mathlib.LinearAlgebra.TensorProduct.Map | [
"one_pow",
"MulOne.toOne",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"DivInvOneMonoid.toDivInvMonoid",
"TensorProduct.addCommMonoid",
"LinearEquiv.rTensor",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
... | true |
Manifold.IsImmersionAtOfComplement.instNormedAddCommGroupSmallComplement._proof_45 | Mathlib.Geometry.Manifold.Immersion | [
"NormedSpace",
"PartialOrder.toPreorder",
"Manifold.IsImmersionAtOfComplement",
"Preorder.toLE",
"Manifold.IsImmersionAtOfComplement.smallComplement",
"Manifold.IsImmersionAtOfComplement.instNormedAddCommGroupSmallComplement._proof_47",
"LE.le",
"TopologicalSpace",
"ModelWithCorners",
"Manifold.Is... | false |
Lean.IR.FnBody.unreachable | Lean.Compiler.IR.Basic | [
"Lean.IR.FnBody",
"Lean.IR.FnBody.unreachable"
] | true |
List.compareLex._sunfold | Init.Data.Ord.Basic | [
"Ordering.gt",
"Ordering.swap.match_1",
"Ordering",
"Ordering.eq",
"List",
"Unit",
"Ordering.lt",
"List.compareLex",
"List.compareLex.match_1"
] | false |
_private.Mathlib.RingTheory.Etale.QuasiFinite.0.Algebra.exists_notMem_and_isIntegral_forall_mem_of_ne_of_liesOver._simp_1_2 | Mathlib.RingTheory.Etale.QuasiFinite | [
"HMul.hMul",
"Mul",
"MulHomClass",
"map_mul",
"Eq.symm",
"Eq",
"DFunLike.coe",
"FunLike",
"instHMul"
] | false |
Affine.Simplex.faceOppositeCentroid_vsub_faceOppositeCentroid | Mathlib.LinearAlgebra.AffineSpace.Simplex.Centroid | [
"Finset.card_univ",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"instNeZeroNatHAdd_1",
"MulOne.toOne",
"Affine.Simplex.points",
"Nat.instMulZeroClass",
"Fintype.card_fin",
"DivInvMonoid.toInv",
"instHSMul",
"instHDiv",
"GroupWithZero.toDivisionMonoid",
"InvOneClass.to... | true |
Module.End.disjoint_iInf_maxGenEigenspace | Mathlib.LinearAlgebra.Eigenspace.Pi | [
"Submodule",
"IsDomain",
"CommRing",
"iInf",
"instTopENat",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"Module.IsTorsionFree",
"Disjoint",
"Exists",
"AddCommGroup",
"Ne",
"Submodule.instPartialOrder",
"Module.End.disjoint_genEigenspace",
"Mo... | true |
CategoryTheory.Functor.LocallyCoverDense.rec | Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology | [
"CategoryTheory.Functor",
"Membership.mem",
"Set.Elem",
"CategoryTheory.Sieve",
"CategoryTheory.Functor.LocallyCoverDense.mk",
"CategoryTheory.Sieve.functorPushforward",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.Functor.LocallyCoverDense",
"Subtype.val",
"CategoryTheory.Sieve.functorP... | false |
FirstOrder.Language.LHom.onBoundedFormula.eq_def | Mathlib.ModelTheory.Syntax | [
"FirstOrder.Language.BoundedFormula.imp",
"Eq.mpr",
"FirstOrder.Language.LHom.onRelation",
"congrArg",
"HEq.refl",
"FirstOrder.Language.BoundedFormula.brecOn",
"FirstOrder.Language.Relations.boundedFormula",
"FirstOrder.Language.LHom.onBoundedFormula._f",
"FirstOrder.Language.LHom.onTerm",
"FirstO... | true |
CategoryTheory.MonObj._aux_Mathlib_CategoryTheory_Monoidal_Mod___unexpand_CategoryTheory_ModObj_smul_2 | Mathlib.CategoryTheory.Monoidal.Mod | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.matchesIdent",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.T... | false |
Homeomorph.coe_punitProd | Mathlib.Topology.Constructions.SumProd | [
"instTopologicalSpaceProd",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"PUnit",
