name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Std.Data.DTreeMap.Internal.Model.0.Std.DTreeMap.Internal.Impl.minEntryD.match_1.eq_1 | Std.Data.DTreeMap.Internal.Model | [
"Std.DTreeMap.Internal.Impl.inner",
"Std.DTreeMap.Internal.Impl.minEntryD.match_1",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Eq.refl",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Sigma"
] | true |
_private.Mathlib.Analysis.Normed.Operator.Banach.0.ContinuousLinearMap.isUnit_iff_bijective._simp_1_2 | Mathlib.Analysis.Normed.Operator.Banach | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"LinearMap.ker_eq_bot",
"LinearMap.ker",
"LinearMap.instFunLike",
"RingHom",
"AddCommGroup",
"Bot.bot",
"LinearMap",
"Submodule.instBot",
"propext",
"Function.Injective",
"Module",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Eq",
"D... | false |
Metric.hausdorffEDist_le_of_mem_edist | Mathlib.Topology.MetricSpace.HausdorffDistance | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Metric.infEDist_le_edist_of_mem",
"PartialOrder.toPreorder",
"Metric.hausdorffEDist_le_of_infEDist",
"Membership.mem",
"Exists",
"LE.le",
"Metric.infEDist",
"PseudoEMetricSpace",
"And.casesOn",
"And",
"Exists.casesOn",
"WeakPseudoEMetricSpace.t... | true |
MapClusterPt | Mathlib.Topology.Defs.Filter | [
"Filter.map",
"TopologicalSpace",
"ClusterPt",
"Filter"
] | true |
Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.defnNatCommRing.inj | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.defnNatCommRing.noConfusion",
"Lean.Grind.CommRing.Poly",
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.defnNatCommRing",
"Lean.Expr",
"Int.Linear.Var",
"And",
"Int.Linear.Expr",
"Lean.Meta.Grind.Arith.CommRing.RingExpr",
"And.intro",
"Lean.Meta.Grind.Arith.... | true |
_private.Mathlib.Tactic.FinCases.0.Lean.Elab.Tactic.getMemType._sparseCasesOn_2 | Mathlib.Tactic.FinCases | [
"Lean.Name.rec",
"Nat.ne_of_beq_eq_false",
"String",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Name.num",
"Lean.Name.ctorIdx",
"Lean.Name.str",
"Lean.Name.anonymous",
"Nat.land",
"Nat",
"Bool",
"Lean.Name",
"Eq.refl",
"OfNat.ofNat",
"Bool.false"
] | false |
CategoryTheory.Limits.comp_preservesFiniteLimits | Mathlib.CategoryTheory.Limits.Preserves.Finite | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.PreservesFiniteLimits",
"CategoryTheory.Limits.comp_preservesLimitsOfShape",
"CategoryTheory.Functor.comp",
"inferInstance",
"CategoryTheory.Limits.PreservesFiniteLimits.mk",
"CategoryTheory.Limits.PreservesFiniteLimits.preservesFiniteLimits",
"Category... | true |
Equiv.Perm.sameCycle_apply_right._simp_1 | Mathlib.GroupTheory.Perm.Cycle.Basic | [
"Equiv.instEquivLike",
"Equiv.Perm.sameCycle_apply_right",
"Equiv.Perm.SameCycle",
"Equiv.Perm",
"propext",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | false |
intervalIntegral.integrableOn_Ioo_cpow_iff | Mathlib.Analysis.SpecialFunctions.Integrability.Basic | [
"MeasureTheory.integrableOn_congr_fun",
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real.instPow",
"Real",
"Preorder.toLT",
"Real.lattice",
"Complex.instNormedAddCommGroup",
"Real.instZero",
"congrArg",
"instHasSolidNormReal",
"IntervalIntegrable",
"SeminormedAddGroup.to... | true |
TrivialLieModule.instAddCommGroup._aux_17 | Mathlib.Algebra.Lie.Abelian | [
"TrivialLieModule",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Int",
"SubNegMonoid.zsmul",
"AddGroup.toSubNegMonoid"
] | false |
FiniteMultiplicity.not_of_one_left | Mathlib.RingTheory.Multiplicity | [
"Monoid",
"MulOne.toOne",
"False",
"Monoid.toMulOneClass",
"congrArg",
"IsUnit",
"FiniteMultiplicity.not_of_isUnit_left._simp_1",
"MulOneClass.toMulOne",
"True",
"FiniteMultiplicity",
"of_eq_true",
"One.toOfNat1",
"OfNat.ofNat",
"not_false_eq_true",
"isUnit_one._simp_2",
"Not",
"Eq.t... | true |
Std.Time.Day.instOrdOrdinal | Std.Time.Date.Unit.Day | [
"Std.Time.Day.instOrdOrdinal._aux_1",
"Ord",
"Ord.mk",
"Std.Time.Day.Ordinal"
] | true |
