name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Action.forget_δ | Mathlib.CategoryTheory.Action.Monoidal | [
"Monoid",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Functor.OplaxMonoidal.δ",
"Action.instMonoidalForget",
"Action.instMonoidalCategory",
"Action.forget",
"CategoryTheory.Functor.Monoidal.toOplaxMo... | true |
ContinuousMonoidHom.instCoeOutOfMonoidHomClassOfContinuousMapClass | Mathlib.Topology.Algebra.ContinuousMonoidHom | [
"Monoid",
"Monoid.toMulOneClass",
"ContinuousMonoidHom.toContinuousMonoidHom",
"ContinuousMapClass",
"CoeOut.mk",
"CoeOut",
"TopologicalSpace",
"MulOneClass.toMulOne",
"ContinuousMonoidHom",
"MonoidHomClass",
"FunLike"
] | true |
CategoryTheory.MorphismProperty.Over.isoMk._proof_3 | Mathlib.CategoryTheory.MorphismProperty.Comma | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"congrArg",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"CategoryTheory.Comma.hom",
"id",
"Category... | false |
_private.Init.Data.Int.LemmasAux.0.Int.ble'_eq_true._proof_1_4 | Init.Data.Int.LemmasAux | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Classical.propDecidable",
"Lean.Omega.Linear... | false |
Std.TreeMap.getKeyD_minKey? | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.minKey?",
"Std.DTreeMap.getKeyD_minKey?",
"Std.TreeMap.inner",
"Option.some",
"Ordering",
"Std.TransCmp",
"Std.TreeMap.getKeyD",
"Eq",
"Std.TreeMap",
"Option"
] | true |
ZMod.valMinAbs_natAbs_eq_min | Mathlib.Data.ZMod.ValMinAbs | [
"Eq.mpr",
"Nat.instMulZeroClass",
"_private.Mathlib.Data.ZMod.ValMinAbs.0.ZMod.valMinAbs_natAbs_eq_min._proof_1_1",
"instHDiv",
"ZMod.valMinAbs_def_pos",
"congrArg",
"ZMod.valMinAbs",
"HSub.hSub",
"id",
"HDiv.hDiv",
"instSubNat",
"instOfNatNat",
"Int",
"LE.le",
"instLENat",
"Nat.cast",... | true |
Std.HashMap.isEmpty_inter_right | Std.Data.HashMap.Lemmas | [
"Std.HashMap",
"LawfulHashable",
"Std.DHashMap.isEmpty_inter_right",
"Inter.inter",
"Bool.true",
"EquivBEq",
"Std.HashMap.isEmpty",
"Bool",
"Std.HashMap.instInter",
"Hashable",
"Std.HashMap.inner",
"BEq",
"Eq"
] | true |
Lean.getAttrParamOptPrio | Lean.Attributes | [
"Pure.pure",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.indentD",
"Lean.Core.instMonadRefCoreM",
"Lean.AttrM",
"String",
"_private.Lean.Attributes.0.Lean.getAttrParamOptPrio.match_1",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.... | true |
CategoryTheory.Preadditive.mono_iff_injective | Mathlib.Algebra.Homology.ShortComplex.ConcreteCategory | [
"Eq.mpr",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.Additive",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.reflectsMonomorphisms_of_faithful",
"Ad... | true |
_private.Init.Data.String.Lemmas.Pattern.Basic.0.String.Slice.Pattern.ToBackwardSearcher.DefaultBackwardSearcher.instIteratorIdSearchStepOfBackwardPattern.match_3.eq_1 | Init.Data.String.Lemmas.Pattern.Basic | [
"String.Slice.Pattern.SearchStep",
"Option.some",
"String.Slice",
"Id",
"Std.IterM.internalState",
"String.Slice.Pattern.ToBackwardSearcher.DefaultBackwardSearcher.currPos",
"Option.none",
"String.Slice.Pattern.ToBackwardSearcher.DefaultBackwardSearcher.instIteratorIdSearchStepOfBackwardPattern.match_... | true |
ArchimedeanClass.FiniteElement._proof_2 | Mathlib.Algebra.Order.Ring.StandardPart | [
"IsDomain.to_noZeroDivisors",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"IsOrderedRing",
"LinearOrder",
"IsStrictOrderedRing",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"DivisionRing.toRing",
"Field.toSemifield",
... | false |
CategoryTheory.HasDetector.casesOn | Mathlib.CategoryTheory.Generator.Basic | [
"CategoryTheory.HasDetector.mk",
"Exists",
"CategoryTheory.HasDetector.rec",
"CategoryTheory.HasDetector",
"CategoryTheory.IsDetector",
"CategoryTheory.Category"
] | false |
PowerSeries.substInvOfIsUnit | Mathlib.RingTheory.PowerSeries.Substitution | [
