name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Meta.Grind.Arith.CollectDecVars.State.noConfusionType | Lean.Meta.Tactic.Grind.Arith.Util | [
"UInt64",
"Std.HashSet",
"Lean.Meta.Grind.Arith.CollectDecVars.State.casesOn",
"instBEqOfDecidableEq",
"Lean.Meta.Grind.Arith.CollectDecVars.State",
"instDecidableEqUInt64",
"Lean.FVarIdSet",
"instHashableUInt64",
"Eq"
] | false |
Std.HashMap.Raw.Equiv.of_forall_getElem?_eq | Std.Data.HashMap.RawLemmas | [
"Std.HashMap.Raw.WF.out",
"LawfulBEq",
"Membership.mem",
"Std.HashMap.Raw.WF",
"Std.HashMap.Raw",
"Std.HashMap.Raw.instGetElem?Mem",
"Std.HashMap.Raw.inner",
"Std.HashMap.Raw.instMembershipOfBEqOfHashable",
"Hashable",
"Std.DHashMap.Raw.Equiv.of_forall_constGet?_eq",
"Std.HashMap.Raw.Equiv",
"... | true |
Subsingleton.monotone | Mathlib.Order.Monotone.Defs | [
"Monotone",
"Preorder.toLE",
"Eq.le",
"LE.le",
"congr_arg",
"Subsingleton",
"Subsingleton.elim",
"Preorder"
] | true |
CompactExhaustion.casesOn | Mathlib.Topology.Compactness.SigmaCompact | [
"Set.univ",
"HasSubset.Subset",
"CompactExhaustion.rec",
"instOfNatNat",
"TopologicalSpace",
"CompactExhaustion.mk",
"instHAdd",
"HAdd.hAdd",
"Nat",
"interior",
"instAddNat",
"CompactExhaustion",
"OfNat.ofNat",
"Eq",
"Set.iUnion",
"IsCompact",
"Set.instHasSubset",
"Set"
] | false |
Multiset.leInductionOn | Mathlib.Data.Multiset.Defs | [
"Quot.sound",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Eq.rec",
"Multiset",
"List.Perm",
"LE.le",
"Quotient.mk",
"List",
"Multiset.ofList",
"Quotient",
"Quotient.inductionOn₂",
"_private.Mathlib.Data.Multiset.Defs.0.Multiset.leInductionOn.match_1_1",
"List.Sublist",
"List.isSetoid",
... | true |
Lean.Elab.Tactic.BVDecide.Frontend.BVDecideConfig.fixedInt | Std.Tactic.BVDecide.Syntax | [
"Bool",
"Lean.Elab.Tactic.BVDecide.Frontend.BVDecideConfig"
] | true |
_private.Std.Internal.Http.Data.URI.Basic.0.Std.Http.URI.Scheme.ofPort._proof_2 | Std.Internal.Http.Data.URI.Basic | [
"List.head?",
"List.all",
"of_decide_eq_true",
"Std.Http.Internal.instDecidableIsLowerCase",
"Char.isAlpha",
"Option.getD",
"Std.Http.Internal.IsLowerCase",
"id",
"instDecidableEqBool",
"Bool.true",
"Option.map",
"And",
"String.toList",
"Bool",
"Eq.refl",
"Char",
"Std.Http.Internal.C... | false |
WithVal.instZero | Mathlib.Topology.Algebra.Valued.WithVal | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"LinearOrderedCommGroupWithZero",
"WithVal",
"Zero.mk",
"Zero.toOfNat0",
"OfNat.ofNat",
"Ring.toSemiring",
"Ring",
"Valuation",
"WithVal.toVal",
"MulZeroClass.toZero",
"instMulZeroClassOfSemiring",
"Zero"
] | true |
Polynomial.map_sum | Mathlib.Algebra.Polynomial.Eval.Defs | [
"RingHom.instRingHomClass",
"RingHomClass.toAddMonoidHomClass",
"Finset",
"RingHom",
"map_sum",
"Polynomial",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"RingHom.instFunLike",
"Polynomial.mapRingHom",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Polynomial.semiring",
"Semiring",
"Polyn... | true |
Perfection.lift._proof_3 | Mathlib.RingTheory.Perfection | [
"PerfectRing",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.Prime",
"Perfection",
"frobeniusEquiv",
"congrArg",