AlgebraicGeometry.affineLocally | Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties | [
"CategoryTheory.MorphismProperty",
"CommRing",
"AlgebraicGeometry.Scheme",
"CommSemiring.toSemiring",
"AlgebraicGeometry.sourceAffineLocally",
"RingHom",
"CommRing.toCommSemiring",
"AlgebraicGeometry.targetAffineLocally",
"CategoryTheory.Category.toCategoryStruct",
"AlgebraicGeometry.Scheme.instCa... | true |
_private.Mathlib.Order.Category.Frm.0.Frm.Hom.mk.noConfusion | Mathlib.Order.Category.Frm | [
"Frm.Hom",
"FrameHom",
"Frm.Hom.noConfusion",
"id",
"_private.Mathlib.Order.Category.Frm.0.Frm.Hom.mk",
"Frm.str",
"heq_of_eq",
"Order.Frame.toCompleteLattice",
"Eq.refl",
"HEq",
"Frm.carrier",
"Frm",
"Eq"
] | false |
_private.Mathlib.SetTheory.Cardinal.ENat.0.Cardinal.toENatAux_eq_nat._simp_1_1 | Mathlib.SetTheory.Cardinal.ENat | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"LE.le",
"And",
"le_antisymm_iff",
"propext",
"Eq"
] | false |
add_neg_of_nonpos_of_neg | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"Preorder.toLT",
"Preorder.toLE",
"Left.add_neg_of_nonpos_of_neg",
"AddZeroClass.toAddZero",
"LE.le",
"AddZero.toZero",
"instHAdd",
"AddZeroClass",
"AddLeftStrictMono",
"HAdd.hAdd",
"LT.lt",
"AddZero.toAdd",
"Zero.toOfNat0",
"OfNat.ofNat",
"Preorder"
] | true |
SimpleGraph.Walk.darts_dropUntil_subset | Mathlib.Combinatorics.SimpleGraph.Walk.Decomp | [
"Eq.mpr",
"congrArg",
"List.instHasSubset",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"Membership.mem",
"SimpleGraph.Walk.take_spec",
"id",
"HasSubset.Subset",
"SimpleGraph.Dart",
"SimpleGraph",
"SimpleGraph.Walk.darts",
"instHAppendOfAppend",
"List",
"List.mem_append",
"List.ins... | true |
IsCusp.smul | Mathlib.NumberTheory.ModularForms.Cusps | [
"OnePoint.instGLAction",
"Matrix.GeneralLinearGroup.isParabolic_conj_iff._simp_1",
"Eq.mpr",
"Semigroup.toMul",
"Real",
"DivInvMonoid.toInv",
"instHSMul",
"MulEquiv.instEquivLike",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Matrix.GeneralLinearGroup.IsParabolic",
"Matrix",
"instDeci... | true |
FP.nextUpPos | Mathlib.Data.FP.Basic | [
"FP.emax",
"Int.instDecidableEq",
"Nat.div2",
"FP.nextUpPos._proof_2",
"Int",
"FP.FloatCfg",
"Nat.cast",
"dite",
"FP.Float",
"FP.Float.inf",
"Nat",
"Int.succ",
"FP.ValidFinite",
"FP.Float.finite",
"instDecidableEqNat",
"instNatCastInt",
"Bool.false",
"Nat.succ",
"Eq",
"Not",
... | true |
CategoryTheory.IsGrothendieckAbelian.mono_of_isColimit_monoOver | Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Subobject | [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.PreservesColimits.preservesFiniteColimits",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limit... | true |
_private.Lean.Server.FileWorker.WidgetRequests.0.Lean.Widget.HighlightedMsgEmbed.traceChildrenOfMsgEmbed.match_1 | Lean.Server.FileWorker.WidgetRequests | [
"Lean.Widget.StrictOrLazy",
"Lean.Server.WithRpcRef",
"Lean.Widget.StrictOrLazy.casesOn",
"Lean.Widget.StrictOrLazy.lazy",
"Lean.Widget.StrictOrLazy.strict",
"Lean.Widget.TaggedText",
"Array",
"Lean.Widget.LazyTraceChildren",
"Lean.Widget.MsgEmbed"
] | false |
toMul_list_sum | Mathlib.Algebra.BigOperators.Group.Finset.Defs | [
"Monoid",
"Eq.mpr",
"MulOne.toOne",
"Equiv.instEquivLike",
"Monoid.toMulOneClass",
"congrArg",
"Additive",
"List.map",
"List.sum",
"Additive.toMul",
"id",
"Equiv",
"MulOne.toMul",
"List.map_id_fun'",
"List",
"MulOneClass.toMulOne",
"Additive.add",
"congrFun",
"Eq.refl",
"instZe... | true |
CategoryTheory.Dial.whiskerLeft_f | Mathlib.CategoryTheory.Dialectica.Monoidal | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.HasPullbacks",
"CategoryTheory.Dial.src",
"CategoryTheory.Dial.tensorObjImpl._proof_1",
"CategoryTheory.Dial.instCategory",
"Categor... | true |
star_nsmul | Mathlib.Algebra.Star.Basic | [
"instHSMul",
"AddMonoid.toAddZeroClass",
"AddEquiv.toAddMonoidHom",
"AddMonoid.toNSMul",
"AddMonoidHom.map_nsmul",
"StarAddMonoid.toInvolutiveStar",
"Nat",
"AddMonoid",
"StarAddMonoid",
"HSMul.hSMul",