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"IsUnit",
"PowerSeries.substInv",
"PowerSeries.coeff",
"instOfNatNat",
"MvPowerSeries.instModule",
"LinearMap",
"MvPowerSeries.instAddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"IsUnit.inverti... | true |
isIrreducible_iff_sInter | Mathlib.Topology.Irreducible | [
"IsPreirreducible",
"Eq.mpr",
"False",
"Finset.coe_singleton",
"Finset.coe_empty",
"Set.sInter_empty",
"congrArg",
"and_self",
"Finset",
"IsIrreducible",
"Set.univ",
"Set.inter_univ",
"forall_eq_or_imp._simp_1",
"Set.sInter_insert",
"instInhabitedTrue",
"Finset.forall_mem_insert",
"M... | true |
deriv_const_add_id | Mathlib.Analysis.Calculus.Deriv.Add | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"deriv",
"NormedSpace.toModule",
"AddGroupWithOne.toAddMonoidWithOne",
"deriv_id''",
"PseudoMetricSpace.toUniformSpace",
"Norm... | true |
derivWithin_const_smul | Mathlib.Analysis.Calculus.Deriv.Mul | [
"NormedCommRing.toNormedRing",
"Monoid",
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"Semiring.toModule",
"NormedRing.toRing",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUnifo... | true |
TendstoLocallyUniformlyOn.comp | Mathlib.Topology.UniformSpace.LocallyUniformConvergence | [
"Filter.instMembership",
"UniformSpace",
"TendstoLocallyUniformlyOn",
"nhdsWithin",
"Filter.Eventually",
"uniformity",
"Function.comp",
"Membership.mem",
"Exists",
"Prod.mk",
"ContinuousWithinAt.preimage_mem_nhdsWithin'",
"And.casesOn",
"Filter.Eventually.mono",
"TopologicalSpace",
"And"... | true |
Hyperreal.instField._proof_7 | Mathlib.Analysis.Real.Hyperreal | [
"Real",
"Add.mk",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"Filter.hyperfilter",
"Hyperreal.instField._aux_4",
"AddSemigroup.mk",
"Field.toCommRing",
"Filter.Germ.instAddMonoid._proof_6",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Nat... | false |
_private.Init.Data.Range.Polymorphic.NatLemmas.0.Nat.toArray_roc_add_succ_right_eq_push._proof_1_1 | Init.Data.Range.Polymorphic.NatLemmas | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.ev... | false |
Lean.KeyedDeclsAttribute.AttributeEntry.ctorIdx | Lean.KeyedDeclsAttribute | [
"Lean.KeyedDeclsAttribute.AttributeEntry",
"Nat"
] | false |
CategoryTheory.Pretriangulated.Opposite.rotateTriangleOpEquivalenceInverseObjRotateUnopIso._proof_4 | Mathlib.CategoryTheory.Triangulated.Opposite.Pretriangulated | [
"CategoryTheory.Equivalence.unitIso",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pretriangulated.Opposite.rotateTriangleOpEquivalenceInverseObjRotateUnopIso._proof_2",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"Quiver.Ho... | false |
_private.Mathlib.RingTheory.KrullDimension.Regular.0.ringKrullDim_quotient_span_singleton_succ_eq_ringKrullDim_of_mem_jacobson._simp_1_1 | Mathlib.RingTheory.KrullDimension.Regular | [
"Submodule.pointwiseDistribMulAction",
"Submodule",
"instHSMul",
"Submodule.ideal_span_singleton_smul",
"Semiring.toModule",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Set.instSingletonSet",
"DistribSMul.toSMulZeroClass",
... | false |
Metric.Snowflaking.instT2Space | Mathlib.Topology.MetricSpace.Snowflaking | [
"Real.instLE",
"Real",
"Metric.Snowflaking.instTopologicalSpace",
"Real.instZero",
"Real.instLT",
"LE.le",
"Real.instOne",
"TopologicalSpace",
"Metric.Snowflaking.homeomorph",
"Homeomorph.symm",
"T2Space",
"LT.lt",
"One.toOfNat1",
"Zero.toOfNat0",
"Metric.Snowflaking",
"OfNat.ofNat",
... | true |
LinearMap.BilinMap.tmul | Mathlib.LinearAlgebra.BilinearForm.TensorProduct | [
"LinearMap.BilinMap.tensorDistrib",
"LinearMap.BilinMap.tensorDistrib._proof_7",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"TensorProduct.addCommMonoid",
"LinearMap.BilinMap",
"AddMonoid.toAddZeroClass",
"LinearMap.BilinMap.tensorDistrib._proof_8",
"LinearMap.in... | true |
