name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
List.sym._unary._proof_3 | Mathlib.Data.List.Sym | [
"Nat.instOne",
"congrArg",
"invImage",
"AddMonoid.toAddZeroClass",
"Nat.instZeroLEOneClass",
"Nat.lt_add_left_iff_pos._simp_1",
"instSizeOfDefault",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"PSigma.casesOn",
"zero_lt_one._simp_1",
"id",
"Prod.Lex",
"Prod.mk",
"instOfNatNat",
"siz... | false |
ChainComplex.cycles₀Iso._proof_3 | Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex | [
"IsRightCancelAdd",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Nat.instAddCancelCommMonoid",
"AddSemigroup.toAdd",
"Nat",
"AddRightCancelMonoid.toAddRightCancelSemigroup",
"AddCancelCommMonoid.toAddCancelMonoid",
"AddRightCancelSemigroup.toIsRightCancelAdd"
... | false |
AddCircle.EndpointIdent.recOn | Mathlib.Topology.Instances.AddCircle.Defs | [
"Iff.mpr",
"Set.right_mem_Icc",
"Preorder.toLT",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Fact",
"AddCommGroup",
"Set.Elem",
"Distr... | false |
Lean.Meta.Grind.Arith.Cutsat.State.rec | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Meta.Grind.Arith.Cutsat.instHashablePoly_lean",
"Lean.Meta.Grind.Arith.Cutsat.ToIntTermInfo",
"Lean.Meta.Grind.Arith.Cutsat.ToIntInfo",
"instHashableProd",
"Lean.Expr.instBEq",
"Lean.PHashMap",
"Rat",
"Lean.PArray",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstr",
"Int.instDecidableEq",
"Lean.Ex... | false |
BitVec.twoPow_mul_eq_shiftLeft | Init.Data.BitVec.Lemmas | [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"HShiftLeft.hShiftLeft",
"BitVec.mul_comm",
"BitVec",
"id",
"BitVec.instHShiftLeftNat",
"Nat",
"BitVec.twoPow",
"Eq.refl",
"Eq",
"BitVec.instMul",
"BitVec.mul_twoPow_eq_shiftLeft",
"instHMul"
] | true |
CategoryTheory.Coyoneda.isIso | Mathlib.CategoryTheory.Yoneda | [
"CategoryTheory.isIso_of_fully_faithful",
"CategoryTheory.Functor",
"CategoryTheory.IsIso",
"Opposite",
"CategoryTheory.coyoneda",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.map",
"CategoryTheory.types",
... | true |
EmbeddingLike.map_eq_one_iff._simp_2 | Mathlib.Algebra.Group.Equiv.Defs | [
"EmbeddingLike",
"One",
"EmbeddingLike.map_eq_one_iff",
"OneHomClass",
"propext",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"FunLike"
] | false |
AddEquiv.toNatLinearEquiv_trans | Mathlib.Algebra.Module.Equiv.Basic | [
"Nat.instNonAssocSemiring",
"AddCommMonoid",
"AddEquiv.toNatLinearEquiv",
"AddEquiv.trans",
"Nat",
"RingHomInvPair.ids",
"LinearEquiv",
"AddEquiv",
"Nat.instSemiring",
"AddCommMonoid.toNatModule",
"AddCommSemigroup.toAddCommMagma",
"AddCommMonoid.toAddCommSemigroup",
"RingHom.id",
"RingHom... | true |
_private.Mathlib.Tactic.Tauto.0.Mathlib.Tactic.Tauto.«term_<;>_» | Mathlib.Tactic.Tauto | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.Name.anonymous",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
CategoryTheory.NatTrans.mapElements_obj | Mathlib.CategoryTheory.Elements | [
"CategoryTheory.categoryOfElements",
"CategoryTheory.Functor.Elements",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.category",
"TypeCat.instFunLikeFun",
"CategoryTheory.NatTrans.mapElements",
"Type... | true |
_private.Mathlib.SetTheory.ZFC.PSet.0.PSet.Subset.congr_right.match_1_5 | Mathlib.SetTheory.ZFC.PSet | [
"Exists",
"PSet.mk",
"PSet",
"Exists.casesOn",
"Exists.intro",
"PSet.Type",
"PSet.Equiv"
] | false |
Lean.Widget.HighlightedMsgEmbed.highlighted | Lean.Server.FileWorker.WidgetRequests | [
"Lean.Widget.HighlightedMsgEmbed.highlighted",
"Lean.Widget.HighlightedMsgEmbed"
] | true |
_private.Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs.0.isLinearSet_iff._simp_1_2 | Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs | [
"Finset",
"Set.Finite",
"Exists",
"Set.Finite.toFinset",
"propext",
"Finset.exists",
"Eq",
"Set"
] | false |
Function.locallyFinsuppWithin.instAddCommGroup._proof_7 | Mathlib.Topology.LocallyFinsupp | [