"InvolutiveStar.toStar",
"starAddEquiv",
"Eq",
"Star.star"
] | true |
mem_coclosed_Lindelof' | Mathlib.Topology.Compactness.Lindelof | [
"Filter.instMembership",
"congrArg",
"Compl.compl",
"Membership.mem",
"Exists",
"Filter.coclosedLindelof",
"HasSubset.Subset",
"Set.instCompl",
"iff_self",
"IsClosed",
"TopologicalSpace",
"funext",
"And",
"Iff",
"True",
"of_eq_true",
"_private.Mathlib.Topology.Compactness.Lindelof.0.... | true |
BoundedContinuousFunction.const | Mathlib.Topology.ContinuousMap.Bounded.Basic | [
"PseudoMetricSpace.toUniformSpace",
"TopologicalSpace",
"PseudoMetricSpace",
"BoundedContinuousFunction.mk",
"ContinuousMap.const",
"UniformSpace.toTopologicalSpace",
"BoundedContinuousFunction.const._proof_2",
"BoundedContinuousFunction"
] | true |
USize.upwardEnumerableLT_ofBitVec | Init.Data.Range.Polymorphic.UInt | [
"congrArg",
"Std.PRange.UpwardEnumerable.LT",
"Option.some",
"Exists",
"BitVec",
"BitVec.instUpwardEnumerable",
"Option.map_eq_some_iff._simp_1",
"instOfNatNat",
"USize.ofBitVec.injEq",
"USize.instUpwardEnumerable",
"iff_self",
"System.Platform.numBits",
"funext",
"instHAdd",
"Option.map... | true |
Lean.Meta.Tactic.TryThis.Suggestion.noConfusion | Lean.Meta.TryThis | [
"Lean.Meta.Tactic.TryThis.Suggestion.noConfusionType",
"Lean.MessageData",
"Lean.Meta.Tactic.TryThis.SuggestionStyle",
"String",
"Lean.Meta.Tactic.TryThis.SuggestionText",
"Lean.Meta.Tactic.TryThis.Suggestion.casesOn",
"Lean.Meta.Tactic.TryThis.Suggestion",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Option"
... | false |
_private.Mathlib.Data.Nat.Bits.0.Nat.bit_lt_bit._proof_1_3 | Mathlib.Data.Nat.Bits | [
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"Classical.byContradiction",
"Nat.not_le_eq",
"Nat.Linear.Expr.mulL",
"id",
"False.casesOn",
"instMulNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.Linear.Expr.num",
"Bool.true",
"instHAdd",
"Nat.Linear.ExprCnstr.eq_false_of_isUnsat",
"HAdd... | false |
_private.Mathlib.Util.Superscript.0.Mathlib.Tactic.Superscript.partitionPoint._unary._proof_1 | Mathlib.Util.Superscript | [
"invImage",
"HSub.hSub",
"PSigma.casesOn",
"Prod.mk",
"instSubNat",
"instOfNatNat",
"sizeOfWFRel",
"Array",
"instHSub",
"Lean.opaqueId",
"Nat",
"instSizeOfNat",
"Prod.instWellFoundedRelation",
"optParam",
"Prod",
"OfNat.ofNat",
"WellFounded",
"PSigma",
"Array.size"
] | false |
CategoryTheory.RegularEpi.unop._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.RegularMono | [
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.RegularEpi.left",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.RegularEpi.right",
"CategoryTheory.Category.opposite",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.RegularE... | false |
Equiv.trans_toPartialEquiv | Mathlib.Logic.Equiv.PartialEquiv | [
"congrArg",
"Equiv.trans",
"PartialEquiv",
"Set.inter_self",
"Set.univ",
"PartialEquiv.trans",
"PartialEquiv.symm",
"Equiv",
"Equiv.toPartialEquiv",
"PartialEquiv.ext",
"True",
"eq_self",
"of_eq_true",
"PartialEquiv.source",
"PartialEquiv.toFun",
"Eq",
"rfl",
"Eq.trans",
"Set"
] | true |
StarHomClass.isSelfAdjoint | Mathlib.Algebra.Star.LinearMap | [
"WithConv.toConv",
"IsSelfAdjoint",
"DistribMulAction.toDistribSMul",
"LinearMap.intrinsicStar",
"InvolutiveStar",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"StarHomClass",
"DistribSMul.toSMulZeroClass",
"StarAddMonoid.toInvolutiveStar",
"LinearMap",
"AddCommMonoid",
"SemilinearM... | true |
pi_nnnorm_const' | Mathlib.Analysis.Normed.Group.Constructions | [
"NNNorm.nnnorm",
"SeminormedGroup",
"NNReal.eq",
"NNReal",
"Fintype",
"SeminormedGroup.toNNNorm",
"Nonempty",
"pi_norm_const'",
"Pi.seminormedGroup",
"Eq"
] | true |
Std.ExtTreeMap.ext_contains_unit | Std.Data.ExtTreeMap.Lemmas | [
"Ordering",
"Std.TransCmp",
"Std.ExtDTreeMap.Const.ext_contains_unit",
"Unit",
"Std.ExtTreeMap",
"_private.Std.Data.ExtTreeMap.Lemmas.0.Std.ExtTreeMap.ext",
"Std.LawfulEqCmp",
"Std.ExtTreeMap.inner",
"Bool",
"Std.ExtTreeMap.contains",
"Eq"
] | true |
