name string | module string | deps list | allowCompletion bool |
|---|---|---|---|
_private.Mathlib.Algebra.EuclideanDomain.Basic.0.EuclideanDomain.«_aux_Mathlib_Algebra_EuclideanDomain_Basic___macroRules__private_Mathlib_Algebra_EuclideanDomain_Basic_0_EuclideanDomain_term_≺__1» | Mathlib.Algebra.EuclideanDomain.Basic | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
SubalgebraClass.seminormedRing._proof_15 | Mathlib.Analysis.Normed.Ring.Basic | [
"SetLike",
"Semiring.toNatCast",
"Ring.toNeg",
"Ring.toNonAssocRing",
"IntCast.intCast",
"SeminormedRing.toRing",
"Membership.mem",
"Subtype",
"instOfNatNat",
"Nat.cast",
"instHAdd",
"HAdd.hAdd",
"SubringClass",
"Nat",
"Ring.intCast_negSucc",
"instAddNat",
"Int.negSucc",
"SubringCl... | false |
SimpleGraph.edgeDensity.eq_1 | Mathlib.Combinatorics.SimpleGraph.Regularity.Chunk | [
"SimpleGraph.edgeDensity",
"Finset",
"SimpleGraph.Adj",
"Rat",
"DecidableRel",
"Rel.edgeDensity",
"SimpleGraph",
"Eq.refl",
"Eq"
] | true |
groupHomology.H0Iso | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | [
"Rep.coinvariantsFunctor",
"CommRing",
"groupHomology.cyclesIso₀._proof_3",
"Nat.instOne",
"ModuleCat",
"CommSemiring.toSemiring",
"groupHomology.opcyclesIso₀",
"groupHomology.H0",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Group",
"Rep.instCategory",
... | true |
Std.ExtTreeMap.maxKey?_le_maxKey?_insert | Std.Data.ExtTreeMap.Lemmas | [
"Std.ExtDTreeMap.maxKey?_le_maxKey?_insert",
"Std.ExtTreeMap.maxKey?",
"Option.some",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.ExtTreeMap",
"Option.get",
"Std.ExtTreeMap.inner",
"Bool",
"Std.ExtTreeMap.insert",
"Ordering.isLE",
"Eq",
"Std.ExtTreeMap.isSome_maxKey?_insert",
"Option"
... | true |
Positive.addLeftCancelSemigroup._proof_1 | Mathlib.Algebra.Order.Positive.Ring | [
"Preorder.toLT",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddLeftCancelMonoid",
"AddZeroClass.toAddZero",
"Subtype",
"Positive.instAddSubtypeLtOfNat_mathlib",
"Subtype.coe_injective",
"AddLeftCancelMonoid.toAddLeftCancelSemigroup",
"AddZero.toZero",
"AddSemigroup.toAdd",
"AddLe... | false |
Homeomorph.piCongrLeft_symm_apply | Mathlib.Topology.Homeomorph.Lemmas | [
"Equiv.instEquivLike",
"Pi.topologicalSpace",
"Homeomorph.piCongrLeft",
"Equiv",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"Homeomorph.symm",
"Homeomorph",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
Lean.JsonRpc.RequestID.num.sizeOf_spec | Lean.Data.JsonRpc | [
"Lean.JsonNumber",
"Lean.JsonNumber._sizeOf_inst",
"Lean.JsonRpc.RequestID.num",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Lean.JsonRpc.RequestID._sizeOf_inst",
"instAddNat",
"Eq.refl",
"Lean.JsonRpc.RequestID",
"OfNat.ofNat",
"Eq"
] | true |
CategoryTheory.Limits.hasStrongEpiImages_of_hasStrongEpiMonoFactorisations | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.Limits.HasImages.has_image",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Classical.choice",
"CategoryTheory.Limits.StrongEpiMonoFactorisation",
"CategoryTheory.Limits.HasStrongEpiMonoFactorisations",
"CategoryTheory.Limits.HasStrongEpiImages.mk",
"CategoryTheory.Limits.str... | true |
CategoryTheory.Functor.copyObj._proof_4 | Mathlib.CategoryTheory.NatIso | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso",
"_private.Mathlib.CategoryTheory.NatIso.0.CategoryTheory.Functor.copyObj._proof_3",
"CategoryTheory.Functor.map",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
... | false |
AddAut.instAddGroup._proof_9 | Mathlib.Algebra.Group.End | [
"Add.mk",
"instHAdd",
"AddAut",
"HAdd.hAdd",
"AddEquiv.trans",
"AddEquiv.refl",
"Zero.mk",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Add",
"rfl"
] | false |
Polynomial.instCommRingUniversalFactorizationRing._proof_45 | Mathlib.RingTheory.Polynomial.UniversalFactorizationRing | [
"Semiring.toNatCast",
"Polynomial.instCommRingUniversalFactorizationRing._aux_1",