"Homeomorph",
"instTopologicalSpacePUnit",
"Prod",
"Eq",
"Homeomorph.punitProd",
"Prod.snd",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
MvPowerSeries.map_algebraMap_eq_subst_X | Mathlib.RingTheory.MvPowerSeries.Substitution | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Nat.instMulZeroClass",
"CommRing",
"instHSMul",
"Semiring.toModule",
"instSMulOfMul",
"HMul.hMul",
"IsScalarTower.right",
"Algebra.algebraMap",
"MvPowerSeries.instCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"... | true |
Std.DHashMap.Raw.size_insertIfNew_le | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"congrArg",
"Std.DHashMap.Internal.Raw.insertIfNew_eq",
"Std.DHashMap.Raw",
"id",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"LE.le",
"instLENat",
"LawfulHashable",
"Subtype.mk",
"instHAdd",
"EquivBEq",
"HAdd.hAdd",
"Nat",
"Std.DHashMap.R... | true |
OrthonormalBasis.toBasis_adjustToOrientation | Mathlib.Analysis.InnerProductSpace.Orientation | [
"InnerProductSpace.toNormedSpace",
"Orientation",
"Real.partialOrder",
"Real",
"Module.Basis.adjustToOrientation",
"Real.instRCLike",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Module.Basis.toBasis_toOrthonormalBasis",
"NormedField.toField",
"Real.commRing",
"Field.toSemifield",
... | true |
_private.Lean.Parser.Attr.0.Lean.Parser.Attr.recursor._regBuiltin.Lean.Parser.Attr.recursor.formatter_7 | Lean.Parser.Attr | [
"Lean.PrettyPrinter.Formatter",
"Lean.Parser.Attr.recursor.formatter",
"Lean.Name.mkStr5",
"IO",
"Unit",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
Std.Sat.AIG.LawfulVecOperator.denote_cast_entry | Std.Sat.AIG.LawfulVecOperator | [
"Std.Sat.AIG.Ref.cast",
"Std.Sat.AIG.Entrypoint.aig",
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.Ref.cast._proof_2",
"congrArg",
"Std.Sat.AIG.Entrypoint",
"Std.Sat.AIG.Entrypoint.ref",
"LE.le",
"instLENat",
"Std.Sat.AIG",
"Nat",
"True",
"eq_self",
"Bool",
"of_eq_true",
"Std.Sat.AIG.LawfulVecOper... | true |
NormedAddGroupHom.sub | Mathlib.Analysis.Normed.Group.Hom | [
"NormedAddGroupHom",
"SeminormedAddCommGroup",
"AddMonoidHom.instSub",
"ZeroHom.toFun",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"AddMonoidHom.toZeroHom",
"Sub.mk",
"AddZeroClass.toAddZero",
"NormedAddGroupHom.sub._proof_1",
"AddZero.toZero",
"instHSub",
"AddGrou... | true |
Matroid.closure_union_closure_right_eq | Mathlib.Combinatorics.Matroid.Closure | [
"Eq.mpr",
"congrArg",
"Set.instUnion",
"id",
"Matroid.closure_closure",
"Matroid.closure",
"Eq.refl",
"Union.union",
"Matroid.closure_closure_union_closure_eq_closure_union",
"Eq.symm",
"Eq",
"Matroid",
"Set"
] | true |
_private.Mathlib.Analysis.Complex.Poisson.0.DiffContOnCl.circleAverage_re_smul_on_ball_zero._simp_1_12 | Mathlib.Analysis.Complex.Poisson | [
"AddGroup.toSubtractionMonoid",
"sub_eq_zero",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq"
] | false |
DihedralGroup.oddCommuteEquiv_apply | Mathlib.GroupTheory.SpecificGroups.Dihedral | [
"Equiv.instEquivLike",
"ZMod.commRing",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"Odd",
"Commute",
"Sum",
"DihedralGroup.instGroup",
"Equiv",
"MulOne.toMul",
"Subtype",
"Distrib.toAdd",
"DihedralGroup.oddCommuteEquiv.match_1",
"DivInvMonoid.toMonoid",
"Prod.mk",
"Sum.inl",
... | true |