"AddGroup.toSubtractionMonoid",
"instHSMul",
"Function.locallyFinsuppWithin.instFunLike",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Function.locallyFinsuppWithin.coe_zsmul",
"SubtractionMonoid.toSubNegZeroMonoid",
"Int",
"SubNegZeroMonoid.toNegZeroClass",
"TopologicalSpace",
"AddGroup.toSubNeg... | false |
SimpleGraph.Walk.length_ofSupport | Mathlib.Combinatorics.SimpleGraph.Walk.Basic | [
"List.head",
"List.getLast",
"SimpleGraph.Walk.ofSupport",
"SimpleGraph.Walk.length",
"SimpleGraph.Adj",
"HSub.hSub",
"List.IsChain",
"instSubNat",
"Ne",
"instOfNatNat",
"SimpleGraph",
"List",
"instHSub",
"Nat",
"OfNat.ofNat",
"Eq",
"List.length",
"_private.Mathlib.Combinatorics.Si... | true |
EuclideanDomain.wellFoundedRelation | Mathlib.Algebra.EuclideanDomain.Defs | [
"EuclideanDomain.r_wellFounded",
"EuclideanDomain.r",
"WellFoundedRelation",
"WellFoundedRelation.mk",
"EuclideanDomain"
] | true |
UInt64.toUSize_mod_of_dvd_usizeSize | Init.Data.UInt.Lemmas | [
"instPowNat",
"Eq.mpr",
"Dvd.dvd",
"UInt64.toUSize",
"congrArg",
"UInt64",
"Nat.mod_mod_eq_mod_mod_mod_of_dvd",
"instModUSize",
"id",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"UInt64.toNat",
"instNatPowNat",
"System.Platform.numBits",
"UInt64.toNat_toUSize",
"HMod.hMod",
"HPow.hP... | true |
_private.Mathlib.Order.SuccPred.LinearLocallyFinite.0.toZ_neg._proof_1_1 | Mathlib.Order.SuccPred.LinearLocallyFinite | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"IsPredArchimedean.exists_pred_iterate_of_le",
"Exists",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"LT.lt.le",
"Nat.iterate",
"Nat",
"Order.pred",
"LT.lt",
"IsSuccArchimedean",
"SuccOrder",
"LinearOrder.isPredA... | false |
Lean.Lsp.Location._sizeOf_1 | Lean.Data.Lsp.Basic | [
"Lean.Lsp.Location",
"instOfNatNat",
"Lean.Lsp.DocumentUri",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Lean.Lsp.Location.rec",
"SizeOf.sizeOf",
"instAddNat",
"String._sizeOf_inst",
"Lean.Lsp.Range._sizeOf_inst",
"Lean.Lsp.Range",
"OfNat.ofNat"
] | false |
Complex.dist_of_im_eq | Mathlib.Analysis.Complex.Norm | [
"Eq.mpr",
"Nat.instMulZeroClass",
"Real",
"Real.lattice",
"Complex.instNormedAddCommGroup",
"sub_self",
"Real.instAddMonoid",
"abs",
"congrArg",
"Complex.im",
"Real.instSub",
"Real.sqrt_sq_eq_abs",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddZeroClass.toAddZero",
"id",
"Real.instAdd... | true |
Real.tendsto_eulerMascheroniSeq' | Mathlib.NumberTheory.Harmonic.EulerMascheroni | [
"Real.instIsOrderedRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Real.instArchimedean",
"Real.instZero",
"Real.instAddMonoid",
"congrArg",
"IsSemitopologicalRing.toIsSemitopologicalSemiring",
"Real.instSub",
"Ad... | true |
Submonoid.mem_saturation_iff | Mathlib.Algebra.Group.Submonoid.Saturation | [
"Eq.mpr",
"MulOne.toOne",
"Semigroup.toMul",
"SaturatedSubmonoid.mulSaturated",
"HMul.hMul",
"CommMonoid.toCommSemigroup",
"mul_mul_mul_comm",
"SaturatedSubmonoid",
"Monoid.toMulOneClass",
"congrArg",
"mul_assoc",
"Membership.mem",
"Exists",
"Submonoid.instSubmonoidClass",
"id",
"MulOn... | true |
vadd_mem_nhds_self._simp_1 | Mathlib.Topology.Algebra.ConstMulAction | [
"Filter.instMembership",
"AddGroup.toSubtractionMonoid",
"instVAddOfAdd",
"ContinuousConstVAdd",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"nhds",
"AddZeroClass.toAddZero",
"Set.vaddSet",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"HVAdd.hVAdd",
"vadd_mem_... | false |
Filter.Tendsto.add_atBot | Mathlib.Topology.Order.LeftRightNhds | [
"OrderTopology",
"AddCommGroup.toAddCommMonoid",
"Filter.Tendsto.add_atTop",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"AddCommGroup.toAddGroup",
"SemilatticeInf.toPartialOrder",
"nhds",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribLattice.toLattice",
"Topolo... | true |
_private.Aesop.Script.StructureStatic.0.Aesop.Script.StaticStructureM.run._proof_2 | Aesop.Script.StructureStatic | [