_private.Mathlib.Algebra.GroupWithZero.Range.0.MonoidWithZeroHom.valueGroup_eq_range._simp_1_7 | Mathlib.Algebra.GroupWithZero.Range | [
"Membership.mem",
"Set.preimage",
"propext",
"Eq",
"Set.instMembership",
"Set.mem_preimage",
"Set"
] | false |
MeasureTheory.AEEqFun.instAddCommGroup._proof_1 | Mathlib.MeasureTheory.Function.AEEqFun | [
"AddMonoid.toAddSemigroup",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"IsTopologicalAddGroup.toContinuousAdd",
"TopologicalSpace",
"AddSemigroup.toAdd",
"AddGroup.toSubNegMonoid",
"SubNegMonoid.toAddMonoid",
"ContinuousAdd",
"IsTopologicalAddGroup"
] | false |
AddSubgroup.normal_addSubgroupOf_of_le_normalizer | Mathlib.Algebra.Group.Subgroup.Basic | [
"Eq.mpr",
"AddSubgroup.instCompleteLattice",
"CompleteLattice.toLattice",
"congrArg",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"AddSubgroup.toAddGroup",
"Membership.mem",
"AddSubgroup.normalizer",
"id",
"Subtype",
"AddSubgroup.le_normalizer",
"Semilattice... | true |
StarSubalgebra.one_mem'._inherited_default | Mathlib.Algebra.Star.Subalgebra | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Algebra.toSMul",
"Membership.mem",
"RingHom.map_one",
"Eq.rec",
"id",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"StarAddMonoid.toInvolutiveStar",
"CommSemiring",
"NonUnitalNo... | false |
Prod.instNeg | Mathlib.Algebra.Notation.Prod | [
"Neg.mk",
"Prod.mk",
"Prod.fst",
"Neg",
"Prod",
"Prod.snd",
"Neg.neg"
] | true |
AddSubsemigroup.unop_closure | Mathlib.Algebra.Group.Subsemigroup.MulOpposite | [
"Eq.mpr",
"Set.preimage_preimage",
"congrArg",
"AddSubsemigroup.unop",
"AddSubsemigroup.op_inj",
"AddOpposite",
"AddOpposite.instAdd",
"AddSubsemigroup.op",
"AddSubsemigroup.closure",
"id",
"Set.preimage",
"AddSubsemigroup.op_unop",
"AddSubsemigroup",
"eq_self",
"propext",
"of_eq_true"... | true |
asymm | Mathlib.Order.Defs.Unbundled | [
"Std.Asymm",
"Std.Asymm.asymm",
"Not"
] | true |
CategoryTheory.Limits.Cofan.combPairIsColimit._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.CombinedProducts | [
"CategoryTheory.Limits.Cofan.IsColimit.desc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.Cofan",
"CategoryTheory.Discrete.functor",
"CategoryTheory.Limits.Cofan.combPairIsColimit._proof_4",
"CategoryTheory.Limits.WalkingPair.right",
"CategoryTheory.Limits.IsColimit"... | false |
Std.DTreeMap.Internal.Impl.minKey?._proof_1 | Std.Data.DTreeMap.Internal.Queries | [
"invImage",
"instSizeOfDefault",
"sizeOfWFRel",
"Std.DTreeMap.Internal.Impl._sizeOf_inst",
"Lean.opaqueId",
"WellFounded",
"Std.DTreeMap.Internal.Impl"
] | false |
PrimeSpectrum.closure_image_comap_zeroLocus | Mathlib.RingTheory.Spectrum.Prime.Topology | [
"PrimeSpectrum.zeroLocus_anti_mono",
"Eq.mpr",
"PrimeSpectrum.mk",
"RingHom.instRingHomClass",
"PrimeSpectrum.isClosed_zeroLocus",
"CommRing",
"Semiring.toModule",
"PrimeSpectrum.zeroLocus",
"Specializes",
"Ideal.minimalPrimes",
"Submodule.toAddSubmonoid",
"PrimeSpectrum.isPrime",
"congrArg"... | true |
Std.Iter.toArray_ensureTermination | Init.Data.Iterators.Lemmas.Consumers.Collect | [
"Std.Iterators.Finite",
"Id",
"Std.Iter.toArray",
"Std.Iterator",
"Array",
"Std.Iter.Total.toArray",
"Std.Iter",
"Std.Iter.ensureTermination",
"Eq",
"rfl"
] | true |
AddSubgroup.quotient_finite_of_isOpen | Mathlib.Topology.Algebra.OpenSubgroup | [
"finite_of_compact_of_discrete",
"DiscreteTopology",
"Finite",
"AddMonoid.toAddZeroClass",
"SeparatelyContinuousAdd",
"AddZeroClass.toAddZero",
"QuotientAddGroup.instCompactSpaceQuotientAddSubgroup",
"CompactSpace",
"AddSubgroup",
"TopologicalSpace",
"HasQuotient.Quotient",
"AddGroup",
"Quot... | true |
lt_self_iff_false._simp_1 | Mathlib.Order.Basic | [
"False",
"Preorder.toLT",
"lt_self_iff_false",
"LT.lt",
"propext",
"Eq",
"Preorder"
] | false |
Option.pmap_some' | Init.Data.Option.Lemmas | [
"Option.some",
"Eq.rec",
"Eq.refl",
"Eq.symm",
"Eq",
"Option.pmap",
"Option"
] | true |
DividedPowers.IsSubDPIdeal.dpow_eq_of_mem | Mathlib.RingTheory.DividedPowers.SubDPIdeal | [