HomologicalComplex.truncLEXIsoCycles | Mathlib.Algebra.Homology.Embedding.TruncLE | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.truncLE'XIsoCycles._proof_1",
"Opposite",
"HomologicalComplex.op",
"HomologicalComplex.opcyclesOpIso",
"HomologicalComplex.HasHomology",
"HomologicalComplex.truncGE",
"HomologicalComplex.opcycles",
"HomologicalComplex",
"CategoryTheory.... | true |
_private.Lean.Level.0.Lean.Level.substParams.go.match_3 | Lean.Level | [
"Unit.unit",
"Lean.Level.ctorIdx",
"Lean.Level.param",
"Nat.hasNotBit",
"Lean.Level.imax",
"Lean.Level",
"Unit",
"Lean.Level.zero",
"_private.Lean.Level.0.Lean.Level.substParams.go._sparseCasesOn_3",
"Lean.Name",
"Lean.Level.succ",
"Lean.Level.max"
] | false |
BooleanSubalgebra.val_top | Mathlib.Order.BooleanSubalgebra | [
"BooleanAlgebra",
"BooleanSubalgebra",
"Membership.mem",
"Subtype",
"BooleanAlgebra.toTop",
"BooleanSubalgebra.instSetLike",
"BooleanSubalgebra.instTopCoe",
"Top.top",
"Subtype.val",
"Eq",
"SetLike.instMembership",
"rfl"
] | true |
SimpleGraph.connected_iff_diam_ne_zero | Mathlib.Combinatorics.SimpleGraph.Diam | [
"Nontrivial",
"not_iff_not",
"Eq.mpr",
"SimpleGraph.connected_iff_ediam_ne_top",
"SimpleGraph.diam_eq_zero_iff_ediam_eq_top",
"instTopENat",
"congrArg",
"Finite",
"Iff.rfl",
"id",
"SimpleGraph.ediam",
"Ne",
"instOfNatNat",
"SimpleGraph.Connected",
"Nontrivial.to_nonempty",
"SimpleGraph... | true |
Finsupp.zipWith_neLocus_eq_right | Mathlib.Data.Finsupp.NeLocus | [
"Finsupp.instFunLike",
"Eq.mpr",
"congrArg",
"Finsupp.neLocus",
"Finset",
"Finset.ext",
"Membership.mem",
"id",
"Function.Injective.ne_iff",
"Ne",
"Iff",
"Finset.instSetLike",
"Finsupp.mem_neLocus._simp_1",
"congr",
"Finsupp.zipWith",
"Zero.toOfNat0",
"Function.Injective",
"OfNat.o... | true |
_private.Mathlib.Algebra.QuadraticAlgebra.Basic.0.QuadraticAlgebra.lift._simp_6 | Mathlib.Algebra.QuadraticAlgebra.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Algebra.toSMul",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Algebra.algebraMap_eq_smul_one",
"CommSemiring",
"AddMonoidWithOne.toOne",
"RingHom.instFunLike",
"Semi... | false |
LieAlgebra.IsKilling.coroot._proof_1 | Mathlib.Algebra.Lie.Weights.Killing | [
"LieRing.toAddCommGroup",
"LieSubalgebra.instSetLike",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddSubmonoidClass",
"Field.toCommRing",
"AddSubgroupClass.toAddSubmonoidClass",
"LieRing",
"AddGroup.toSubNegMonoid",
"LieSubalgebra",
"LieAlgebra",
"SubNegMonoid.toAddMonoid",
"Fie... | false |
TopCat.hasForgetToMeasCat._proof_2 | Mathlib.MeasureTheory.Category.MeasCat | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopCat.instCategory",
"ContinuousMap",
"MeasCat.instLargeCategory",
"Measurable",
"MeasCat.carrier",
"MeasCat",
"id",
"MeasCat.of",
"borel",
"Continuous.borel_measurable",
"TopCat.Hom.hom'",
"Subtype.mk",
"TopCat.str",
"TopCat.ca... | false |
Turing.TM2to1.Λ'.normal.noConfusion | Mathlib.Computability.TuringMachine.StackTuringMachine | [
"HEq.refl",
"id",
"Turing.TM2to1.Λ'",
"Turing.TM2to1.Λ'.noConfusion",
"heq_of_eq",
"Eq.refl",
"HEq",
"Eq",
"Turing.TM2to1.Λ'.normal"
] | false |
CliffordAlgebra.evenOdd_mul_le | Mathlib.LinearAlgebra.CliffordAlgebra.Grading | [
"Iff.mpr",
"Eq.mpr",
"Submodule",
"CliffordAlgebra.ι",
"CommRing",
"Submodule.mul_mem_mul",
"HMul.hMul",
"IsScalarTower.right",