"_private.Aesop.Script.StructureStatic.0.Aesop.Script.StaticStructureM.run._proof_1",
"Std.Legacy.Range.stop",
"Membership.mem",
"inferInstance",
"id",
"instOfNatNat",
"Membership",
"Array",
"GetElem.getElem",
"_private.Aesop.Script.StructureStatic.0.Aesop.Script.StaticStructureM.run._proof_3",
... | false |
Int.floor_lt_ceil_of_lt | Mathlib.Algebra.Order.Floor.Ring | [
"Int.cast",
"Preorder.toLT",
"Int.floor",
"Ring.toNonAssocRing",
"IsOrderedRing.toZeroLEOneClass",
"IsOrderedRing",
"Int.le_ceil",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Int.cast_lt",
"NonUnitalNonAssocRing.toNonUnitalNonAssocS... | true |
MeasureTheory.volume_pi_ball | Mathlib.MeasureTheory.Constructions.Pi | [
"Real",
"MeasureTheory.Measure",
"pseudoMetricSpacePi",
"Finset.univ",
"Real.instZero",
"MeasureTheory.SigmaFinite",
"MeasureTheory.MeasureSpace.toMeasurableSpace",
"Real.instLT",
"MeasureTheory.Measure.pi_ball",
"Metric.ball",
"ENNReal.instCommSemiring",
"Finset.prod",
"Fintype",
"Measure... | true |
Dioph._aux_Mathlib_NumberTheory_Dioph___unexpand_Dioph_eq_dioph_1 | Mathlib.NumberTheory.Dioph | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
Std.Net.IPv4Addr.octets | Std.Net.Addr | [
"Vector",
"Std.Net.IPv4Addr",
"instOfNatNat",
"Nat",
"OfNat.ofNat",
"UInt8"
] | true |
_private.Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex.0.NumberField.nrComplexPlaces_eq_zero_iff._simp_1_2 | Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex | [
"Subtype",
"IsEmpty",
"isEmpty_subtype",
"propext",
"Eq",
"Not"
] | false |
FintypeCat.instFiniteAut | Mathlib.CategoryTheory.FintypeCat | [
"_private.Mathlib.CategoryTheory.FintypeCat.0.FintypeCat.instFiniteAut._proof_1",
"Finite",
"FintypeCat",
"CategoryTheory.types",
"CategoryTheory.Aut",
"CategoryTheory.ObjectProperty.FullSubcategory.category"
] | true |
AdicCompletion.isAdicCauchy_iff | Mathlib.RingTheory.AdicCompletion.Basic | [
"Submodule",
"le_refl",
"CommRing",
"instHSMul",
"SModEq.mono",
"Semiring.toModule",
"IsScalarTower.right",
"Submodule.smul_mono",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.Quotient.mk",
"PartialOrder.toPreorder",
"Submodule.hasQuotient",
"AddCommGroup",
"Alge... | true |
CategoryTheory.Functor.PullbackObjObj.mapArrowRight._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Functor.PullbackObjObj.π",
"CategoryTheory.Comma.right",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.Hom.right",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Funct... | false |
Lean.Meta.Grind.Arith.CommRing.CommSemiring.noConfusionType | Lean.Meta.Tactic.Grind.Arith.CommRing.Types | [
"Lean.Expr",
"Lean.Meta.Grind.Arith.CommRing.Semiring",
"Nat",
"Lean.Meta.Grind.Arith.CommRing.CommSemiring.casesOn",
"Lean.Meta.Grind.Arith.CommRing.CommSemiring",
"Eq",
"Option"
] | false |
Finsupp.uniqueLinearEquiv_symm_apply | Mathlib.LinearAlgebra.Finsupp.Pi | [
"LinearEquiv.symm",
"Finsupp.module",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Finsupp.uniqueLinearEquiv",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
"AddZero.toZero",
"RingHomInvPair.ids",
"LinearEquiv",
"Semiring",
"LinearEquiv.instEquivLike",
"Subsingleton",
"Eq.refl",
... | true |
Std.Do.SPred.forall_nil | Std.Do.SPred.SPred | [
"Std.Do.SPred.forall",
"Std.Do.SPred",
"ULift.up",
"Eq",
"ULift.down",
"rfl",
"List.nil"
] | true |
Std.DTreeMap.Internal.Impl.insert._proof_24 | Std.Data.DTreeMap.Internal.Operations | [
"_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.insert._proof_23",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.inner",
"instOfNatNat",
"LE.le",
"instLENat",
"Std.DTreeMap.Internal.Impl.BalanceLPrecond",
"instHAdd"... | false |
CategoryTheory.Iso.coreLeftUnitor | Mathlib.CategoryTheory.Core | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.coreComp",
"CategoryTheory.Core.hom_ext",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"CategoryTheory.coreCategory",