"Mul.mk",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Semiring.toModule",
"Equiv.instEquivLike",
"One.mk",
"Polynomial.MonicDegreeEq",
"Polynomial.instCommRingUniversalFactorizationRing._aux_1... | false |
Fintype.expect_ite_zero | Mathlib.Algebra.BigOperators.Expect | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"NNRat.instInv",
"Finset.univ",
"Finset.expect",
"Finset.expect_ite_zero",
"congrArg",
"NNRat.instSemifield",
"DistribMulAction.toDistribSMul",
"Finset",
"AddMonoid.toAddZeroClass",
"instInhabitedTrue",
"Membership.mem",
"... | true |
RightCosetEquivalence | Mathlib.GroupTheory.Coset.Basic | [
"instHSMul",
"Mul.toSMulMulOpposite",
"MulOpposite",
"Mul",
"HSMul.hSMul",
"Eq",
"Set.smulSet",
"MulOpposite.op",
"Set"
] | true |
ENNReal.inv_eq_zero | Mathlib.Data.ENNReal.Inv | [
"Eq.rec",
"Iff",
"inv_inj",
"Inv.inv",
"ENNReal.instInvolutiveInv",
"ENNReal",
"Zero.toOfNat0",
"ENNReal.instInv",
"ENNReal.instTop",
"ENNReal.inv_top",
"ENNReal.instZero",
"Top.top",
"OfNat.ofNat",
"Eq"
] | true |
CompactCoherentification.t2space | Mathlib.Topology.Compactness.CompactlyCoherentSpace | [
"Equiv.instEquivLike",
"CompactCoherentification.mk",
"CompactCoherentification.continuous_mk_symm",
"T2Space.of_injective_continuous",
"Equiv",
"TopologicalSpace",
"T2Space",
"Equiv.injective",
"Equiv.symm",
"CompactCoherentification",
"CompactCoherentification.instTopologicalSpace",
"DFunLik... | true |
_private.Init.Data.List.Lemmas.0.List.dropLast_append_of_ne_nil.match_1_1 | Init.Data.List.Lemmas | [
"Ne",
"List.cons",
"List",
"List.casesOn",
"List.nil"
] | false |
MagmaCat.instCategory._proof_3 | Mathlib.Algebra.Category.Semigrp.Basic | [
"id",
"MulHom.comp",
"MagmaCat.Hom.hom'",
"MagmaCat.carrier",
"MagmaCat.str",
"Eq.refl",
"_private.Mathlib.Algebra.Category.Semigrp.Basic.0.MagmaCat.Hom.mk",
"Eq",
"MagmaCat",
"MagmaCat.Hom"
] | false |
Lean.Elab.WF.GuessLex.RecCallCache.mk'' | Lean.Elab.PreDefinition.WF.GuessLex | [
"Lean.Elab.WF.GuessLex.BasicMeasure",
"Lean.Elab.WF.GuessLex.RecCallCache",
"Lean.Elab.WF.GuessLex.RecCallWithContext",
"Array",
"Lean.Elab.WF.GuessLex.GuessLexRel",
"Lean.Name",
"IO.Ref",
"Lean.Elab.DecreasingBy",
"Lean.Elab.WF.GuessLex.RecCallCache.mk''",
"Option"
] | true |
ProbabilityTheory.indepSet_iff_measure_inter_eq_mul | Mathlib.Probability.Independence.Basic | [
"MeasureTheory.Measure",
"HMul.hMul",
"MeasurableSet",
"CommSemiring.toSemiring",
"MeasureTheory.IsZeroOrProbabilityMeasure",
"ProbabilityTheory.IndepSet",
"ProbabilityTheory.indepSets_singleton_iff",
"Set.instSingletonSet",
"ProbabilityTheory.indepSet_iff_measure_inter_eq_mul._auto_1",
"ENNReal.i... | true |
FreeSemigroup.mk._flat_ctor | Mathlib.Algebra.Free | [
"FreeSemigroup.mk",
"List",
"FreeSemigroup"
] | false |
Set.image_sigmaMk_preimage_sigmaMap_subset | Mathlib.Data.Set.Sigma | [
"Iff.mpr",
"Membership.mem",
"HasSubset.Subset",
"And",
"Set.preimage",
"Sigma.map",
"And.intro",
"Exists.intro",
"Set.image",
"Set.image_subset_iff",
"Sigma.mk",
"Eq",
"Set.instMembership",
"Sigma",
"rfl",
"Set.instHasSubset",
"Set"
] | true |
_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.coeff_weierstrassPExceptSeries._simp_1_3 | Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass | [
"Subtype",
"Subtype.ext_iff",
"propext",
"Subtype.val",
"Eq"
] | false |
exists_zsmul_surjective | Mathlib.Algebra.Group.Defs | [
"IsAddCyclic.exists_zsmul_surjective",
"instHSMul",
"SMul",
"Exists",
"Int",
"HSMul.hSMul",
"IsAddCyclic",
"Function.Surjective"
] | true |
Lean.Meta.mkLetValCongr | Lean.Meta.AppBuilder | [
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Meta.mkAppM",
"List.toArray",
"List.cons",
"Lean.Name.mkStr1",
"List.nil"
] | true |
CategoryTheory.Lax.OplaxTrans.LaxFunctor.bicategory._proof_10 | Mathlib.CategoryTheory.Bicategory.FunctorBicategory.Lax | [
"CategoryTheory.Lax.OplaxTrans.Hom.as",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Lax.OplaxTrans.whiskerRight",