"ZMod.commRing",
"_private.Mathlib.LinearAlgebra.CliffordAlgebra.Grading.0.CliffordAlgebra.evenOdd_mul_le._simp_1_3",
"Monoid.toMulOneClass",
"congrArg",
"CommSemir... | true |
cfcL._proof_3 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"instSMulOfMul",
"CommSemiring.toSemiring",
"IsTopologicalSemiring",
"SeparatelyContinuousMul.to_continuousSMul",
"PseudoMetricSpace.toUniformSpace",
"ContinuousConstSMul",
"instDistribOfSemiring",
"CommSemiring",
"IsSemitopologicalSemiring.toSeparatelyContinuousMul",
"MetricSpace",
"Distrib.toM... | false |
AlgebraicGeometry.Scheme.Cover.instCategoryI₀Pullback₁._proof_8 | Mathlib.AlgebraicGeometry.Cover.Directed | [
"CategoryTheory.MorphismProperty",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.Category.comp_id._autoParam",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgebraicGeometry.Scheme.isJointlySurjectivePreserving",
"CategoryTheory.CategoryStruct.id",
"Al... | false |
Function.ExtendByOne.hom._proof_2 | Mathlib.Algebra.Group.Pi.Lemmas | [
"MulOne.toOne",
"Function.extend_one",
"MulOneClass.toMulOne",
"Function.extend",
"Pi.instOne",
"One.toOfNat1",
"MulOneClass",
"OfNat.ofNat",
"Eq"
] | false |
_private.Mathlib.Data.Set.Insert.0.Set.forall_of_forall_insert._proof_1_1 | Mathlib.Data.Set.Insert | [
"False",
"eq_false",
"Lean.Grind.iff_eq",
"Classical.byContradiction",
"Lean.Grind.eq_false_of_imp_eq_true",
"Membership.mem",
"Eq.mp",
"id",
"Insert.insert",
"Lean.Grind.eq_false_of_or_eq_false_right",
"Iff",
"Set.instInsert",
"True",
"eq_true",
"Eq.refl",
"Or",
"Set.mem_insert_iff"... | false |
CategoryTheory.IsPullback.inr_fst' | Mathlib.CategoryTheory.Limits.Shapes.Pullback.IsPullback.BicartesianSq | [
"CategoryTheory.Limits.BinaryBicone.fst",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.BinaryBicone.inr_snd",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.IsPullback.zero_right._simp_1",
"CategoryTheory.IsPullback",
"CategoryTheory.Limits.Bi... | true |
synthesizeUsing | Mathlib.Util.SynthesizeUsing | [
"Pure.pure",
"Lean.instantiateMVars",
"Lean.NameMap",
"Lean.MetavarKind.natural",
"Lean.Elab.Term.LevelMVarErrorInfo",
"Lean.Elab.Term.Context.mk",
"Lean.Elab.Term.State.mk",
"Lean.MVarIdMap",
"monadFunctorRefl",
"Lean.Meta.State",
"Lean.Elab.AutoBoundImplicitContext",
"Lean.Elab.Tactic.run",
... | true |
OpenPartialHomeomorph.Simps.symm_apply | Mathlib.Topology.OpenPartialHomeomorph.Defs | [
"OpenPartialHomeomorph.toFun'",
"TopologicalSpace",
"OpenPartialHomeomorph",
"OpenPartialHomeomorph.symm"
] | true |
_private.Mathlib.Analysis.Calculus.UniformLimitsDeriv.0.uniformCauchySeqOn_ball_of_fderiv._simp_1_4 | Mathlib.Analysis.Calculus.UniformLimitsDeriv | [
"imp_true_iff",
"True",
"propext",
"Eq"
] | false |
_private.Std.Time.Date.Basic.0.Std.Time.Second.Offset.ofWeeks._proof_1 | Std.Time.Date.Basic | [
"Rat.instOfNat",
"Int.cast",
"Rat.instMul",
"instHDiv",
"HMul.hMul",
"of_decide_eq_true",
"Rat",
"Rat.instIntCast",
"id",
"HDiv.hDiv",
"Int",
"Bool.true",
"instOfNat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"instDecidableEqRat",
"Decidable.decide",
"Eq",
"Rat.instDiv",
"instHMul"
... | false |
Submonoid.IsMulPointed.eq_one_of_mem_of_inv_mem | Mathlib.Algebra.Group.Submonoid.Support | [
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"Submonoid.IsMulPointed",