"congrArg",
"CategoryTheory.Functor.coreId",
"CategoryTheory.Functor.category",
"Cate... | true |
CategoryTheory.ShortComplex.ShortExact.singleTriangleIso._proof_3 | Mathlib.Algebra.Homology.DerivedCategory.SingleTriangle | [
"CategoryTheory.Abelian.toPreadditive",
"HomologicalComplex.instCategory",
"CategoryTheory.ShortComplex.ShortExact.singleδ._proof_1",
"AddMonoid.toAddSemigroup",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"CochainComplex.instHasShiftInt",
"CategoryTheory.Functor.co... | false |
_private.Mathlib.Analysis.Normed.Unbundled.SmoothingSeminorm.0.isNonarchimedean_smoothingFun._simp_1_1 | Mathlib.Analysis.Normed.Unbundled.SmoothingSeminorm | [
"Filter.Eventually",
"Preorder.toLE",
"Exists",
"GE.ge",
"Filter.atTop",
"IsDirectedOrder",
"propext",
"Nonempty",
"Filter.eventually_atTop",
"Eq",
"Preorder"
] | false |
Rat.instMetricSpace._proof_5 | Mathlib.Topology.Instances.Rat | [
"UniformSpace.comap._proof_1",
"Real",
"iInf",
"PseudoMetricSpace.uniformity_dist._autoParam",
"Real.lattice",
"Real.instZero",
"Dist.mk",
"abs",
"PseudoMetricSpace.induced._proof_6",
"Filter.instInfSet",
"Real.instSub",
"Real.instRatCast",
"Rat",
"uniformity",
"setOf",
"HSub.hSub",
... | false |
_private.Mathlib.Algebra.Order.Antidiag.Pi.0.Finset.mem_piAntidiag._proof_1_4 | Mathlib.Algebra.Order.Antidiag.Pi | [
"False",
"dite_congr",
"Equiv.instEquivLike",
"Lean.Grind.nestedProof",
"eq_false",
"congrArg",
"Equiv.symm_apply_apply",
"HEq.refl",
"Finset",
"AddMonoid.toAddZeroClass",
"Classical.byContradiction",
"Function.comp",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"Eq.mp",
"id... | false |
CategoryTheory.nerve.homEquiv._proof_4 | Mathlib.AlgebraicTopology.SimplicialSet.Nerve | [
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"CategoryTheory.ComposableArrows",
"Equiv",
"instOfNatNat",
"instHAdd",
"CategoryTheory.nerveEquiv",
"CategoryTheory.ComposableArrows.homM... | false |
_private.Init.Data.Nat.Lemmas.0.Nat.lt_of_add_lt_add_right.match_1_1 | Init.Data.Nat.Lemmas | [
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"Nat.zero",
"instLTNat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
BitVec.cpopNatRec_allOnes | Init.Data.BitVec.Lemmas | [
"BitVec.getElem_allOnes",
"Eq.mpr",
"Nat.recAux",
"congrArg",
"Bool.toNat",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.cpopNatRec_allOnes._proof_1_2",
"BitVec.cpopNatRec_add",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.cpopNatRec_allOnes._proof_1_3",
"BitVec.allOnes",
"BitVec",
"BitVec.getLsbD",... | true |
Std.Slice.length_iter_eq_size | Std.Data.Iterators.Lemmas.Producers.Slice | [
"Std.Slice.iter",
"Std.IteratorLoop",
"Std.Iterators.Finite",
"Std.ToIterator",
"Std.Slice.size_eq_length_iter",
"Std.Iter.length",
"Id",
"Std.Iterator",
"Nat",
"Std.Slice.LawfulSliceSize",
"Std.LawfulIteratorLoop",
"Std.Slice.size",
"Id.instMonad",
"Eq.symm",
"Eq",
"Std.Slice",
"Std... | true |
IsAddConj.setoid.eq_1 | Mathlib.Algebra.Group.Conj | [
"IsAddConj",
"Setoid",
"Setoid.mk",
"AddMonoid",
"Eq.refl",
"Eq",
"IsAddConj.setoid",
"IsAddConj.setoid._proof_1"
] | true |
_private.Init.Data.String.Decode.0.ByteArray.utf8DecodeChar?.parseFirstByte_eq_invalid_of_isInvalidContinuationByte_eq_false | Init.Data.String.Decode | [
"ByteArray.utf8DecodeChar?.parseFirstByte",
"ByteArray.utf8DecodeChar?.FirstByte.invalid",
"BitVec.getElem_append._proof_2",
"of_eq_false",
"BitVec.setWidth",
"False",
"of_decide_eq_true",
"congrArg",
"_private.Init.Data.String.Decode.0.ByteArray.utf8DecodeChar?.toBitVec_eq_of_parseFirstByte_eq_twoM... | true |
Lean.EnvExtension.instInhabitedAsyncMode | Lean.Environment | [
"Lean.EnvExtension.instInhabitedAsyncMode.default",
"Lean.EnvExtension.AsyncMode",
"Inhabited",
"Inhabited.mk"
] | true |
_private.Mathlib.Analysis.Normed.Lp.lpSpace.0.Memℓp.const_smul._simp_1_5 | Mathlib.Analysis.Normed.Lp.lpSpace | [
"Real",
"HMul.hMul",
"NNReal",