"CategoryTheory.Lax.OplaxTrans.instCategoryStructLaxFunctor",
"CategoryTheory.CategoryStruct.id",
"inferInstance",
"CategoryTheory.Lax.OplaxTrans.... | false |
Set.surjOn_of_subsingleton | Mathlib.Data.Set.Function | [
"Set.SurjOn",
"id",
"Set.surjOn_of_subsingleton'",
"Set.Nonempty",
"Subsingleton",
"Set"
] | true |
not_forall_of_exists_not | Init.PropLemmas | [
"False",
"Exists",
"_private.Init.PropLemmas.0.not_forall_of_exists_not.match_1_1",
"Not"
] | true |
IntermediateField.essFiniteType_iff | Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra | [
"Eq.mpr",
"Set.image_univ",
"Lattice.toSemilatticeSup",
"instSMulOfMul",
"Equiv.instEquivLike",
"Equiv.exists_congr_left",
"IntermediateField.FG",
"CompleteLattice.toLattice",
"Iff.of_eq",
"congrArg",
"IntermediateField",
"AlgHom",
"Finset",
"_private.Mathlib.FieldTheory.IntermediateField.... | true |
Lean.Parser.Tactic.Conv._aux_Init_Conv___macroRules_Lean_Parser_Tactic_Conv_convRepeat__1 | Init.Conv | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"Lean.Name.mkStr5",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.i... | false |
_private.Mathlib.Topology.UniformSpace.UniformConvergenceTopology.0.instSubsingletonUniformOnFun._proof_1 | Mathlib.Topology.UniformSpace.UniformConvergenceTopology | [
"Pi.instSubsingleton",
"Subsingleton",
"UniformOnFun",
"Set"
] | false |
_private.Lean.Meta.Basic.0.Lean.Meta.realizeValue.realizeAndReport | Lean.Meta.Basic | [
"Applicative.toSeqLeft",
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.instBEqFVarId",
"Lean.Core.Context.diag",
"Lean.MessageData",
"UInt64.instOfNat",
"Inhabited.default",
"Array.mkEmpty",
"Lean.Core.State.mk",
"Lean.Elab.InfoState.mk",
"Lean.Name.mkNum",
"Task",
"Lean.LocalContext... | true |
Subgroup.comap_upperCentralSeries_quotient_center | Mathlib.GroupTheory.Nilpotent | [
"Eq.mpr",
"Nat.recAux",
"Trans.trans",
"Monoid.toMulOneClass",
"Subgroup.normal_comap",
"congrArg",
"eq_isEquiv",
"Subgroup.upperCentralSeries",
"Group",
"_private.Mathlib.GroupTheory.Nilpotent.0.Subgroup.comap_center_subst",
"Subgroup.normal_of_characteristic",
"Subgroup.instNormalCenter",
... | true |
CategoryTheory.Functor.PullbackObjObj.ofIsTerminal | Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj | [
"CategoryTheory.Limits.IsTerminal.from",
"CategoryTheory.Functor",
"CategoryTheory.Functor.PullbackObjObj.mk",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.IsTerminal",
"CategoryTheory.Functor.PullbackObjObj",
"CategoryTheory.Functor.category",
"Catego... | true |
Nat.bitIndices_two_pow_mul | Mathlib.Data.Nat.BitIndices | [
"Eq.mpr",
"MulOne.toOne",
"Semigroup.toMul",
"Nat.recAux",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Nat.bitIndices",
"List.map",
"Nat.instMonoid",
"AddMonoid.toAddZeroClass",
"mul_assoc",
"Nat.instMulOneClass",
"Nat.instAddMonoid",
"pow_add",
"Function.comp",
"AddZeroClass.t... | true |
birkhoffSum_one' | Mathlib.Dynamics.BirkhoffSum.Basic | [
"instOfNatNat",
"AddCommMonoid",
"birkhoffSum",
"funext",
"Nat",
"OfNat.ofNat",
"Eq",
"birkhoffSum_one"
] | true |
Lean.ExtraModUse.casesOn | Lean.ExtraModUses | [
"Lean.ExtraModUse.rec",
"Lean.ExtraModUse.mk",
"Bool",
"Lean.Name",
"Lean.ExtraModUse"
] | false |
Bicategory.Opposite.Hom2.unop2 | Mathlib.CategoryTheory.Bicategory.Opposites | [
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.unop",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Bicategory.homCategory",
"Opposite.unop",
"Bicategory.O... | true |
Equiv.Perm.support_eq_empty_iff | Mathlib.GroupTheory.Perm.Support | [
"Eq.mpr",
"Equiv.Perm.support",
"False",
"Equiv.instEquivLike",
"Equiv.Perm.instOne",
"iff_false",
"congrArg",
"Finset",
"Membership.mem",
"_private.Mathlib.GroupTheory.Perm.Support.0.Equiv.Perm.support_eq_empty_iff._simp_1_1",
"id",
"Ne",
"_private.Mathlib.GroupTheory.Perm.Support.0.Equiv.P... | true |