"Inv.inv",
"One.toOfNat1",
"InvOneClass.toInv",
... | true |
Lean.Meta.Grind.TheoremGuard.check | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.TheoremGuard",
"Bool"
] | true |
Int32.toInt16_xor | Init.Data.SInt.Bitwise | [
"Int16.toBitVec_xor",
"Int32.toBitVec",
"Int16",
"BitVec.instXorOp",
"congrArg",
"BitVec",
"instXorOpInt32",
"instOfNatNat",
"Int32.toBitVec_toInt16",
"Int32.toBitVec_xor",
"Int32.toInt16",
"Nat",
"Int16.toBitVec",
"congr",
"BitVec.signExtend_xor",
"True",
"HXor.hXor",
"instXorOpIn... | true |
Std.DTreeMap.Raw.Equiv.of_keysArray_unit_perm | Std.Data.DTreeMap.Raw.Lemmas | [
"Iff.mpr",
"Ordering",
"Std.DTreeMap.Raw.Equiv",
"Array.Perm",
"Std.DTreeMap.Raw.keysArray",
"Unit",
"Std.DTreeMap.Raw.Const.equiv_iff_keysArray_unit_perm",
"Std.DTreeMap.Raw"
] | true |
_private.Mathlib.RingTheory.MvPolynomial.MonomialOrder.0.MonomialOrder.monic_X_add_C._simp_1_1 | Mathlib.RingTheory.MvPolynomial.MonomialOrder | [
"not_le",
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"LT.lt",
"propext",
"Eq.symm",
"LinearOrder.toPartialOrder",
"Eq",
"Not"
] | false |
PartialEquiv.trans_transEquiv | Mathlib.Logic.Equiv.PartialEquiv | [
"PartialEquiv.transEquiv",
"congrArg",
"PartialEquiv",
"PartialEquiv.trans",
"Equiv",
"Equiv.toPartialEquiv",
"PartialEquiv.transEquiv_eq_trans",
"congr",
"True",
"eq_self",
"of_eq_true",
"PartialEquiv.trans_assoc",
"Eq",
"Eq.trans"
] | true |
FiniteGaloisIntermediateField.instIsSeparableSubtypeMemIntermediateFieldMin | Mathlib.FieldTheory.Galois.GaloisClosure | [
"instSMulOfMul",
"IntermediateField",
"IntermediateField.toField",
"Algebra",
"Membership.mem",
"Field.toDivisionRing",
"CompleteLattice.toConditionallyCompleteLattice",
"Algebra.toModule",
"Subtype",
"DivisionRing.toRing",
"SemilatticeInf.toMin",
"Field.toSemifield",
"Field.toCommRing",
"... | true |
AlgebraicGeometry.germ_injective_of_isIntegral | Mathlib.AlgebraicGeometry.FunctionField | [
"AlgebraicGeometry.IsIntegral",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"RingHom.instRingHomClass",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"RingHomClass.toAddMonoidHomClass",
"CommRingCat.Hom.hom",
"Opposite",
"CommRingCat.carrier",
"Al... | true |
Set.prod_eq_biUnion_left | Mathlib.Data.Set.Lattice.Image | [
"Set.instSProd",
"Eq.mpr",
"SProd.sprod",
"congrArg",
"Membership.mem",
"id",
"Prod.mk",
"Set.image2_mk_eq_prod",
"Set.iUnion_image_left",
"Set.image2",
"Eq.refl",
"Set.image",
"Prod",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | true |
PiTensorProduct.dualDistribEquiv.eq_1 | Mathlib.LinearAlgebra.PiTensorProduct.Dual | [
"PiTensorProduct.instModule",
"CommRing",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Finite",
"PiTensorProduct.dualDistribEquivOfBasis",
"AddCommGroup",
"Algebra.id",
"PiTensorProduct.instAddCommMonoid",
"LinearMap.module",
"M... | true |
LowerSet.instPartialOrder._proof_1 | Mathlib.Order.UpperLower.CompleteLattice | [
"SetLike.coe_injective",
"LE",
"SetLike.coe",
"Function.Injective",
"LowerSet",
"Set",
"LowerSet.instSetLike"
] | false |
Equiv.permCongrHom_coe | Mathlib.Algebra.Group.End | [
"MulEquiv.instEquivLike",
"Equiv.instEquivLike",
"Equiv",
"Equiv.permCongr",
"Equiv.permCongrHom",
"Equiv.Perm",
"Equiv.Perm.instMul",
"MulEquiv",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