ENNReal.toNNReal_natCast_eq_toNNReal | Mathlib.Data.ENNReal.Basic | [
"Real.instIsOrderedRing",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real",
"Real.instZeroLEOneClass",
"congrArg",
"Nat.cast_nonneg",
"AddGroupWithOne.toAddMonoidWithOne",
"Real.semiring",
"id",
"NNReal.mk",
"Nat.cast_nonneg'",
"AddMonoidWithOne.toNatCast",
... | true |
Cardinal.lift_eq_zero | Mathlib.SetTheory.Cardinal.Order | [
"Cardinal.lift_zero",
"Cardinal",
"Cardinal.lift",
"Function.Injective.eq_iff'",
"Iff",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Cardinal.instZero",
"Cardinal.lift_injective"
] | true |
ContinuousMap.Homotopy.mk.inj | Mathlib.Topology.Homotopy.Basic | [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"ContinuousMap.Homotopy.mk.noConfusion",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceProd",
"Membership.mem",
"Real.semiring",
"Set.Elem",
"Prod.mk",
"TopologicalSpace",
"eq_of_heq",
... | true |
Lean.Omega.Coeffs.isZero | Init.Omega.Coeffs | [
"Membership.mem",
"Int",
"List.instMembership",
"instOfNat",
"Lean.Omega.Coeffs",
"OfNat.ofNat",
"Eq"
] | true |
CartanMatrix.E₆.eq_1 | Mathlib.Data.Matrix.Cartan | [
"Equiv.instEquivLike",
"Matrix",
"Matrix.of",
"Equiv",
"Int.instNegInt",
"instOfNatNat",
"Int",
"instOfNat",
"Nat",
"CartanMatrix.E₆",
"Matrix.vecEmpty",
"Eq.refl",
"OfNat.ofNat",
"Fin",
"Eq",
"DFunLike.coe",
"Matrix.vecCons",
"Neg.neg",
"EquivLike.toFunLike"
] | true |
Aesop.IndexMatchLocation.none.elim | Aesop.Index.Basic | [
"PULift.up",
"Aesop.IndexMatchLocation.ctorElim",
"Nat",
"Aesop.IndexMatchLocation.ctorIdx",
"Eq.symm",
"Eq",
"Aesop.IndexMatchLocation.none",
"Aesop.IndexMatchLocation"
] | false |
CategoryTheory.ComposableArrows.threeδ₃Toδ₂.congr_simp | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.ComposableArrows",
"Eq.rec",
"Preorder.smallCategory",
"instOfNatNat",
"instHAdd",
"CategoryTheory.ComposableArrows.mk₂",
"Fin.instPartialOrder",
"HAdd.hAdd",
... | true |
Unitization.inrRangeEquiv._proof_1 | Mathlib.Algebra.Algebra.Unitization | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"CommSemiring.toSemiring",
"Unitization.instDistribMulAction",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"StarAddMonoid.toInvolutiveStar",
"NonUnitalStarAlgHom.instFunLike",
"CommSemirin... | false |
Right.inv_le_self | Mathlib.Algebra.Order.Group.Unbundled.Basic | [
"Iff.mpr",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Preorder.toLE",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"MulRightMono",
"LE.le",
"Right.inv_le_one_iff",
"Group.toDivInvMonoid",... | true |
Batteries.RBMap.instForInValuesOfMonad | Batteries.Data.RBMap.Basic | [
"Batteries.RBNode.WF",
"Batteries.RBNode",
"Ordering.byKey",
"Ordering",
"ForInStep",
"Prod.fst",
"ForIn.mk",
"ForIn",
"Batteries.RBNode.forIn",
"Prod",
"Monad",
"Subtype.val",
"Prod.snd",
"Batteries.RBMap.Values"
] | true |
Prod.smulZeroClass | Mathlib.Algebra.GroupWithZero.Action.Prod | [
"SMulZeroClass",
"Prod.instSMul",
"SMulZeroClass.mk",
"Prod.instZero",
"Prod.smulZeroClass._proof_1",
"SMulZeroClass.toSMul",
"Prod",
"Zero"
] | true |
_private.Mathlib.Algebra.Polynomial.RuleOfSigns.0.Polynomial.signVariations_eraseLead_mul_X_sub_C._proof_1_1 | Mathlib.Algebra.Polynomial.RuleOfSigns | [
"Int.Linear.eq_of_core",
"Polynomial.C",
"Int.Linear.not_eq_norm_expr",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"Polynomial.nextCoeff_of_natDegree_pos",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Int.Linear.norm_le",
"eq_false",
"L... | false |
IsPurelyInseparable.tower_bot | Mathlib.FieldTheory.PurelyInseparable.Basic | [
"IsSeparable.eq_1",
"Subring.instSetLike",
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"congrArg",
"CommSemiring.toSemiring",
"IsScalarTower",
"IsPurelyInseparable.isIntegral'",
"Algebra",
"RingHom",
"Algebra.toSMul",
"Membership.mem",