Std.TreeMap.Raw.compare_getKey_self | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.WF.out",
"Membership.mem",
"Ordering",
"Std.TreeMap.Raw.instMembership",
"Ordering.eq",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"Std.TreeMap.Raw.getKey",
"Eq",
"Std.DTreeMap.Raw.compare_getKey_self"
] | true |
Rat.isFractionRing | Mathlib.RingTheory.Localization.FractionRing | [
"Int.cast",
"Eq.mpr",
"Nat.Coprime",
"GroupWithZero.toMonoidWithZero",
"RingHom.instRingHomClass",
"Int.instIsStrictOrderedRing",
"HMul.hMul",
"Int.cast_inj",
"Algebra.algebraMap",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"Int.instLinearOrder",
"IsFractionRing",
"Ra... | true |
_private.Mathlib.LinearAlgebra.Lagrange.0.Lagrange.interpolate._simp_2 | Mathlib.LinearAlgebra.Lagrange | [
"Finset.sum_add_distrib",
"Finset",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddCommMonoid",
"instHAdd",
"HAdd.hAdd",
"AddZero.toAdd",
"AddCommMonoid.toAddMonoid",
"Eq.symm",
"Eq",
"Finset.sum"
] | false |
Subgroup.adjoinNegOne_eq_self_iff._simp_1 | Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | [
"Subgroup.adjoinNegOne_eq_self_iff",
"Ring.toNonAssocRing",
"Matrix",
"Subgroup.adjoinNegOne",
"Membership.mem",
"Units.instNeg",
"Subgroup",
"Units.instGroup",
"NonAssocRing.toNonUnitalNonAssocRing",
"Units.instOne",
"NonUnitalNonAssocRing.toHasDistribNeg",
"Fintype",
"Semiring.toMonoid",
... | false |
BotHom.instSemilatticeInf._proof_2 | Mathlib.Order.Hom.Bounded | [
"OrderBot.toBot",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"SemilatticeInf.toPartialOrder",
"Bot",
"LE.le",
"BotHom.instFunLike",
"SemilatticeInf",
"Iff",
"Pi.instSemilatticeInf",
"DFunLike.coe",
"BotHom"
] | false |
Nat.Linear.ExprCnstr.lhs | Init.Data.Nat.Linear | [
"Nat.Linear.Expr",
"Nat.Linear.ExprCnstr"
] | true |
MeasureTheory.SimpleFunc.approxOn | Mathlib.MeasureTheory.Function.SimpleFuncDense | [
"Measurable",
"MeasureTheory.SimpleFunc",
"Function.comp",
"Membership.mem",
"Set.Elem",
"MeasureTheory.SimpleFunc.approxOn._proof_1",
"PseudoEMetricSpace",
"MeasurableSpace",
"MeasureTheory.SimpleFunc.nearestPt",
"PseudoEMetricSpace.toUniformSpace",
"Nat",
"OpensMeasurableSpace",
"instTopol... | true |
Quiver.Path.isChain_toList_nonempty._f | Mathlib.Combinatorics.Quiver.Path | [
"List.IsChain.cons_cons",
"Quiver.Hom",
"Quiver.Path.nil",
"Quiver.Path.toList",
"List.IsChain",
"List.IsChain.singleton",
"Nonempty.intro",
"Quiver.Path",
"Quiver.Path.below",
"Quiver.Path.cons",
"Unit",
"List.IsChain.nil",
"Quiver",
"Nonempty",
"_private.Mathlib.Combinatorics.Quiver.Pa... | false |
isMIntegralCurveAt_eventuallyEq_of_contMDiffAt_boundaryless | Mathlib.Geometry.Manifold.IntegralCurve.ExistUnique | [
"IsMIntegralCurveAt",
"Real",
"Prod.normedSpace",
"instAddMonoidWithOneENat",
"Prod.normedAddCommGroup",
"TangentSpace.fiberBundle",
"NormedSpace",
"BoundarylessManifold.isInteriorPoint",
"Real.denselyNormedField",
"PseudoMetricSpace.toUniformSpace",
"nhds",
"Bundle.TotalSpace.mk",
"Filter.E... | true |
_private.Mathlib.SetTheory.Cardinal.NatCard.0.Finite.card_eq_zero_iff._simp_1_1 | Mathlib.SetTheory.Cardinal.NatCard | [
"Fintype.card",
"instOfNatNat",
"IsEmpty",
"Fintype",
"Fintype.card_eq_zero_iff",
"Nat",
"propext",
"OfNat.ofNat",
"Eq"
] | false |
AddCon.comapQuotientEquivOfSurj_symm_mk' | Mathlib.GroupTheory.Congruence.Basic | [
"Iff.mpr",
"AddCon",
"AddEquivClass.instAddMonoidHomClass",
"AddMonoidHomClass.toAddMonoidHom",
"AddCon.hasAdd",
"AddCon.comapQuotientEquivOfSurj",
"AddZeroClass.toAddZero",
"Quotient.mk",
"AddCon.comap",
"AddEquiv.surjective",
"AddCon.toSetoid",
"AddZeroClass",
"AddEquiv.symm_apply_eq",
"... | true |
ContinuousLinearMap.integrableAtFilter_comp | Mathlib.MeasureTheory.Integral.IntegrableOn | [
"Filter.instMembership",
"MeasureTheory.Measure",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"RingHom",
"RingHomIsometric",
"Function.comp",
"Membership.mem",
"NormedField.toField",