"Eq.mpr",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring",
"Decidable",
"Membership.mem",
"id",
"DividedPowers.IsSubDPIdeal.dividedPowers",
"if_pos",
"Ideal",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"DividedPowers.IsSubDPIdeal",
"NonAssocSemiring.toNonUnital... | true |
_private.Mathlib.Probability.Process.HittingTime.0.MeasureTheory.Adapted.isStoppingTime_hittingBtwn_isStoppingTime._simp_1_2 | Mathlib.Probability.Process.HittingTime | [
"Set.mem_union",
"Membership.mem",
"Set.instUnion",
"propext",
"Or",
"Union.union",
"Eq",
"Set.instMembership",
"Set"
] | false |
Mathlib.Meta.Positivity.PositivityExt.rec | Mathlib.Tactic.Positivity.Core | [
"Mathlib.Meta.Positivity.Strictness",
"Mathlib.Meta.Positivity.PositivityExt",
"Lean.Expr.const",
"Mathlib.Meta.Positivity.PositivityExt.mk",
"Lean.Meta.MetaM",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Name.mkStr1",
"List.nil"
] | false |
Std.Http.Trailer.mk.inj | Std.Internal.Http.Data.Chunk | [
"Std.Http.Trailer",
"Std.Http.Trailer.mk",
"Std.Http.Trailer.mk.noConfusion",
"Std.Http.Headers",
"Eq"
] | true |
biSup_le_eq_of_monotone | Mathlib.Order.CompleteLattice.Basic | [
"Iff.mpr",
"le_rfl",
"iSup",
"PartialOrder.toPreorder",
"Monotone",
"ge_of_eq",
"Preorder.toLE",
"iSup_pos",
"LE.le",
"CompleteLattice.toCompleteSemilatticeInf",
"le_antisymm",
"CompleteSemilatticeInf.toPartialOrder",
"le_iSup_of_le",
"iSup₂_le_iff",
"CompleteSemilatticeSup.toSupSet",
... | true |
ProbabilityTheory.setBernoulli_ae_subset | Mathlib.Probability.Distributions.SetBernoulli | [
"Filter.instMembership",
"MeasureTheory.ae",
"Set.ext",
"Eq.mpr",
"Inhabited.default",
"ENNReal.instAdd",
"_private.Mathlib.Probability.Distributions.SetBernoulli.0.ProbabilityTheory.setBernoulli_ae_subset._simp_1_4",
"False",
"Real",
"instHSMul",
"Trans.trans",
"MeasureTheory.Measure",
"Lat... | true |
Std.DTreeMap.Internal.Impl.mem_of_mem_insertIfNew | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"Std.TransOrd",
"Membership.mem",
"Ordering",
"Ordering.eq",
"Std.DTreeMap.Internal.Impl.size",
"id",
"Ne",
"instOfNatNat",
"Std.DTreeMap.Internal.Impl.WF",
"Ord.compare",
"Std.DTreeMap.Internal.Impl.WF.balanced",
"Std... | true |
Std.DHashMap.Internal.Raw₀.Const.Equiv.beq | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.DHashMap.Internal.Raw.WF.out",
"congrArg",
"Std.DHashMap.Raw",
"id",
"List.Perm",
"instOfNatNat",
"Std.DHashMap.Internal.Raw₀.Const.beq",
"Std.Internal.List.Const.beqModel",
"LawfulHashable",
"Std.DHashMap.Raw.Equiv",
"Bool.true",
"EquivBEq",
"_priva... | true |
_private.Mathlib.Data.Seq.Computation.0.Computation.lift_eq_iff_equiv.match_1_1 | Mathlib.Data.Seq.Computation | [
"Membership.mem",
"Exists",
"Computation",
"And.casesOn",
"And",
"And.intro",
"Computation.instMembership",
"Eq",
"Computation.LiftRel"
] | false |
Convexity.IsAffineMap.rec | Mathlib.Geometry.Convex.ConvexSpace.Defs | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Convexity.ConvexSpace",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"PartialOrder",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddMonoidWithOne.toOne",
"Convexity.ConvexSpace.sConvexCom... | false |
Lean.instReprConstantKind.repr | Lean.Environment | [
"Std.Format.group",
"GE.ge",
"instOfNatNat",
"Int",
"instLENat",
"_private.Lean.Environment.0.Lean.instReprConstantKind.repr.match_1",
"Unit",
"instOfNat",
"Nat",
"Lean.ConstantKind",
"Std.Format",
"Repr.addAppParen",
"OfNat.ofNat",
"Nat.decLe",
"Std.Format.nest",
"Std.Format.text",
... | true |
_private.Init.Data.List.Lemmas.0.List.getLast?_dropLast._simp_1_3 | Init.Data.List.Lemmas | [
"Nat.sub_add_eq",
"HSub.hSub",
"instSubNat",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.symm",
"Eq"
] | false |
_private.Mathlib.Data.Nat.Nth.0.Nat.image_nth_Iio_card._simp_1_1 | Mathlib.Data.Nat.Nth | [
"Set.mem_image",
"Membership.mem",
"Exists",
"And",
"propext",
"Set.image",
"Eq",
"Set.instMembership",
"Set"
] | false |