"instDistribOfSemiring",
"HPow.hPow",
"NNReal.instPowReal",
"Distrib.toMul",
"NNReal.instSemiring",
"instHPow",
"Eq.symm",
"NNReal.mul_rpow",
"Eq",
"instHMul"
] | false |
Nat.factorial_pos._f | Mathlib.Data.Nat.Factorial.Basic | [
"Nat.mul_pos",
"instOfNatNat",
"Nat.below",
"Unit",
"Nat.factorial",
"Nat",
"Nat.succ_pos",
"LT.lt",
"instLTNat",
"OfNat.ofNat",
"Nat.succ",
"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_pos.match_1_1",
"Nat.zero_lt_one"
] | false |
Aesop.LIFOQueue.mk.sizeOf_spec | Aesop.Search.Queue | [
"Aesop.LIFOQueue._sizeOf_inst",
"ST.Ref._sizeOf_inst",
"Aesop.Goal",
"instSizeOfDefault",
"Aesop.LIFOQueue",
"IO.RealWorld",
"instOfNatNat",
"Array._sizeOf_inst",
"Array",
"Aesop.GoalRef",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Aes... | true |
IO.Promise.noConfusion | Init.System.Promise | [
"_private.Init.System.Promise.0.IO.PromisePointed",
"IO.Promise",
"eq_of_heq",
"Eq.ndrec",
"Nonempty",
"Eq.refl",
"HEq",
"NonemptyType.type",
"Eq",
"IO.Promise.noConfusionType",
"IO.Promise.casesOn"
] | false |
Sep.mk.noConfusion | Init.Core | [
"outParam",
"Sep",
"id",
"heq_of_eq",
"Sep.mk",
"Sep.noConfusion",
"Eq.refl",
"HEq",
"Eq"
] | false |
Rep.linearization._proof_4 | Mathlib.RepresentationTheory.Rep.Basic | [
"Finsupp.instFunLike",
"Monoid",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Rep.V",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"LinearMap.comp.congr_simp",
"Finsupp.module",
"CommRing.toNonUnitalCommRing",
"Finsupp.ext",
"CategoryTheory.CategoryStruct.to... | false |
isUnit_star._simp_1 | Mathlib.Algebra.Star.Basic | [
"Monoid",
"Monoid.toMulOneClass",
"StarMul",
"IsUnit",
"MulOne.toMul",
"MulOneClass.toMulOne",
"StarMul.toInvolutiveStar",
"propext",
"InvolutiveStar.toStar",
"isUnit_star",
"Eq",
"Star.star"
] | false |
Finset.map_toDual_max | Mathlib.Data.Finset.Max | [
"OrderDual.toDual",
"Eq.mpr",
"Finset.min_eq_inf_withTop",
"WithBot",
"Equiv.instEquivLike",
"LinearOrder.toDecidableEq",
"congrArg",
"WithTop.map_id",
"Finset",
"OrderDual.instDecidableEq",
"LinearOrder",
"PartialOrder.toPreorder",
"WithTop.map",
"Preorder.toLE",
"Function.comp",
"Fin... | true |
Mathlib.Tactic.AtomM.addAtom | Mathlib.Util.AtomM | [
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Mathlib.Tactic.AtomM.containsThenAdd",
"Mathlib.Tactic.AtomM.Context",
"Lean.Meta.instMonadMetaM",
"StateRefT'",
"StateRefT'.instMonad",
"Nat",
"Bool",
"Prod",
"Mathlib.Tactic.AtomM",
"ReaderT.instFunctorOfMonad",
"Prod.snd",
"Functor.map"... | true |
CategoryTheory.PreZeroHypercover.pullback₂_I₀ | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.PreZeroHypercover.X",
"CategoryTheory.PreZeroHypercover.pullback₂",
"CategoryTheory.PreZeroHypercover.I₀",
"CategoryTheory.PreZeroHypercover",
"Eq.refl",... | true |
Matrix.uniformContinuous | Mathlib.Topology.UniformSpace.Matrix | [
"Matrix.instUniformSpace",
"UniformContinuous",
"UniformSpace",
"Eq.mpr",
"iInf",
"congrArg",
"Matrix",
"Filter.instInfSet",
"uniformity",
"Function.comp",
"id",
"Prod.mk",
"Prod.fst",
"_private.Mathlib.Topology.UniformSpace.Matrix.0.Matrix.uniformContinuous._simp_1_1",
"Iff",
"Filter.... | true |
List.zipWithLeft'._f | Batteries.Data.List.Basic | [
"List.map",
"Option.some",
"Prod.mk",
"Prod.fst",
"List.cons",
"List.zipWithLeft'.match_1",
"Option.none",
"List",
"List.below",
"Prod",
"Prod.snd",
"List.nil",
"Option"
] | false |
_private.Mathlib.Algebra.NeZero.0.not_neZero._simp_1_1 | Mathlib.Algebra.NeZero | [
"Ne",
"propext",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"neZero_iff",
"Zero"
] | false |
CategoryTheory.Limits.ReflectsColimitsOfSize.reflectsColimitsOfShape._autoParam | Mathlib.CategoryTheory.Limits.Preserves.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
mod_natCard_zsmul | Mathlib.GroupTheory.OrderOfElement | [
"Iff.mpr",
"Eq.mpr",
"instHSMul",
"Dvd.dvd",
"congrArg",
"addOrderOf",
"id",
"Nat.card",
"instHMod",