"SeminormedAddG... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.getVert_sub_one_ne_getVert_add_one._proof_1_6 | Mathlib.Combinatorics.SimpleGraph.Paths | [
"Lean.RArray.leaf",
"False",
"of_decide_eq_true",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"SimpleGraph.Walk.length",
"Classical.byContradiction",
"HSub.hSub",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"SimpleGraph.Walk",
"GE.ge",
"Eq.mp",
"Lean.RArray.branch",
"Nat.ToInt.natCast_... | false |
OpenPartialHomeomorph.isOpen_symm_image_iff_of_subset_target | Mathlib.Topology.OpenPartialHomeomorph.Basic | [
"Eq.mpr",
"congrArg",
"PartialEquiv.target",
"PartialEquiv.symm",
"id",
"OpenPartialHomeomorph.isOpen_image_of_subset_source",
"Set.inter_subset_left",
"HasSubset.Subset",
"OpenPartialHomeomorph.toFun'",
"Set.instInter",
"PartialEquiv.image_symm_image_of_subset_target",
"Inter.inter",
"Topol... | true |
OnePoint.nhdsNE_infty_neBot | Mathlib.Topology.Compactification.OnePoint.Basic | [
"Eq.mpr",
"OnePoint.infty",
"congrArg",
"Filter.map",
"Compl.compl",
"Filter.NeBot",
"nhdsWithin",
"OnePoint.some",
"inferInstance",
"Set.instSingletonSet",
"id",
"Filter.coclosedCompact",
"Set.instCompl",
"Filter.map_neBot",
"TopologicalSpace",
"OnePoint.nhdsNE_infty_eq",
"instNeBot... | true |
controlled_prod_of_mem_closure_range | Mathlib.Analysis.Normed.Group.Continuity | [
"Norm.norm",
"Eq.mpr",
"MonoidHom.range",
"Real",
"MonoidHom.instFunLike",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Real.instZero",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"SeminormedCommGroup.toPseudoMetricSpace",
"PseudoMe... | true |
_private.Mathlib.Algebra.Lie.Nilpotent.0.LieModule.isNilpotent_iff._simp_1_1 | Mathlib.Algebra.Lie.Nilpotent | [
"LieSubmodule.instBot",
"LieSubmodule",
"LieModule.isNilpotent_iff_int",
"Exists",
"AddCommGroup",
"Bot.bot",
"Int",
"LieRing",
"Int.instCommRing",
"LieModule.lowerCentralSeries",
"Nat",
"LieRingModule",
"propext",
"AddCommGroup.toIntModule",
"LieModule.IsNilpotent",
"LieRing.instLieAl... | false |
List.isGE_compare_nil_right | Init.Data.Ord.Basic | [
"Ord",
"List.isGE_compareLex_nil_right",
"Ord.compare",
"Bool.true",
"List",
"List.instOrd",
"Bool",
"Ordering.isGE",
"Eq",
"List.nil"
] | true |
IsOpen.isEverywherePos | Mathlib.MeasureTheory.Measure.EverywherePos | [
"Filter.instMembership",
"MeasureTheory.Measure",
"Preorder.toLT",
"nhdsWithin",
"PartialOrder.toPreorder",
"Membership.mem",
"Exists",
"IsOpen.measure_pos",
"HasSubset.Subset",
"mem_nhdsWithin",
"Set.instInter",
"Inter.inter",
"And.casesOn",
"MeasurableSpace",
"TopologicalSpace",
"Mea... | true |
CategoryTheory.CatEnrichedOrdinary.instQuiverHom | Mathlib.CategoryTheory.Bicategory.CatEnriched | [
"CategoryTheory.Cat.category",
"Quiver.mk",
"CategoryTheory.EnrichedOrdinaryCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CatEnrichedOrdinary",
"CategoryTheory.CatEnrichedOrdinary.instCategory",
"CategoryTheory.Cat",
"CategoryTheory.SemiCartesianMonoidalCategory.... | true |
MeasureTheory.Lp.fourierTransformₗᵢ._proof_11 | Mathlib.Analysis.Fourier.LpSpace | [
"InnerProductSpace.toNormedSpace",
"Real",
"measureSpaceOfInnerProductSpace",
"Real.instRCLike",
"NormedSpace.toModule",
"MeasureTheory.MeasureSpace.toMeasurableSpace",
"PseudoMetricSpace.toUniformSpace",
"BorelSpace",
"MeasurableSpace",
"BorelSpace.opensMeasurable",
"FiniteDimensional",
"Semi... | false |
ftaylorSeriesWithin_fun_zero | Mathlib.Analysis.Calculus.ContDiff.Basic | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"FormalMultilinearSeries.instAddCommGroup",
"FormalMultilinearSeries",
"DistribMulAction.toDistribSMul",
"Ad... | true |
Finset.sum_boole_mul | Mathlib.Algebra.BigOperators.Ring.Finset | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"congrArg",
"Finset",
"MulZeroClass.zero_mul",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"NonAssocSemiring.toMulZeroOneClass",