Nat.primeFactorsList_one | Mathlib.Data.Nat.Factors | [
"Eq.mpr",
"congrArg",
"id",
"instOfNatNat",
"Nat.primeFactorsList.eq_2",
"List",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Nat.primeFactorsList",
"List.nil"
] | true |
_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.succ_ascFactorial.match_1_1 | Mathlib.Data.Nat.Factorial.Basic | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
ContinuousMultilinearMap.prodEquiv._proof_1 | Mathlib.Topology.Algebra.Module.Multilinear.Basic | [
"Function.LeftInverse",
"ContinuousLinearMap.compContinuousMultilinearMap",
"instTopologicalSpaceProd",
"ContinuousMultilinearMap",
"Prod.mk",
"ContinuousLinearMap.snd",
"Prod.fst",
"AddCommMonoid",
"TopologicalSpace",
"Semiring",
"ContinuousLinearMap.fst",
"Eq.refl",
"Module",
"Prod",
"... | false |
CategoryTheory.Abelian.FreydMitchell.instRingEmbeddingRing._proof_26 | Mathlib.CategoryTheory.Abelian.FreydMitchell | [
"CategoryTheory.Abelian.FreydMitchell.instRingEmbeddingRing._proof_6",
"Mul.mk",
"Semigroup.toMul",
"CategoryTheory.Abelian.FreydMitchell.instRingEmbeddingRing._aux_8",
"CategoryTheory.Abelian.FreydMitchell.instRingEmbeddingRing._proof_12",
"Opposite",
"One.mk",
"HMul.hMul",
"AddMonoid.toAddSemigrou... | false |
ConvexCone.instAdd | Mathlib.Geometry.Convex.Cone.Basic | [
"DistribMulAction.toDistribSMul",
"Add.mk",
"AddMonoid.toAddZeroClass",
"ConvexCone.instSetLike",
"AddZeroClass.toAddZero",
"PartialOrder",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"AddZero.toZero",
"instHAdd",
"Set.add",
"SetLike.coe",
"ConvexCone.mk",
"HAdd.hAdd",
"ConvexCone.in... | true |
Lean.Meta.Sym.AlphaShareCommon.State._sizeOf_1 | Lean.Meta.Sym.AlphaShareCommon | [
"instOfNatNat",
"Lean.Meta.Sym.instBEqAlphaKey",
"Lean.PHashSet",
"Lean.PersistentHashSet._sizeOf_inst",
"Lean.Meta.Sym.AlphaKey",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Lean.Meta.Sym.AlphaKey._sizeOf_inst",
"SizeOf.sizeOf",
"instAddNat",
"Lean.Meta.Sym.AlphaShareCommon.State.rec",
"Lean.Meta.Sym.... | false |
NumberField.InfinitePlace.nat_card_stabilizer_eq_one_or_two | Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | [
"Mathlib.Tactic.Push.not_exists._simp_1",
"Set.ext",
"Eq.mpr",
"Fintype.card_ofFinset",
"False",
"Set.fintypeSingleton",
"SetLike.coe_sort_coe",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"eq_false",
"NumberField.ComplexEmbedding.IsConj",
"congrArg",
"NumberField.ComplexEmbedding.... | true |
IsCompact.finite_cover_balls | Mathlib.Topology.MetricSpace.Pseudo.Basic | [
"Real",
"Real.instZero",
"PseudoMetricSpace.toUniformSpace",
"Real.instLT",
"Set.Finite",
"Membership.mem",
"Exists",
"Metric.ball",
"HasSubset.Subset",
"finite_cover_balls_of_compact",
"And",
"PseudoMetricSpace",
"LT.lt",
"Zero.toOfNat0",
"OfNat.ofNat",
"UniformSpace.toTopologicalSpac... | true |
SimpleGraph.deleteEdges_sup | Mathlib.Combinatorics.SimpleGraph.DeleteEdges | [
"SimpleGraph.deleteEdges",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"SimpleGraph.fromEdgeSet",
"CompleteDistribLattice.toCoframe",
"SimpleGraph",
"Max.max",
"sup_sdiff",
"CoheytingAlgebra.toGeneralizedCoheytingAlgebra",
"SimpleGraph.completeAtomicBooleanAlgebra",
"Eq",
"SimpleGraph.ins... | true |
LinearMap.BilinForm.isCompl_span_singleton_orthogonal | Mathlib.LinearAlgebra.BilinearForm.Orthogonal | [