StarAlgHom.realContinuousMapOfNNReal._proof_4 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique | [
"NNReal.instTopologicalSpace",
"NonAssocSemiring.toAddCommMonoidWithOne",
"NNReal.instCommSemiring",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Ring.toNonAssocRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"ContinuousMap.instAddCommGroupContinuousMap",
"sub_self",
"AddGroupWith... | false |
_private.Lean.Compiler.LCNF.Simp.InlineCandidate.0.Lean.Compiler.LCNF.Simp.inlineCandidate?._sparseCasesOn_24 | Lean.Compiler.LCNF.Simp.InlineCandidate | [
"Lean.Compiler.LCNF.LetValue.reuse",
"Lean.Compiler.LCNF.Arg",
"Lean.Compiler.LCNF.LetValue.pap",
"Nat.ne_of_beq_eq_false",
"Lean.Compiler.LCNF.LitValue",
"Lean.Compiler.LCNF.LetValue.oproj",
"Lean.Compiler.LCNF.LetValue.rec",
"Lean.Compiler.LCNF.LetValue",
"Nat.shiftRight",
"Lean.Compiler.LCNF.Le... | false |
AddCommGrpCat.leftExactFunctorForgetEquivalence.unitIso._proof_3 | Mathlib.Algebra.Category.Grp.LeftExactFunctor | [
"CategoryTheory.Limits.PreservesFiniteLimits",
"AddCommGrpCat.instCategory",
"AddCommGrpCat.forget_preservesLimits",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier",
"AddZeroClass.toAddZero",
"AddCommGrpCat.carrier",
"AddGroup.toSubNegMo... | false |
ClassGroup.mkMMem_surjective | Mathlib.NumberTheory.ClassNumber.Finite | [
"IsDomain",
"CommRing",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instConditionallyCompleteLinearOrder",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"MonoidHom",
"instCommGroupClassGroup",
"Monoid.toMulOneClass",
"CommSemiring.toS... | true |
Num.oneBits | Mathlib.Data.Num.Bitwise | [
"PosNum.oneBits",
"instOfNatNat",
"List",
"Num",
"Unit",
"Nat",
"PosNum",
"OfNat.ofNat",
"Num.oneBits.match_1",
"List.nil"
] | true |
Std.Internal.List.isNone_maxKey?_eq_isEmpty | Std.Data.Internal.List.Associative | [
"Option.isNone",
"Ord",
"inferInstance",
"List",
"List.isEmpty",
"Ord.opposite",
"Std.Internal.List.isNone_minKey?_eq_isEmpty",
"Std.Internal.List.maxKey?",
"Bool",
"Eq",
"Sigma"
] | true |
Set.powersetCard.coe_compl | Mathlib.Data.Set.PowersetCard | [
"Equiv.instEquivLike",
"Set.powersetCard.compl",
"Compl.compl",
"Finset",
"Membership.mem",
"BooleanAlgebra.toCompl",
"Set.Elem",
"Fintype.card",
"Equiv",
"instHAdd",
"Fintype",
"HAdd.hAdd",
"Nat",
"Finset.booleanAlgebra",
"instAddNat",
"Subtype.val",
"Eq",
"Set.instMembership",
... | true |
Finset.mem_shatterer | Mathlib.Combinatorics.SetFamily.Shatter | [
"Eq.mpr",
"Finset.instDecidablePredShatters",
"congrArg",
"Finset",
"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.mem_shatterer._simp_1_2",
"Membership.mem",
"_private.Mathlib.Combinatorics.SetFamily.Shatter.0.Finset.mem_shatterer._simp_1_1",
"Exists",
"id",
"HasSubset.Subset",
"Fin... | true |
_private.Init.Data.String.Basic.0.String.utf8ByteSize_push._simp_1_1 | Init.Data.String.Basic | [
"String",
"String.toByteArray",
"String.utf8ByteSize",
"Nat",
"Eq.symm",
"Eq",
"ByteArray.size",
"String.size_toByteArray"
] | false |
_private.Lean.Meta.ExprDefEq.0.Lean.Meta.processConstApprox.defaultCase | Lean.Meta.ExprDefEq | [
"Lean.Expr",
"Lean.Meta.MetaM",
"_private.Lean.Meta.ExprDefEq.0.Lean.Meta.assignConst",
"Array",
"Bool",
"Array.size"
] | true |
CategoryTheory.Idempotents.Karoubi.mk._flat_ctor | Mathlib.CategoryTheory.Idempotents.Karoubi | [
"CategoryTheory.Idempotents.Karoubi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"autoParam",
"CategoryTheory.Idempotents.Karoubi.idem._autoParam",
"CategoryTheory.Idempotents.Karoubi.mk",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"Categor... | false |
RootPairing.Equiv.coweightEquiv | Mathlib.LinearAlgebra.RootSystem.Hom | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"RootPairing.Equiv.weightEquiv._proof_1",
"RootPairing.Equiv.toHom",
"RootPairing.Equiv.bijective_coweightMap",
"CommRing.toCommSemiring",
"RingHomInvPair.ids",
"LinearEquiv",
"RootPairing.Equiv",
"Module",
... | true |