"AddCommMonoidWithOne.toAddMonoidWithOn... | true |
BilinForm.toMatrix_apply | Mathlib.LinearAlgebra.Matrix.BilinearForm | [
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Matrix.module",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Matrix",
"LinearMap.instSMulCommClass",
"LinearMap.instFunLike",
"LinearMap.BilinForm.toMatrix",
"LinearMap.BilinForm.toMatrix_apply",
"Algebra... | true |
ContinuousMultilinearMap.toMultilinearMap_add | Mathlib.Topology.Algebra.Module.Multilinear.Basic | [
"MultilinearMap.instAdd",
"ContinuousMultilinearMap",
"ContinuousMultilinearMap.instAdd",
"MultilinearMap",
"AddCommMonoid",
"TopologicalSpace",
"instHAdd",
"ContinuousMultilinearMap.toMultilinearMap",
"HAdd.hAdd",
"Semiring",
"AddCommSemigroup.toAddCommMagma",
"Module",
"ContinuousAdd",
"... | true |
instCommRingBDeRhamPlus._proof_18 | Mathlib.RingTheory.Perfectoid.BDeRham | [
"Submodule",
"fontaineThetaInvertP",
"Mul.mk",
"Submodule.Quotient.addCommMonoid",
"Semigroup.toMul",
"CommRing",
"instHSMul",
"Nat.Prime",
"Semiring.toModule",
"instSMulOfMul",
"AdicCompletion.instCommRing._proof_1",
"One.mk",
"HMul.hMul",
"instCommRingBDeRhamPlus._aux_16",
"AdicComplet... | false |
CategoryTheory.Functor.PreOneHypercoverDenseData.noConfusion | Mathlib.CategoryTheory.Sites.DenseSubsite.OneHypercoverDense | [
"CategoryTheory.Functor.PreOneHypercoverDenseData.casesOn",
"CategoryTheory.Functor.PreOneHypercoverDenseData.noConfusionType",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Functor.PreOneHypercoverDenseData",
"CategoryTheory.Functor.map"... | false |
groupHomology.mapCycles₂_comp | Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | [
"Eq.mpr",
"Submodule",
"Rep.V",
"groupHomology.mapCycles₂",
"CommRing",
"Finsupp.module",
"groupHomology.mapShortComplexH2",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"ModuleCat",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAd... | true |
UInt32.toUInt64._proof_1 | Init.Data.UInt.BasicAux | [
"instPowNat",
"of_decide_eq_true",
"id",
"instOfNatNat",
"instNatPowNat",
"Bool.true",
"HPow.hPow",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"instHPow",
"instLTNat",
"OfNat.ofNat",
"Decidable.decide",
"Eq"
] | false |
Dynamics.coverEntropyInf_eq_iSup_netEntropyInfEntourage | Mathlib.Dynamics.TopologicalEntropy.NetEntropy | [
"Dynamics.coverEntropyInfEntourage_le_netEntropyInfEntourage",
"Filter.instMembership",
"Dynamics.coverEntropyInfEntourage_antitone",
"UniformSpace",
"iSup₂_le",
"SetRel.symmetrize",
"SetRel",
"iSup",
"CompletelyDistribLattice.toCompleteLattice",
"le_iSup₂",
"uniformity",
"PartialOrder.toPreor... | true |
instContinuousSqrtNNReal._proof_1 | Mathlib.Topology.ContinuousMap.ContinuousSqrt | [
"NNReal.instTopologicalSpace",
"PartialOrder.toPreorder",
"setOf",
"HSub.hSub",
"ContinuousOn.sub",
"instTopologicalSpaceProd",
"Preorder.toLE",
"Function.comp",
"ContinuousOn.snd",
"OrderIso",
"NNReal",
"LE.le",
"NNReal.continuous_sqrt",
"Prod.fst",
"NNReal.sqrt",
"NNReal.instPartialO... | false |
Lean.Syntax.eqWithInfo | Lean.Syntax | [
"Inhabited.default",
"instInhabitedBool",
"Lean.Syntax",
"Bool"
] | true |
PrimeMultiset.ofNatList.eq_1 | Mathlib.Data.PNat.Factors | [
"Nat.Prime",
"PrimeMultiset.ofNatList",
"Membership.mem",
"PrimeMultiset.ofNatMultiset",
"List",
"Multiset.ofList",
"List.instMembership",
"Nat",
"Eq.refl",
"Eq",
"PrimeMultiset"
] | true |
Nonneg.coeAddMonoidHom | Mathlib.Algebra.Order.Nonneg.Basic | [
"Nonneg.addMonoid",
"AddMonoid.toAddSemigroup",
"Nonneg.coeAddMonoidHom._proof_1",
"AddMonoid.toAddZeroClass",
"AddLeftMono",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"AddMonoidHom.mk",
"Subtype",
"LE.le",
"ZeroHom.mk",
"AddZero.toZero",
"AddSemigroup.toAdd",
"AddMonoid",
"Zero.toOfNat... | true |
RootPairing.coroot_mem_or_neg_mem_closure_of_root | Mathlib.LinearAlgebra.RootSystem.BaseExists | [
"Rat.addCommMonoid",