"Submodule",
"LinearMap.BilinForm",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"CompleteLattice.toBoundedOrder",
"AddCommGroup",
"Set.instSingletonSet",
"Submodule.instPartialOrder",
"LinearMap.BilinForm.IsOrtho",
"Field.toSemifield",
"IsCompl",
"Semifield.toDivisionSemiring"... | true |
MonCat.FilteredColimits.colimitCocone.eq_1 | Mathlib.Algebra.Category.MonCat.FilteredColimits | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"MonCat.FilteredColimits.colimit",
"CategoryTheory.Functor.category",
"MonCat.FilteredColimits.colimitCocone._proof_2",
"MonCat.FilteredColimits.coconeMorphism",
"CategoryTheory.Limits.Cocone.mk",
"MonCat",
"CategoryTheory.SmallCategory",
"... | true |
Lean.Widget.instRpcEncodableWidgetInstance.enc._@.Lean.Widget.Types.2243429567._hygCtx._hyg.1 | Lean.Widget.Types | [
"Pure.pure",
"Lean.Json",
"UInt64",
"Monad.toApplicative",
"Lean.instToJsonName",
"Lean.instFromJsonName",
"Lean.Widget.RpcEncodablePacket.mk._@.Lean.Widget.Types.2243429567._hygCtx._hyg.1",
"Lean.ToJson.toJson",
"Lean.Widget.WidgetInstance",
"Id",
"Applicative.toPure",
"Lean.instToJsonJson",
... | false |
Differentiable.inversion | Mathlib.Geometry.Euclidean.Inversion.Calculus | [
"Differentiable",
"InnerProductSpace.toNormedSpace",
"Real",
"Semiring.toModule",
"NormedSpace",
"Real.denselyNormedField",
"Real.instRCLike",
"NormedAddCommGroup.toMetricSpace",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"Ne",
"Real.instAddCommGroup",... | true |
PeriodPair.«term℘'[_-_]» | Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass | [
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
Std.Do.PredTrans.pure | Std.Do.PredTrans | [
"Std.Do.PostCond",
"Std.Do.Assertion",
"Std.Do.PostShape",
"Prod.fst",
"Std.Do.PredTrans.pure._proof_1",
"Std.Do.PredTrans.mk",
"Std.Do.PredTrans",
"Std.Do.ExceptConds"
] | true |
_private.Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Defs.0.EisensteinSeries.D2_mul._simp_1_3 | Mathlib.NumberTheory.ModularForms.EisensteinSeries.E2.Defs | [
"HMul.hMul",
"Mul",
"instHAdd",
"HAdd.hAdd",
"LeftDistribClass",
"mul_add",
"Eq.symm",
"Eq",
"Add",
"instHMul"
] | false |
CategoryTheory.MonoidalClosed.internalHomAdjunction₂._proof_2 | Mathlib.CategoryTheory.Monoidal.Closed.Basic | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.MonoidalClosed.coev_app_comp_pre_app",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ihom.coev",
"Quiver.Hom.op",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor... | false |
CategoryTheory.CountableCategory.instCountableHomAsType | Mathlib.CategoryTheory.Countable | [
"Countable.of_equiv",
"CategoryTheory.CountableCategory.countableObj",
"CategoryTheory.CountableCategory.HomAsType",
"Countable",
"equivShrink",
"Countable.toSmall",
"CategoryTheory.CountableCategory",
"CategoryTheory.Category"
] | true |
Filter.Tendsto.limsup_comp_le_limsup | Mathlib.Order.LiminfLimsup | [
"Filter.limsup_comp",
"Eq.mpr",
"congrArg",
"Filter.Tendsto.limsup_comp_le_limsup._auto_1",
"Filter.Tendsto.limsup_comp_le_limsup._auto_3",
"Filter.map",
"PartialOrder.toPreorder",
"ConditionallyCompleteLattice",
"Preorder.toLE",
"Filter.IsCoboundedUnder",
"Function.comp",
"id",
"LE.le",
"... | true |
LinearMap.IsSymm.tmul | Mathlib.LinearAlgebra.BilinearForm.TensorProduct | [