Order.IsNormal.isClub_range | Mathlib.SetTheory.Cardinal.Cofinality.Club | [
"StrictMono.le_apply",
"Preorder.toLT",
"IsClub.mk",
"LinearOrder",
"WellFoundedLT",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Order.IsNormal.dirSupClosed_range",
"LE.le",
"IsClub",
"And",
"And.intro",
"E... | true |
WeierstrassCurve.j_eq_zero | Mathlib.AlgebraicGeometry.EllipticCurve.Weierstrass | [
"Eq.mpr",
"Nat.instMulZeroClass",
"CommRing",
"WeierstrassCurve.IsElliptic",
"congrArg",
"CommSemiring.toSemiring",
"WeierstrassCurve.j",
"WeierstrassCurve.j_eq_zero_iff'",
"WeierstrassCurve.c₄",
"id",
"instOfNatNat",
"WeierstrassCurve",
"Monoid.toPow",
"CommRing.toCommSemiring",
"Monoid... | true |
Std.ExtDHashMap.mem_of_getKey?_eq_some | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Option.some",
"Membership.mem",
"Std.ExtDHashMap.inductionOn",
"Std.ExtDHashMap.mk",
"LawfulHashable",
"Std.ExtDHashMap.getKey?",
"EquivBEq",
"Std.ExtDHashMap",
"Hashable",
"BEq",
"Eq",
"Std.DHashMap",
"Option",
"Std.DHashMap.m... | true |
Std.DTreeMap.Raw.Equiv.getEntryLTD_eq | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.getEntryLTD",
"Ord.mk",
"Ordering",
"Std.DTreeMap.Raw.Equiv",
"Std.TransCmp",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Std.DTreeMap.Raw.Equiv.inner",
"Eq",
"Std.DTreeMap.Internal.Impl.Equiv.getEntryLTD_eq",
"Sigma",
"Std.DTreeMap.Raw.WF",
"Std.DTreeMap.Raw"
] | true |
NumberField.mixedEmbedding.normAtAllPlaces_normAtAllPlaces | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.Basic | [
"instInnerProductSpaceRealComplex",
"Pi.Function.module",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"NumberField.mixedEmbedding.realSpace",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"Pi.topologicalSpace",
"Re... | true |
_private.Mathlib.Analysis.ODE.PicardLindelof.0.ContDiffAt.exists_forall_mem_closedBall_exists_eq_forall_mem_Ioo_hasDerivAt₀.match_1_1 | Mathlib.Analysis.ODE.PicardLindelof | [
"Real",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"Real.denselyNormedField",
"Real.instZero",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Real.instSub",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"HasDerivAt",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace... | false |
spectralNorm.normedField._proof_7 | Mathlib.Analysis.Normed.Unbundled.SpectralNorm | [
"Eq.mpr",
"Algebra.IsAlgebraic.isAlgebraic",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"spectralNorm_neg",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Ring.toNeg",
"AddMonoid.toAddSemigroup",
"AddGroupWithOne.toAddGroup",
"congrA... | false |
FourierModule.ctorIdx | Mathlib.Analysis.Fourier.Notation | [
"outParam",
"SMul",
"Nat",
"FourierModule",
"Add"
] | false |
CategoryTheory.Projective.zero_projective | Mathlib.CategoryTheory.Preadditive.Projective.Basic | [
"CategoryTheory.Limits.isZero_zero",
"CategoryTheory.Limits.IsZero.projective",
"CategoryTheory.Limits.HasZeroObject",
"Zero.toOfNat0",
"CategoryTheory.Projective",
"OfNat.ofNat",
"CategoryTheory.Limits.HasZeroObject.zero'",
"CategoryTheory.Category"
] | true |
Int.instLinearOrder | Mathlib.Data.Int.Order.Basic | [
"Int.instMax",
"LinearOrder",
"Int.decLe",
"Int.le_total",
"Preorder.mk",
"Int.instDecidableEq",
"Int",
"Int.instLTInt",
"Int.instLinearOrder._proof_3",
"LinearOrder.mk",
"Int.le_trans",
"Int.instLinearOrder._proof_2",
"instOrdInt",
"Int.decLt",
"Int.instLinearOrder._proof_1",
"Int.le_... | true |
CochainComplex.ofHom | Mathlib.Algebra.Homology.HomologicalComplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"One",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.Hom.mk",
"AddRightCancelSemigroup.toAddSemigroup",
"instHAdd",
"AddSemigroup.toAdd",
"AddRightCancelSemigroup",
"HAdd.hAdd",
"CochainC... | true |
AlgebraicTopology.DoldKan.Γ₀.Obj.summand._proof_1 | Mathlib.AlgebraicTopology.DoldKan.FunctorGamma | [
"IsRightCancelAdd",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Nat.instAddCancelCommMonoid",
"AddSemigroup.toAdd",
"Nat",