"_private.Mathlib.LinearAlgebra.RootSystem.BaseExists.0.RootPairing.coroot_mem_or_neg_mem_closure_of_root._simp_1_1",
"Rat.instOfNat",
"_private.Mathlib.LinearAlgebra.RootSystem.BaseExists.0.RootPairing.coroot_mem_or_neg_mem_closure_of_root._simp_1_2",
"RootPairing.coroot_eq_polarizatio... | true |
CategoryTheory.Triangulated.AbelianSubcategory.hasCokernel | Mathlib.CategoryTheory.Triangulated.TStructure.AbelianSubcategory | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Triangulated.AbelianSubcategory.πQ",
"CategoryTheory.Triangulated.AbelianSubcategory.mor₁_πQ",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Triangulated.... | true |
CategoryTheory.Arrow.arrow_mk_comp_eqToHom | Mathlib.CategoryTheory.Comma.Arrow | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.Arrow.left",
"CategoryTheory.Arrow.hom",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"of_eq_true",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Arrow",
"C... | true |
egauge_empty | Mathlib.Analysis.Convex.EGauge | [
"False",
"instHSMul",
"iInf",
"Set.mem_empty_iff_false._simp_1",
"CompleteLattice.toLattice",
"Iff.of_eq",
"congrArg",
"Set.smul_set_empty",
"CompletelyDistribLattice.toCompleteLattice",
"SMul",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
... | true |
_private.Mathlib.Topology.Connected.Clopen.0.IsClopen.isPreconnected_iff._proof_1_6 | Mathlib.Topology.Connected.Clopen | [
"Lean.Grind.of_eq_eq_true",
"Set.mem_union",
"Lean.Grind.eq_false_of_not_eq_true",
"Set.ext",
"Lean.RArray.leaf",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Lean.Grind.AC.Expr.op",
"Lean.Grind.not_not",
"eq_false",
"Lean.Grind.iff_eq",
"Set.subset_def",
"CompleteBooleanAlgebra.toComplet... | false |
instIsScalarTowerTensorProductKaehlerDifferential._proof_1 | Mathlib.RingTheory.Kaehler.Basic | [
"CommRing",
"Algebra.to_smulCommClass",
"TensorProduct.leftHasSMul",
"Semiring.toModule",
"IsScalarTower.right",
"instAddCommGroupKaehlerDifferential",
"CommSemiring.toSemiring",
"Algebra.TensorProduct.instCommRing",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTowe... | false |
CategoryTheory.Sieve.instCompleteLattice._proof_9 | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Sieve.arrows",
"CategoryTheory.Sieve",
"And",
"And.right",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | false |
Complex.real_lt_real._simp_1 | Mathlib.Analysis.Complex.Order | [
"Real",
"Preorder.toLT",
"PartialOrder.toPreorder",
"Real.instLT",
"Complex.ofReal",
"LT.lt",
"propext",
"Complex.real_lt_real",
"Complex",
"Eq",
"Complex.partialOrder"
] | false |
SubStarSemigroup.toSubsemigroup | Mathlib.Algebra.Star.NonUnitalSubsemiring | [
"SubStarSemigroup",
"Mul",
"Star",
"Subsemigroup"
] | true |
_private.Mathlib.Order.CompactlyGenerated.Basic.0.isAtomic_of_complementedLattice._simp_1 | Mathlib.Order.CompactlyGenerated.Basic | [
"Subtype",
"Subtype.ext_iff",
"propext",
"Subtype.val",
"Eq"
] | false |
CategoryTheory.AB5OfSize.rec | Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic | [
"CategoryTheory.HasExactColimitsOfShape",
"CategoryTheory.AB5OfSize",
"CategoryTheory.AB5OfSize.mk",
"CategoryTheory.IsFiltered",
"CategoryTheory.Limits.hasColimitsOfShape_of_has_filtered_colimits",
"CategoryTheory.Limits.HasFilteredColimitsOfSize",
"CategoryTheory.Category"
] | false |
_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.Cpop.0.Std.Tactic.BVDecide.BVExpr.bitblast.denote_blastExtractAndExtendBit._proof_1_4 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.Cpop | [
"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 |
List.getElem_set | Init.Data.List.Lemmas | [
"False",
"eq_false",
"congrArg",
"List.getElem_set_ne",
"Eq.rec",
"List.set",
"ite_cond_eq_true",
"dite",
"List.getElem_set_ne._proof_1",
"List.getElem_set_self",
"GetElem.getElem",
"List",
"Nat",
"congr",
"LT.lt",
"True",
"eq_self",
"of_eq_true",
"Eq.ndrec",
"instDecidableEqNa... | true |