"Field.toDivisionRing",
"Eq.rec",
"Eq.mp",
"IsPur... | true |
CategoryTheory.Limits.image.lift_mk_factorThruImage_assoc | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.Limits.MonoFactorisation.I",
"CategoryTheory.Limits.factorThruImage",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.image.lift_mk_factorThruImage",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.image.ι",
"Eq.mp",
"CategoryTheor... | true |
Std.Http.Status.notFound.sizeOf_spec | Std.Internal.Http.Data.Status | [
"Std.Http.Status.notFound",
"instOfNatNat",
"Std.Http.Status",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Std.Http.Status._sizeOf_inst"
] | true |
Lean.DataValue.recOn | Lean.Data.KVMap | [
"Lean.DataValue.ofInt",
"Lean.DataValue.rec",
"String",
"Lean.Syntax",
"Int",
"Nat",
"Lean.DataValue.ofBool",
"Lean.DataValue.ofString",
"Bool",
"Lean.Name",
"Lean.DataValue",
"Lean.DataValue.ofSyntax",
"Lean.DataValue.ofNat",
"Lean.DataValue.ofName"
] | false |
Perfection.lift | Mathlib.RingTheory.Perfection | [
"PerfectRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Nat.Prime",
"RingHom.mk",
"Perfection",
"frobeniusEquiv",
"CommSemiring.toSemiring",
"RingEquiv.instEquivLike",
"OneHom.mk",
"RingHom",
"Fact",
"Equiv.mk",
"Equiv",
"Distrib.toAdd",
"Perfection.lift._proof_9",
... | true |
Polynomial.instFree | Mathlib.LinearAlgebra.Finsupp.VectorSpace | [
"LinearEquiv.symm",
"Semiring.toModule",
"AddMonoidAlgebra.addAddCommMonoid",
"Polynomial",
"Module.Free",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Polynomial.semiring",
"Nat",
"RingHomInvPair.ids",
"Module.Free.of_equiv",
"Module.Free.self"... | true |
Lean.Elab.Frontend.State.ctorIdx | Lean.Elab.Frontend | [
"Lean.Elab.Frontend.State",
"Nat"
] | false |
Polynomial.separable_C_mul_X_pow_add_C_mul_X_add_C | Mathlib.FieldTheory.Separable | [
"Polynomial.derivative",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"Polynomial.C",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"MulOne.toOne",
"Polynomial.derivative_mul",
"Polynomial.instOne",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonA... | true |
CategoryTheory.ShortComplex.π₂_map | Mathlib.Algebra.Homology.ShortComplex.Basic | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.ShortComplex.Hom.τ₂",
"CategoryTheory.Functor.map",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"C... | true |
zpow_mod_orderOf | Mathlib.GroupTheory.OrderOfElement | [
"zpow_natCast",
"Eq.mpr",
"MulOne.toOne",
"Int.instDiv",
"Trans.trans",
"zpow_add",
"instHDiv",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"zpow_mul",
"DivInvMonoid.toZPow",
"Group",
"one_zpow",
"Group.toDivisionMonoid",
"... | true |
Matrix.instNonAssocRing._proof_5 | Mathlib.Data.Matrix.Mul | [
"AddMonoid.toAddSemigroup",
"Matrix",
"AddMonoid.toZero",
"AddCommGroup.toAddGroup",
"NonAssocRing",
"NonAssocRing.toAddCommGroupWithOne",
"instHAdd",
"AddSemigroup.toAdd",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"SubNegMonoid.toNeg",
"Matrix.instAddCommGroupWithOne",
"Zero.toOfNat0",
"Sub... | false |
Nat.prod_mem_smoothNumbers | Mathlib.NumberTheory.SmoothNumbers | [
"Nat.instOne",
"congrArg",
"Finset",
"Decidable.decide.congr_simp",
"_private.Mathlib.NumberTheory.SmoothNumbers.0.Nat.prod_mem_smoothNumbers._simp_1_1",
"Membership.mem",
"instMulNat",
"Finset.range",
"Nat.smoothNumbers_eq_factoredNumbers",
"funext",
"List",
"Nat.factoredNumbers",
"Finset.i... | true |
CategoryTheory.Functor.FullyFaithful.addMonObj._proof_3 | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.Functor.FullyFaithful.map_injective",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.FullyFaithful.addMonObj._proof_4",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"... | false |
String.Pos.isUTF8FirstByte_getUTF8Byte_offset | Init.Data.String.Lemmas.Order | [
"Eq.mpr",
"String.instLTRaw",