"Int",
"addOrderOf_dvd_natCard",
"mod_addOrderOf_zsmul",
"eq_comm",
"Nat.cast",
"Int.instDvd",
"HMod.hMod",
"AddGroup",
"AddGroup.toSubNegMonoid",
"Nat.instDvd",
"Nat",
"Int.e... | true |
_private.Lean.Elab.Tactic.Grind.ShowState.0.Lean.Elab.Tactic.Grind.ppEqcs?._sparseCasesOn_1 | Lean.Elab.Tactic.Grind.ShowState | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"List.rec",
"List.cons",
"Nat.land",
"List",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"List.ctorIdx",
"List.nil"
] | false |
MonoidHom.submonoidMap_injective | Mathlib.Algebra.Group.Submonoid.Operations | [
"MonoidHom.instMonoidHomClass",
"MonoidHom.instFunLike",
"_private.Mathlib.Algebra.Group.Submonoid.Operations.0.MonoidHom.submonoidMap_injective._proof_1_1",
"MonoidHom",
"Membership.mem",
"Subtype",
"Submonoid.toMulOneClass",
"Submonoid.map",
"MulOneClass.toMulOne",
"Submonoid.instSetLike",
"Fu... | true |
Matrix.decidableEq | Mathlib.Data.Matrix.Basic | [
"Matrix",
"Fintype",
"Fintype.decidablePiFintype",
"DecidableEq"
] | true |
CategoryTheory.StrictlyUnitaryLaxFunctor.mapIdIso._proof_1 | Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.StrictlyUnitaryLaxFunctor.mapId_eq_eqToHom",
"CategoryTheory.StrictlyUnitaryLaxFunctor.map_id",
"CategoryThe... | false |
_private.Mathlib.RingTheory.Polynomial.ScaleRoots.0.Polynomial.scaleRoots_dvd_iff._simp_1_1 | Mathlib.RingTheory.Polynomial.ScaleRoots | [
"HMul.hMul",
"CommSemiring.toSemiring",
"Polynomial.scaleRoots_mul",
"Polynomial",
"instDistribOfSemiring",
"CommSemiring",
"Distrib.toMul",
"Polynomial.scaleRoots",
"Eq.symm",
"Eq",
"instHMul"
] | false |
AddAction.period_pos_of_addOrderOf_pos | Mathlib.GroupTheory.GroupAction.Period | [
"addOrderOf",
"AddAction.period",
"instOfNatNat",
"AddAction",
"Nat",
"AddAction.period_dvd_addOrderOf",
"LT.lt",
"AddMonoid",
"instLTNat",
"Nat.pos_of_dvd_of_pos",
"OfNat.ofNat"
] | true |
_private.Mathlib.Order.Partition.Finpartition.0.Finpartition.atomise_empty._simp_1_4 | Mathlib.Order.Partition.Finpartition | [
"imp_true_iff",
"True",
"propext",
"Eq"
] | false |
Int.toArray_roc_eq_push | Init.Data.Range.Polymorphic.IntLemmas | [
"Std.Rco",
"Array.push",
"Std.Rco.toArray",
"congrArg",
"Int.add_le_add_right",
"Std.PRange.instUpwardEnumerableInt",
"HSub.hSub",
"Int.decLe",
"Int.toArray_roc_eq_toArray_rco",
"Int.add_sub_cancel",
"Int",
"Std.PRange.instIsAlwaysFiniteInt_1",
"Array",
"Int.instLTInt",
"Int.sub_add_canc... | true |
Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.DerivedLitsInvariant._proof_1 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult | [
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.assignments",
"Fin.val",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula",
"Array",
"Nat",
"LT.lt",
"Std.Sat.CNF.Clause",
"Eq.ndrec",
"Std.Tactic.BVDecide.LRAT.Internal.Assignment",
"instLTNat",
"Fin",
"Std.Tactic.BVDecide.LRAT.Internal.PosFi... | false |
Bornology.ext_iff' | Mathlib.Topology.Bornology.Basic | [
"Filter.instMembership",
"Bornology.ext_iff",
"Membership.mem",
"Filter.ext_iff",
"Iff",
"Iff.trans",
"Bornology.cobounded",
"Eq",
"Bornology",
"Filter",
"Set"
] | true |
Nat.count_true | Mathlib.Data.Nat.Count | [
"trivial",
"instDecidableTrue",
"Nat.count_of_forall",
"Nat",
"LT.lt",
"True",
"Nat.count",
"instLTNat",
"Eq"
] | true |
Std.Tactic.BVDecide.BVExpr.bitblast.ReplicateTarget.mk.sizeOf_spec | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Replicate | [
"HMul.hMul",
"Std.Sat.AIG.RefVec._sizeOf_inst",
"Std.Tactic.BVDecide.BVExpr.bitblast.ReplicateTarget._sizeOf_inst",
"instSizeOfDefault",
"Std.Tactic.BVDecide.BVExpr.bitblast.ReplicateTarget",
"instMulNat",
"instOfNatNat",
"instHAdd",
"Std.Tactic.BVDecide.BVExpr.bitblast.ReplicateTarget.mk",
"Std.S... | true |
Std.Tactic.BVDecide.BVExpr.bitblast.blastCpopTreeTarget.mk.sizeOf_spec | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Cpop | [
"HMul.hMul",
"Std.Sat.AIG.RefVec._sizeOf_inst",