Ordnode.findLtAux._sunfold | Mathlib.Data.Ordmap.Ordnode | [
"Ordnode",
"LE.le",
"LE",
"DecidableLE",
"Nat",
"Ordnode.findLtAux",
"Ordnode.findMin'.match_1",
"ite"
] | false |
_private.Lean.Meta.Sym.Canon.0.Lean.Meta.Sym.Canon.canon.canonCond._unsafe_rec | Lean.Meta.Sym.Canon | [
"Pure.pure",
"_private.Lean.Meta.Sym.Canon.0.Lean.Meta.Sym.Canon.canon.canonInsideType._unsafe_rec",
"_private.Lean.Meta.Sym.Canon.0.Lean.Meta.Sym.Canon.CanonM",
"Lean.mkApp4",
"Lean.Meta.Sym.Context",
"ReaderT.instMonad",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instDecidableEqBool",
"A... | false |
Lean.Meta.RefinedDiscrTree.LazyEntry.stack | Mathlib.Lean.Meta.RefinedDiscrTree.Basic | [
"Lean.Meta.RefinedDiscrTree.StackEntry",
"List",
"Lean.Meta.RefinedDiscrTree.LazyEntry"
] | true |
Aesop.elabGlobalRuleIdent? | Aesop.RuleTac.ElabRuleTerm | [
"Pure.pure",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Term.resolveId?",
"Lean.Elab.Term.instAddErrorMessageContextTermElabM",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Bool.not",
"instMonadExceptOfMonadExceptOf",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.Mo... | true |
SetLike.isCoatom_iff | Mathlib.Order.Atoms | [
"SetLike",
"Eq.mpr",
"Preorder.toLT",
"_private.Mathlib.Order.Atoms.0.SetLike.isCoatom_iff._simp_1_4",
"congrArg",
"PartialOrder.toPreorder",
"_private.Mathlib.Order.Atoms.0.SetLike.isCoatom_iff._simp_1_3",
"Preorder.toLE",
"Membership.mem",
"Exists",
"PartialOrder",
"id",
"Ne",
"_private.... | true |
Lean.Doc.Parser.header | Lean.DocString.Parser | [
"Lean.Doc.Parser.fakeAtom",
"_private.Lean.DocString.Parser.0.Lean.Doc.Parser.textLine",
"bne",
"_private.Lean.DocString.Parser.0.Lean.Doc.Parser.withInfoSyntaxFn",
"HAndThen.hAndThen",
"String",
"Lean.SourceInfo",
"_private.Lean.DocString.Parser.0.Lean.Doc.Parser.header.checkNonIndented",
"instHAnd... | true |
_private.Init.Data.String.Extra.0.String.findLeadingSpacesSize.consumeSpaces._mutual._proof_3 | Init.Data.String.Extra | [
"PSum.casesOn",
"String.Pos.next",
"String",
"invImage",
"PSum",
"PSum.inr",
"PSigma.casesOn",
"id",
"PSum.inl",
"String.instLTPos",
"Nat",
"LT.lt",
"String.Pos",
"String.Pos.IsAtEnd",
"PSigma.mk",
"of_eq_true",
"String.Pos.lt_next._simp_1",
"String.Pos.instWellFoundedRelation",
... | false |
Int.neg_one_pow_ne_zero | Mathlib.Data.Int.Order.Units | [
"Int.instAddCommGroup",
"NegZeroClass.toNeg",
"False",
"IsDomain.to_noZeroDivisors",
"Int.instNeZeroOfNatOfNat",
"congrArg",
"neg_eq_zero._simp_1",
"AddGroupWithOne.toAddMonoidWithOne",
"Int.instNontrivial",
"false_and",
"one_ne_zero._simp_1",
"Int.instNegInt",
"Ne",
"SubtractionMonoid.toS... | true |
ListSlice | Init.Data.Slice.List.Basic | [
"Std.Slice.Internal.ListSliceData",
"Std.Slice"
] | true |
_private.Mathlib.RingTheory.Valuation.ValuativeRel.Basic.0.ValuativeRel.ValueGroupWithZero.embed._simp_4 | Mathlib.RingTheory.Valuation.ValuativeRel.Basic | [
"Monoid",
"Units.val",
"Units",
"Units.val_inj",
"propext",
"Eq.symm",
"Eq"
] | false |
List.nodup_append | Init.Data.List.Pairwise | [
"Membership.mem",
"Ne",
"List.pairwise_append",
"List.Nodup",
"instHAppendOfAppend",
"List",
"And",
"Iff",
"List.instMembership",
"List.instAppend",
"HAppend.hAppend"
] | true |
Std.DTreeMap.Internal.Impl.ExplorationStep.noConfusionType | Std.Data.DTreeMap.Internal.Model | [
"Ordering.gt",
"Ord",
"Std.DTreeMap.Internal.Impl.ExplorationStep.gt.elim",
"Ordering",
"Std.DTreeMap.Internal.Impl.ExplorationStep",
"Std.DTreeMap.Internal.Cell",
"dite",
"Std.DTreeMap.Internal.Impl.ExplorationStep.casesOn",
"List",
"Std.DTreeMap.Internal.Impl.ExplorationStep.ctorIdx",
"Orderin... | false |
leOfOrd | Init.Data.Ord.Basic | [
"Ord",
"Ord.compare",
"LE",
"Bool.true",
"LE.mk",
"Bool",
"Ordering.isLE",
"Eq"
] | true |
Lean.Expr.lt | Lean.Expr | [
"Inhabited.default",
"instInhabitedBool",
"Lean.Expr",
"Bool"
] | true |
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