"AddRightCancelMonoid.toAddRightCancelSemigroup",
"AddCancelCommMonoid.toAddCancelMonoid",
"AddRightCancelSemigroup.toIsRightCancelAdd"
... | false |
_private.Init.Data.Nat.Lemmas.0.Nat.sub_min_sub_right.match_1_1 | Init.Data.Nat.Lemmas | [
"instOfNatNat",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
instReprId | Init.Data.Repr | [
"instReprId._aux_1",
"id",
"Repr"
] | true |
MeasureTheory.Measure.rnDeriv_smul_right_of_ne_top' | Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | [
"ENNReal.coe_toNNReal",
"MeasureTheory.ae",
"Iff.mpr",
"Eq.mpr",
"MeasureTheory.Measure.rnDeriv_smul_right'",
"ENNReal.toNNReal_eq_zero_iff",
"False",
"ENNReal.ofNNReal",
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"ENNReal.smul_def",
"IsScalarTower.right",
"eq_false",
"congrA... | true |
SubMulAction.instBot | Mathlib.GroupTheory.GroupAction.SubMulAction | [
"SMul",
"SubMulAction.mk",
"Bot",
"Set.instEmptyCollection",
"SubMulAction.instBot._proof_1",
"EmptyCollection.emptyCollection",
"SubMulAction",
"Bot.mk",
"Set"
] | true |
CategoryTheory.Limits.colimit.ι_pre_assoc | Mathlib.CategoryTheory.Limits.HasLimits | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.colimit.ι_pre",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.Limits.colimit",
"CategoryTh... | true |
Std.ExtDTreeMap.Const.ofList | Std.Data.ExtDTreeMap.Basic | [
"Std.ExtDTreeMap.mk",
"Std.ExtDTreeMap.Const.ofList._auto_1",
"Ordering",
"Std.DTreeMap.Const.ofList",
"autoParam",
"List",
"Std.ExtDTreeMap",
"Prod"
] | true |
_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_3 | Mathlib.Combinatorics.SimpleGraph.Triangle.Basic | [
"forall_eq_or_imp",
"And",
"propext",
"Or",
"Eq"
] | false |
LightCondMod | Mathlib.Condensed.Light.Module | [
"ModuleCat",
"LightCondensed",
"ModuleCat.moduleCategory",
"Ring"
] | true |
derivWithin_fun_const_smul' | Mathlib.Analysis.Calculus.Deriv.Mul | [
"instHSMul",
"derivWithin_fun_const_smul_field",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"NormedField.toField",
"AddZeroClass.toAddZero",
... | true |
_private.Mathlib.Tactic.NormNum.Basic.0.Mathlib.Meta.NormNum.Result.add._proof_1 | Mathlib.Tactic.NormNum.Basic | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Qq.Quoted.unsafeMk",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Name.mkStr1",
"Qq.QuotedDefEq.unsafeIntro",
"List.nil"
] | false |
ContinuousMap.IccExtendCM | Mathlib.Topology.ContinuousMap.Interval | [
"OrderTopology",
"ContinuousMap.mk",
"LinearOrder",
"ContinuousMap",
"PartialOrder.toPreorder",
"ContinuousMap.comp",
"ContinuousMap.projIccCM",
"Preorder.toLE",
"Membership.mem",
"ContinuousMap.IccExtendCM._proof_1",
"SemilatticeInf.toPartialOrder",
"Fact",
"Set.Elem",
"DistribLattice.toL... | true |
BialgCat.MonoidalCategory.inducingFunctorData._proof_8 | Mathlib.Algebra.Category.BialgCat.Monoidal | [
"BialgCat.instBialgebra",
"BialgCat.category",
"CommRing",
"Coalgebra.toCoalgebraStruct",
"CategoryTheory.MonoidalCategory.tensorIso",
"BialgCat",
"Ring.toNonAssocRing",
"AlgCat.instCategory",
"Bialgebra.toCoalgebra",
"CommSemiring.toSemiring",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor"... | false |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Inv.0.Lean.Meta.Grind.Arith.Cutsat.checkDvds.match_1 | Lean.Meta.Tactic.Grind.Arith.Cutsat.Inv | [
"Option.ctorIdx",
"Option.some",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Inv.0.Lean.Meta.Grind.Arith.Cutsat.checkDvds._sparseCasesOn_1",
"Nat.hasNotBit",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstr",
"Option"
] | false |
compactOperator_topologicalClosure | Mathlib.Analysis.Normed.Operator.Compact.Basic | [
"NormedCommRing.toNormedRing",
"UniformSpace",
"Submodule",
"CompleteSpace",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"NormedSpace",
"ContinuousLinearMap.topologicalAddGroup",
"ContinuousLinearMap.topologicalSpace",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGro... | true |
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