"instSizeOfDefault",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastCpopTreeTarget._sizeOf_inst",
"instMulNat",
"instOfNatNat",
"instHAdd",
"Std.Sat.AIG",
"HAdd.hAdd",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastCpopTreeTarget",
"Nat",
"LT.lt",
"SizeO... | true |
instCommRingPointedContMDiffMap._aux_4 | Mathlib.Geometry.Manifold.DerivationBundle | [
"NormedCommRing.toSeminormedCommRing",
"chartedSpaceSelf",
"NormedSpace",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"ContMDiffMap.const",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"AddZeroClass.toAddZero",
"NormedCommRing.toNonUnitalNormedCommRing",
"Field.toCommRin... | false |
CategoryTheory.PreZeroHypercover.empty | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PEmpty",
"PEmpty.elim",
"CategoryTheory.PreZeroHypercover",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
Std.HashSet.get!_diff_of_mem_right | Std.Data.HashSet.Lemmas | [
"Inhabited.default",
"Std.HashMap.getKey!_diff_of_mem_right",
"Std.HashSet.instMembership",
"Std.HashSet",
"Membership.mem",
"Std.HashSet.instSDiff",
"LawfulHashable",
"SDiff.sdiff",
"Unit",
"EquivBEq",
"Std.HashSet.inner",
"Inhabited",
"Hashable",
"BEq",
"Eq",
"Std.HashSet.get!"
] | true |
Array.mergeSort_perm | Init.Data.Array.Sort.Lemmas | [
"Eq.mpr",
"Array.mergeSort",
"congrArg",
"_private.Init.Data.Array.Sort.Lemmas.0.Array.mergeSort_perm._simp_1_1",
"Array.mergeSort_eq_toArray_mergeSort_toList",
"id",
"List.Perm",
"Array.toList",
"List.toArray",
"Array",
"Array.Perm",
"Bool",
"congrFun'",
"List.mergeSort_perm",
"Eq",
"... | true |
UInt32.reduceAdd._regBuiltin.UInt32.reduceAdd.declare_1._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt.2998934274._hygCtx._hyg.33 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt | [
"IO",
"Bool.true",
"Unit",
"Sum.inr",
"Lean.Meta.Simp.DSimproc",
"UInt32.reduceAdd",
"Lean.Name.mkStr2",
"Lean.Meta.Simp.addSimprocBuiltinAttr",
"Lean.Meta.Simp.Simproc"
] | false |
WeierstrassCurve.Jacobian.negY_of_Z_eq_zero | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula | [
"Eq.mpr",
"NegZeroClass.toNeg",
"Nat.instMulZeroClass",
"CommRing",
"HMul.hMul",
"MulZeroClass.toMul",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"sub_zero",
"WeierstrassCurve.Jacobian.negY",
"HSub.hSub",
"id",
"Fin.instOfNat",
"SubtractionMonoid.toSubNegZeroMon... | true |
CategoryTheory.ShortComplex.mapHomologyIso | Mathlib.Algebra.Homology.ShortComplex.PreservesHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.HasHomology",
"CategoryTheory.ShortComplex.LeftHomologyData.map",
"CategoryTheory.Iso",
"CategoryTheory.ShortComplex.HomologyData.left",
"CategoryTheory.ShortComplex.LeftHomo... | true |
instFieldCyclotomicField._proof_41 | Mathlib.NumberTheory.Cyclotomic.Basic | [
"instFieldCyclotomicField._aux_32",
"Neg.mk",
"instFieldCyclotomicField._aux_37",
"Polynomial.cyclotomic",
"Field.toDivisionRing",
"DivisionRing.toRing",
"Int",
"Nat.cast",
"autoParam",
"Polynomial.instCommRingSplittingField._proof_41",
"Nat",
"CyclotomicField",
"instNatCastInt",
"Int.negS... | false |
differentiable_finCons | Mathlib.Analysis.Calculus.FDeriv.Prod | [
"Differentiable",
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Fin.cons_succ",
"NormedSpace",
"Pi.topologicalSpace",
"Fin.succ",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Pi.module",
"PseudoMetricSpace.toUniformSpace",
"Fin.cons",
"NormedField.toField",
"id",
"Fin.instO... | true |
CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_hom | Mathlib.CategoryTheory.Monoidal.Category | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.hom_inv_whiskerRight",
"CategoryTheory.CategoryStruct.id",
"id",
... | true |
Mathlib.Tactic.Ring.Common.ExtractCoeff.mk.inj | Mathlib.Tactic.Ring.Common | [
"Lean.Expr.const",
"Lean.Level",
"List.cons",
"And",
"Qq.Quoted",
"Lean.Level.zero",
"And.intro",
"Mathlib.Tactic.Ring.Common.ExtractCoeff",