"congrArg",
"String.Pos.byte",
"String",
"String.Pos.getUTF8Byte_offset._proof_1",
"id",
"String.getUTF8Byte",
"String.Pos.Raw",
"String.rawEndPos",
"UInt8.IsUTF8FirstByte",
"String.Pos.isUTF8FirstByte_byte",
"LT.lt",
"String.Pos",
"String.Pos.getUTF8Byte_of... | true |
_private.Mathlib.Data.Finset.Sym.0.Finset.not_isDiag_mk_of_mem_offDiag._proof_1_1 | Mathlib.Data.Finset.Sym | [
"Lean.Grind.eq_false_of_not_eq_true",
"False",
"Lean.Grind.not_not",
"Finset",
"Classical.byContradiction",
"Membership.mem",
"Eq.mp",
"id",
"And",
"Finset.instSetLike",
"True",
"eq_true",
"Lean.Grind.intro_with_eq",
"Lean.Grind.eq_true_of_and_eq_true_right",
"Eq.symm",
"Eq",
"Not",
... | false |
_private.Std.Time.Date.Unit.Year.0.Std.Time.Year.instReprEra.repr.match_1 | Std.Time.Date.Unit.Year | [
"Std.Time.Year.Era.casesOn",
"Unit.unit",
"Std.Time.Year.Era.bce",
"Std.Time.Year.Era",
"Unit",
"Std.Time.Year.Era.ce"
] | false |
Filter.map_neg | Mathlib.Order.Filter.Pointwise | [
"Filter.map",
"Filter.instNeg",
"Neg",
"Eq",
"Filter",
"Neg.neg",
"rfl"
] | true |
DirectLimit.instMulActionOfMulActionHomClass._proof_4 | Mathlib.Algebra.Colimit.DirectLimit | [
"MulActionHomClass",
"Monoid",
"MulOne.toOne",
"instHSMul",
"DirectLimit.instSMul",
"Monoid.toMulOneClass",
"DirectLimit.instMulActionOfMulActionHomClass._proof_2",
"Preorder.toLE",
"LE.le",
"DirectLimit",
"MulOneClass.toMulOne",
"MulAction",
"IsDirectedOrder",
"Monoid.toSemigroup",
"One... | false |
_private.Mathlib.Data.Seq.Parallel.0.Computation.parallel.aux1.match_1.eq_3 | Mathlib.Data.Seq.Parallel | [
"Stream'.Seq",
"Option.some",
"Prod.mk",
"Computation",
"_private.Mathlib.Data.Seq.Parallel.0.Computation.parallel.aux1.match_1",
"Option.none",
"Unit",
"Stream'.Seq1",
"Eq.refl",
"Eq",
"Option"
] | true |
CategoryTheory.Retract.trans._proof_2 | Mathlib.CategoryTheory.Retract | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Retract.retract",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Retract.i",
"CategoryTheory.Retract",
"CategoryTheory.Retract.r",
"True",
"eq_self",
"CategoryTheory.Catego... | false |
Subsemiring.centralizer_eq_top_iff_subset | Mathlib.Algebra.Ring.Subsemiring.Basic | [
"Subsemiring.instSetLike",
"Subsemiring.centralizer",
"Set.centralizer_eq_top_iff_subset",
"SemigroupWithZero.toSemigroup",
"HasSubset.Subset",
"NonUnitalSemiring.toSemigroupWithZero",
"Subsemiring",
"Iff",
"SetLike.coe",
"Subsemiring.instTop",
"SetLike.ext'_iff",
"Iff.trans",
"Semiring",
... | true |
VAdd.mk._flat_ctor | Mathlib.Algebra.Notation.Defs | [
"VAdd",
"VAdd.mk"
] | false |
Std.Rxc.LawfulHasSize.size_eq_succ_of_succ?_eq_some | Init.Data.Range.Polymorphic.Basic | [
"Std.PRange.UpwardEnumerable",
"Std.Rxc.HasSize",
"Option.some",
"Std.Rxc.LawfulHasSize",
"instOfNatNat",
"LE.le",
"Std.PRange.UpwardEnumerable.succ?",
"LE",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Std.Rxc.HasSize.size",
"OfNat.ofNat",
"Eq",
"Option"
] | true |
right_eq_ite_iff | Init.PropLemmas | [
"Eq.mpr",
"False",
"Decidable.casesOn",
"eq_false",
"congrArg",
"instInhabitedTrue",
"Decidable",
"id",
"if_pos",
"false_implies",
"iff_self",
"Iff",
"implies_congr",
"instNonemptyOfInhabited",
"forall_const._simp_1",
"congr",
"True",
"eq_self",
"eq_true",
"of_eq_true",
"Eq.r... | true |
isDedekindDomain_iff | Mathlib.RingTheory.DedekindDomain.Basic | [
"Iff.mpr",
"IsDomain",
"IsDedekindDomain.toIsDomain",
"IsDedekindRing.toIsIntegralClosure",
"CommRing",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"IsFractionRing",
"Algebra",
"RingHom",
"Exists",
"inferInstance",
"IsNoetherianRing",
"IsDedekindDomain.toIsDedekindRing",
"And",
"I... | true |
Lean.RBNode.fold._unsafe_rec | Lean.Data.RBMap | [
"Lean.RBColor",
"Lean.RBNode",
"_private.Lean.Data.RBMap.0.Lean.RBNode.fold.match_1",
"Lean.RBNode.fold._unsafe_rec"
] | false |
AddSubgroup.index_pi | Mathlib.GroupTheory.Index | [