"Eq.mpr",
"IsScalarTower.to_smulCommClass'",
"Algebra.to_smulCommClass",
"instHSMul",
"Semiring.toModule",
"IsScalarTower.right",
"LinearMap.ext",
"LinearMap.isSymm_iff_eq_flip",
"LinearMap.BilinForm",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
... | true |
SNum.le | Mathlib.Data.Num.Lemmas | [
"Int",
"SNum",
"LE.le",
"LE",
"LE.mk",
"Int.instLEInt",
"Int.ofSnum"
] | true |
disjoint_compl_left_iff | Mathlib.Order.BooleanAlgebra.Basic | [
"Eq.mpr",
"BooleanAlgebra",
"compl_compl",
"congrArg",
"Compl.compl",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"BooleanAlgebra.toCompl",
"SemilatticeInf.toPartialOrder",
"id",
"BiheytingAlgebra.toHeytingAlgebra",
"BiheytingAlgebra.toCoheytingAlgebra",
"LE.le",
... | true |
AlgebraicGeometry.HasAffineProperty.affineAnd_le_affineAnd | Mathlib.AlgebraicGeometry.Morphisms.AffineAnd | [
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CommRing",
"AlgebraicGeometry.Scheme",
"ChainCompletePartialOrder.instOfCompleteLattice",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"congrArg",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Preorder.toLE",
"RingHom",
"i... | true |
Std.TreeMap.Raw.Equiv.mergeWith | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.Equiv.constMergeWith",
"Std.TreeMap.Raw.Equiv.inner",
"Ordering",
"Std.TreeMap.Raw.Equiv",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"Std.LawfulEqCmp",
"Std.TreeMap.Raw.Equiv.mk",
"Std.TreeMap.Raw.mergeWith"
] | true |
_private.BatteriesRecycling.RBTree.Lemmas.0.RBTree.RBNode.isOrdered.match_1.eq_2 | BatteriesRecycling.RBTree.Lemmas | [
"Eq.mpr",
"False",
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"congrArg",
"RBTree.RBNode.all₂._sparseCasesOn_1.else_eq",
"False.elim",
"RBTree.RBNode.isOrdered.match_1",
"Nat.shiftRight",
"Option.some",
"id",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
... | true |
Std.Async.System.CPUTimes.recOn | Std.Async.System | [
"Std.Async.System.CPUTimes",
"Std.Time.Millisecond.Offset",
"Std.Async.System.CPUTimes.mk",
"Std.Async.System.CPUTimes.rec"
] | false |
Mathlib.Tactic.TFAE.Parser.tfaeHaveDecl.formatter | Mathlib.Tactic.TFAE | [
"Lean.PrettyPrinter.Formatter",
"Lean.PrettyPrinter.Formatter.orelse.formatter",
"Lean.ppSpace.formatter",
"Mathlib.Tactic.TFAE.Parser.tfaeHaveIdDecl.formatter",
"Lean.Name.mkStr5",
"Lean.Parser.withCache.formatter",
"Lean.Parser.leadingNode.formatter",
"instOfNatNat",
"Lean.PrettyPrinter.Formatter.... | true |
Lean.Meta.Grind.ExprWithAnchor.anchor | Lean.Meta.Tactic.Grind.Anchor | [
"UInt64",
"Lean.Meta.Grind.ExprWithAnchor"
] | true |
CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite | Mathlib.CategoryTheory.Preadditive.Opposite | [
"Semiring.toModule",
"CategoryTheory.moduleEndLeft",
"LinearEquiv.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"MulOpposite",
"CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpposite.match_1",
"CategoryTheory.Preadditive.homSelfLinearEquivEndMulOpp... | true |
Lean.Meta.UnificationHintEntry.mk.noConfusion | Lean.Meta.UnificationHint | [
"Lean.Meta.UnificationHintKey",
"id",
"Array",
"Lean.Name",
"Lean.Meta.UnificationHintEntry.mk",
"Eq",
"Lean.Meta.UnificationHintEntry",
"Lean.Meta.UnificationHintEntry.noConfusion"
] | false |
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