"Mathlib.Tactic.Ring.Common.ExtractCoeff.mk",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"HEq",
"Lean.Level.succ",
"Mathlib.Tactic.Ring.Common.ExProdNat",
... | true |
instTopologicalSpaceModelPi._aux_1 | Mathlib.Geometry.Manifold.ChartedSpace | [
"Pi.topologicalSpace",
"TopologicalSpace",
"ModelPi"
] | false |
BoundedContinuousFunction.comp._proof_3 | Mathlib.Topology.ContinuousMap.Bounded.Basic | [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real.instLE",
"Real",
"HMul.hMul",
"Real.instZero",
"dist_nonneg",
"SemilatticeSup.toMax",
"Real.semiring",
"NNReal.instSemilatticeSup",
"BoundedContinuousFunction.instFunLike",
"NNReal",
"LE.le",
"NNReal.instZero",
"TopologicalSpace",
"P... | false |
Std.HashMap.getKey?_eq_some_iff | Std.Data.HashMap.Lemmas | [
"Std.HashMap.getKey",
"Option.some",
"Membership.mem",
"Exists",
"Std.DHashMap.getKey?_eq_some_iff",
"Std.HashMap",
"LawfulHashable",
"Iff",
"EquivBEq",
"Std.HashMap.getKey?",
"Hashable",
"Std.HashMap.inner",
"BEq",
"Eq",
"Std.HashMap.instMembership",
"Option"
] | true |
_private.Std.Data.DTreeMap.Internal.Balancing.0.Std.DTreeMap.Internal.Impl.balance!.match_3.eq_2 | Std.Data.DTreeMap.Internal.Balancing | [
"Std.DTreeMap.Internal.Impl.inner",
"Std.DTreeMap.Internal.Impl.balance!.match_3",
"Unit",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Eq.refl",
"Eq",
"Std.DTreeMap.Internal.Impl"
] | true |
Finset.noncommProd_commute | Mathlib.Data.Finset.NoncommProd | [
"Monoid",
"Eq.mpr",
"Multiset.map",
"Function.onFun",
"Monoid.toMulOneClass",
"congrArg",
"Multiset.noncommProd_commute",
"Finset",
"Multiset.mem_map",
"Commute",
"Membership.mem",
"Exists",
"Finset.noncommProd_lemma",
"Multiset",
"id",
"MulOne.toMul",
"Set.Pairwise",
"Finset.val",... | true |
SameRay.pos_smul_left | Mathlib.LinearAlgebra.Ray | [
"SameRay.nonneg_smul_left",
"instHSMul",
"Preorder.toLT",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Algebra",
"Algebra.toSMul",
"SMulPosMono",
"AddZeroClass.toAddZero",
"Parti... | true |
BoxIntegral.TaggedPrepartition.casesOn | Mathlib.Analysis.BoxIntegral.Partition.Tagged | [
"Real",
"BoxIntegral.TaggedPrepartition.mk",
"BoxIntegral.Prepartition",
"BoxIntegral.Box.Icc",
"Membership.mem",
"BoxIntegral.TaggedPrepartition.rec",
"Set.instLE",
"BoxIntegral.Box.instLE",
"OrderEmbedding",
"Set.instMembership",
"DFunLike.coe",
"BoxIntegral.TaggedPrepartition",
"BoxIntegr... | false |
String.Pos.toSlice_le._simp_1 | Init.Data.String.Basic | [
"String.toSlice",
"String.instLEPos_1",
"String",
"String.Pos.toSlice",
"LE.le",
"propext",
"String.Pos",
"String.instLEPos",
"String.Slice.Pos",
"String.Pos.toSlice_le",
"Eq"
] | false |
CategoryTheory.Pseudofunctor.whiskerRight_mapId_inv | Mathlib.CategoryTheory.Bicategory.Functor.Pseudofunctor | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Pseudofunctor.mapId",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"Eq.mp",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Iso",
"CategoryTheory.PrelaxFunctorStruct.map₂",
"Cate... | true |
Lean.Meta.Match.matchEqnsExt | Lean.Meta.Match.MatchEqsExt | [
"Inhabited.default",
"Lean.instInhabitedEnvExtension",
"Lean.EnvExtension",
"Lean.Meta.Match.MatchEqnsExtState"
] | true |
Mathlib.Tactic.Abel.AbelMode.casesOn | Mathlib.Tactic.Abel | [
"Mathlib.Tactic.Abel.AbelMode.rec",
"Mathlib.Tactic.Abel.AbelMode",
"Mathlib.Tactic.Abel.AbelMode.raw",
"Mathlib.Tactic.Abel.AbelMode.term"
] | false |
SSet.Subcomplex.Pairing.RankFunction.rec | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.Rank | [
"Preorder.toLT",
"PartialOrder.toPreorder",
"SSet.Subcomplex.N",
"PartialOrder",
"Set.Elem",
"SSet",
"SSet.Subcomplex.Pairing",
"SSet.Subcomplex.Pairing.RankFunction",
"LT.lt",
"SSet.Subcomplex.Pairing.AncestralRel",
"SSet.Subcomplex",
"SSet.Subcomplex.Pairing.II",
"SSet.Subcomplex.Pairing.R... | false |
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