"Eq.mpr",
"Setoid.piQuotientEquiv",
"Pi.addGroup",
"Finset.univ",
"congrArg",
"AddSubgroup.index",
"Equiv.trans",
"Finset",
"Set.univ",
"Iff.rfl",
"Membership.mem",
"id",
"Nat.card",
"Setoid",
"Finset.prod_congr",
"Finset.prod",
"AddSubgroup",
"piSetoid",
"Quotient.congrRight",
... | true |
_private.Mathlib.CategoryTheory.Shift.ShiftSequence.0.CategoryTheory.Functor.ShiftSequence.tautological._simp_4 | Mathlib.CategoryTheory.Shift.ShiftSequence | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.map",
"CategoryTheory.Functor.map_comp_assoc",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq.symm",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheor... | false |
Real.summable_Lp_add_of_nonneg | Mathlib.Analysis.MeanInequalities | [
"Real.instPow",
"Real.instLE",
"Real",
"instHDiv",
"Real.instZero",
"Real.instDivInvMonoid",
"PseudoMetricSpace.toUniformSpace",
"HDiv.hDiv",
"Real.Lp_add_le_tsum_of_nonneg",
"LE.le",
"Real.instAdd",
"Real.instOne",
"instHAdd",
"HPow.hPow",
"And.left",
"HAdd.hAdd",
"tsum",
"DivInvM... | true |
Lean.Elab.Tactic.ResolveSimpIdResult._sizeOf_1 | Lean.Elab.Tactic.Simp | [
"Lean.Meta.Simp.SimprocEntry",
"Lean.ScopedEnvExtension._sizeOf_inst",
"Option._sizeOf_inst",
"Lean.Meta.Simp.SimprocOLeanEntry",
"instSizeOfDefault",
"Lean.Elab.Tactic.ResolveSimpIdResult",
"Lean.Expr",
"Lean.Meta.Simp.Simprocs._sizeOf_inst",
"instOfNatNat",
"Lean.Meta.SimpEntry._sizeOf_inst",
... | false |
Seminorm.closedBall_zero' | Mathlib.Analysis.Seminorm | [
"Real",
"Set.eq_univ_of_subset",
"Real.instZero",
"Set.univ",
"SMul",
"Real.instLT",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Seminorm.closedBall",
"Seminorm",
"Seminorm.instZero",
"Seminorm.ball_zero'",
"Seminorm.ball",
"LT.lt",
"Seminorm.ball_subset_closedBall",
"Zero.toOfNat0",
... | true |
_private.Mathlib.Algebra.NoZeroSMulDivisors.Defs.0.instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors._simp_1 | Mathlib.Algebra.NoZeroSMulDivisors.Defs | [
"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 |
Encodable.decidableRangeEncode.match_1 | Mathlib.Logic.Encodable.Basic | [
"Membership.mem",
"Exists.casesOn",
"Nat",
"Exists.intro",
"Encodable.encode",
"Set.range",
"Eq",
"Set.instMembership",
"Encodable",
"Set"
] | false |
Polynomial.coeff_hermite_succ_zero | Mathlib.RingTheory.Polynomial.Hermite.Basic | [
"CharP.cast_eq_zero",
"Polynomial.derivative",
"Polynomial.coeff_derivative",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"congrArg",
"MulZeroClass.zero_mul",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Linea... | true |
Cross.lieRing._proof_1 | Mathlib.LinearAlgebra.CrossProduct | [
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Function.smulCommClass",
"Algebra.id",
"Function.hasSMul",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"instOfNatNat"... | false |
SimpleGraph.Copy.mapNeighborSet | Mathlib.Combinatorics.SimpleGraph.Copy | [
"SimpleGraph.Copy.mapNeighborSet._proof_2",
"Membership.mem",
"SimpleGraph.neighborSet",
"Function.Embedding.mk",
"SimpleGraph.Copy",
"Set.Elem",
"Function.Embedding",
"SimpleGraph.Copy.instFunLike",
"Subtype.mk",
"SimpleGraph",
"SimpleGraph.Copy.mapNeighborSet._proof_1",
"Subtype.val",
"Eq"... | true |
WithVal.instOne | Mathlib.Topology.Algebra.Valued.WithVal | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"One",
"One.mk",
"AddGroupWithOne.toAddMonoidWithOne",
"LinearOrderedCommGroupWithZero",
"AddMonoidWithOne.toOne",
"WithVal",
"One.toOfNat1",
"OfNat.ofNat",
"Ring",
"Ring.toAddGroupWithOne",
"Valuation",
"WithVal.toVal"
] | true |
AffineSubspace.sSameSide_vadd_left_iff | Mathlib.Analysis.Convex.Side | [
"Eq.mpr",
"Submodule",
"CommRing",
"AddMonoid.toAddSemigroup",
"AffineSubspace.SSameSide.eq_1",
"congrArg",
"CommSemiring.toSemiring",
"AffineSubspace.SSameSide",
"AddCommGroup.toAddCommMonoid",
"Iff.rfl",
"IsStrictOrderedRing",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AffineSubspace.... | true |
if_true | Init.ByCases | [
"trivial",
"Decidable",
"if_pos",
"True",
"Eq",
"ite"
] | true |
Subsemiring.mk'.congr_simp | Mathlib.Algebra.Ring.Subsemiring.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Subsemiring.mk'",
"AddMonoid.toAddZeroClass",
"Eq.rec",
"AddSubmonoid",
"NonAssocSemiring.toMulZeroOneClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Subsemiring",
"MulZeroOneClass.toMulOneClass",
"NonAssocSemiring",
"SetLike.coe",
"Eq.ndrec",
... | true |
ZFSet.coe_union._simp_1 | Mathlib.SetTheory.ZFC.Basic | [
"ZFSet",
"Set.instUnion",
"ZFSet.instUnion",
"SetLike.coe",
"Union.union",
"Eq.symm",
"Eq",
"ZFSet.instSetLike",
"ZFSet.coe_union",
"Set"
] | false |
Computation.LiftRel.swap | Mathlib.Data.Seq.Computation | [
"Function.swap",
"Membership.mem",
"Exists",
"and_comm",
"Computation",
"And",
"Iff",
"Computation.instMembership",
"Computation.LiftRel"
] | true |
Filter.tendsto_inv₀_cobounded | Mathlib.Analysis.Normed.Field.Lemmas | [
"GroupWithZero.toDivisionMonoid",
"PseudoMetricSpace.toBornology",
"DivInvOneMonoid.toInvOneClass",
"Compl.compl",
"Filter.instCompleteLatticeFilter",
"nhdsWithin",
"NormedDivisionRing.toNormedRing",
"PseudoMetricSpace.toUniformSpace",
"DivisionSemiring.toGroupWithZero",
"NormedDivisionRing.toDivi... | true |
_private.Mathlib.Combinatorics.Matroid.Constructions.0.Matroid.restrict_empty._simp_1_1 | Mathlib.Combinatorics.Matroid.Constructions | [
"Matroid.E",
"Matroid.emptyOn",
"propext",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq.symm",
"Eq",
"Matroid",
"Matroid.ground_eq_empty_iff",
"Set"
] | false |
_private.Mathlib.Topology.Algebra.OpenSubgroup.0.IsTopologicalAddGroup.exist_add_closure_nhds.match_1_1 | Mathlib.Topology.Algebra.OpenSubgroup | [
"Filter.instMembership",
"AddGroup.toSubtractionMonoid",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Exists",
"nhds",
"AddZeroClass.toAddZero",
"HasSubset.Subset",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"And.casesOn",
"TopologicalSpace",
"instHAdd",
"... | false |
CategoryTheory.SingleFunctors.postcomp._proof_1 | Mathlib.CategoryTheory.Shift.SingleFunctors | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.shiftFunctor",
"CategoryThe... | false |
_private.Lean.Meta.Tactic.Grind.SimpUtil.0.Lean.Meta.Grind.reduceCtorEqCheap._sparseCasesOn_1 | Lean.Meta.Tactic.Grind.SimpUtil | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
Polynomial.coeffList.eq_1 | Mathlib.Algebra.Polynomial.CoeffList | [
"List.map",
"WithBot.succ",
"List.range",
"Polynomial.degree",
"Polynomial",
"Polynomial.coeff",
"List",
"Nat.instSuccOrder",
"Polynomial.coeffList",
"Nat.instPreorder",
"Nat",
"List.reverse",
"Semiring",
"Eq.refl",
"Nat.instOrderBot",
"Eq"
] | true |
Module.restrictScalars | Mathlib.Algebra.Algebra.RestrictScalars | [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"AddCommMonoid",
"CommSemiring",
"Module.compHom",
"Semiring",
"Module"
] | true |
_private.Mathlib.Tactic.Translate.Core.0.Mathlib.Tactic.Translate.copyInstanceAttribute.match_1 | Mathlib.Tactic.Translate.Core | [
"Unit.unit",
"Nat.hasNotBit",
"Lean.ReducibilityStatus.implicitReducible",
"_private.Mathlib.Tactic.Translate.Core.0.Mathlib.Tactic.Translate.copyInstanceAttribute._sparseCasesOn_1",
"Unit",
"Lean.ReducibilityStatus.ctorIdx",
"Lean.ReducibilityStatus"
] | false |
_private.Mathlib.Order.CompactlyGenerated.Basic.0.iSupIndep_iff_supIndep.match_1_10 | Mathlib.Order.CompactlyGenerated.Basic | [
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"Finset",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toBoundedOrder",
"Bot.bot",
"And.casesOn",
"And",
"Finset.instSetLike",
"And.intro",
"BoundedOrder.toOrderBot",
"Semilattice... | false |
Hyperreal.inv_epsilon | Mathlib.Analysis.Real.Hyperreal | [
"Hyperreal.instField",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"DivisionMonoid.toDivInvOneMonoid",
"Hyperreal.omega",
"DivisionMonoid.toInvolutiveInv",
"Field.toSemifield",
"Inv.inv",
"inv_inv",
"Hyperreal.epsilon",
"Semifield.toCommGroupWithZero",
"Hyperreal",
... | true |
instCompleteAtomicBooleanAlgebraLanguage._aux_14 | Mathlib.Computability.Language | [
"Set.instInter",
"Inter.inter",
"List",
"Language",
"Set"
] | false |
Vector.scanl | Batteries.Data.Vector.Basic | [
"Pure.pure",
"Vector",
"Monad.toApplicative",
"instOfNatNat",
"Id.run",
"Id",
"Applicative.toPure",
"Vector.scanlM",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Id.instMonad",
"OfNat.ofNat"
] | true |
Hindman.FP_partition_regular | Mathlib.Combinatorics.Hindman | [
"Hindman.exists_idempotent_ultrafilter_le_FP",
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"Hindman.FP",
"_private.Mathlib.Combinatorics.Hindman.0.Hindman.FP_partition_regular.match_1_1",
"Filter.Eventually",
"setOf",
"Ultrafilter.mul",
"Set.sUnion",
"Set.Finite",
"Membership.mem",
"Exists"... | true |
List.sum_flatten | Batteries.Data.List.Lemmas | [
"congrArg",
"List.map",
"List.sum",
"List.rec",
"List.cons",
"instHAppendOfAppend",
"List",
"instHAdd",
"HAdd.hAdd",
"True",
"eq_self",
"List.sum_append",
"of_eq_true",
"Zero.toOfNat0",
"Std.LawfulIdentity.toLawfulLeftIdentity",
"congrFun'",
"List.instAppend",
"OfNat.ofNat",
"Eq"... | true |
ProbabilityTheory.IsMeasurableRatCDF.le_one | Mathlib.Probability.Kernel.Disintegration.MeasurableStieltjes | [
"Real.instLE",
"Real",
"Real.lattice",
"instHasSolidNormReal",
"Monotone.ge_of_tendsto",
"Rat",
"PseudoMetricSpace.toUniformSpace",
"ProbabilityTheory.IsMeasurableRatCDF.isRatStieltjesPoint",
"Real.normedAddCommGroup",
"LE.le",
"ProbabilityTheory.IsRatStieltjesPoint.mono",
"Real.instOne",
"M... | true |
TopologicalSpace.Clopens.ctorIdx | Mathlib.Topology.Sets.Closeds | [
"TopologicalSpace",
"Nat",
"TopologicalSpace.Clopens"
] | false |
Fin.addCases._proof_2 | Init.Data.Fin.Lemmas | [
"Fin.natAdd",
"Fin.val",
"instHAdd",
"Fin.cast",
"HAdd.hAdd",
"Nat",
"Fin.subNat",
"LT.lt",
"Fin.natAdd_subNat_cast",
"instAddNat",
"Fin.addCases._proof_1",
"instLTNat",
"Fin",
"Eq",
"Not",
"Nat.le_of_not_lt",
"Nat.add_comm"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.maxKey?_erase_le_maxKey?._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
_private.Mathlib.Data.List.Chain.0.List.exists_isChain_ne_nil_of_relationReflTransGen._proof_1_2 | Mathlib.Data.List.Chain | [
"False",
"Lean.Grind.not_false",
"congrArg",
"False.elim",
"noConfusion_of_Nat",
"List.cons",
"List",
"True",
"Eq.substr",
"eq_false'",
"Eq",
"List.ctorIdx",
"Not",
"Eq.trans",
"True.intro",
"List.nil"
] | false |
Lean.Compiler.LCNF.MonadCodeBind.mk.noConfusion | Lean.Compiler.LCNF.Bind | [
"id",
"Lean.FVarId",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.MonadCodeBind.noConfusion",
"Lean.Compiler.LCNF.Code",
"heq_of_eq",
"Eq.refl",
"HEq",
"Lean.Compiler.LCNF.MonadCodeBind.mk",
"Eq",
"Lean.Compiler.LCNF.MonadCodeBind"
] | false |
_private.Mathlib.RingTheory.WittVector.Frobenius.0.WittVector.frobenius._simp_2 | Mathlib.RingTheory.WittVector.Frobenius | [
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"SubNegMonoid",
"AddZeroClass.toAddZero",
"SubNegMonoid.toSub",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"SubNegMonoid.toNeg",
"AddZero.toAdd",
"SubNegMonoid.toAddMonoid",
"Eq.symm",
"Eq",
"Neg.neg"
] | false |
Lean.Meta.Grind.Arith.CommRing.EqCnstrProof.simp | Lean.Meta.Tactic.Grind.Arith.CommRing.Types | [
"Lean.Meta.Grind.Arith.CommRing.EqCnstrProof.simp",
"Int",
"Lean.Meta.Grind.Arith.CommRing.EqCnstrProof",
"Lean.Meta.Grind.Arith.CommRing.EqCnstr",
"Lean.Grind.CommRing.Mon"
] | true |
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