"CommSemiring.toSemiring",
"RingEquiv.instEquivLike",
"Function.RightInverse.iterate",
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"RingHom",
"Perfection.instCh... | false |
Std.HashSet.Raw.size_le_size_insertMany_list | Std.Data.HashSet.RawLemmas | [
"Std.HashSet.Raw.size",
"instForInOfForIn'",
"Std.HashSet.Raw.inner",
"Std.HashSet.Raw.insertMany",
"Std.HashSet.Raw.WF",
"inferInstance",
"LE.le",
"instLENat",
"Id",
"Membership",
"LawfulHashable",
"List",
"EquivBEq",
"Std.HashSet.Raw.WF.out",
"List.instMembership",
"Nat",
"Id.instM... | true |
Std.DTreeMap.Internal.Impl.getEntryGT? | Std.Data.DTreeMap.Internal.Queries | [
"Ord",
"Std.DTreeMap.Internal.Impl.getEntryGT?.go",
"Option.none",
"Std.DTreeMap.Internal.Impl",
"Sigma",
"Option"
] | true |
Lean.Grind.CommRing.Stepwise.div_cert | Init.Grind.Ring.CommSolver | [
"Bool.and'",
"Lean.Grind.CommRing.Poly",
"Bool.not",
"Lean.Grind.CommRing.Poly.beq'",
"Int",
"Lean.Grind.CommRing.Poly.mulConst_k",
"instOfNat",
"Int.beq'",
"Bool",
"OfNat.ofNat"
] | true |
_private.Mathlib.MeasureTheory.Measure.Stieltjes.0.StieltjesFunction.measure_const._simp_1_2 | Mathlib.MeasureTheory.Measure.Stieltjes | [
"HSub.hSub",
"OrderedSub",
"LE.le",
"tsub_le_iff_right",
"LE",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"propext",
"Eq",
"Add",
"Sub"
] | false |
LinOrd.Iso.mk._proof_3 | Mathlib.Order.Category.LinOrd | [
"PartialOrder.toPreorder",
"LinOrd.carrier",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"LinOrd.str",
"DistribLattice.toLattice",
"RelIso.instRelHomClass",
"LE.le",
"LinOrd",
"RelIso",
"RelIso.instFunLike",
"RelHomClass",
"instDistribLatticeOfLinearOrder",
"Lattice.toSemilatticeInf"... | false |
_private.Lean.Elab.DeclNameGen.0.Lean.Elab.Command.NameGen.getParentProjArg._sparseCasesOn_1 | Lean.Elab.DeclNameGen | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
OrderIso.toOrderEmbedding | Mathlib.Order.Hom.Basic | [
"OrderIso",
"LE.le",
"LE",
"RelIso.toRelEmbedding",
"OrderEmbedding"
] | true |
_private.Init.Data.Array.QSort.Basic.0.Array.qsort._proof_13 | Init.Data.Array.QSort.Basic | [
"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.max_mem | Init.Data.List.MinMax | [
"List.max?_eq_some_max",
"Membership.mem",
"Max",
"Ne",
"List",
"List.max?_mem",
"List.instMembership",
"Std.MaxEqOr",
"List.nil",
"List.max"
] | true |
List.head?_dropLast | Init.Data.List.Lemmas | [
"List.head?",
"Nat.zero_lt_succ._simp_1",
"congrArg",
"Option.some",
"List.dropLast",
"instOfNatNat",
"ite_cond_eq_true",
"_private.Init.Data.List.Lemmas.0.List.head?_dropLast._simp_1_1",
"List.cons",
"Option.none",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"True",
"List.cases... | true |
Lean.Parser.Level.paren.parenthesizer | Lean.Parser.Level | [
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"Lean.Parser.withoutPosition.parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.leadingNode.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer.andthen.parenthesizer",
"Bool.... | true |
Int.multichoose | Mathlib.RingTheory.Binomial | [
"Units.val",
"Nat.choose",
"HMul.hMul",
"HSub.hSub",
"Int.multichoose.match_1",
"instSubNat",
"instOfNatNat",
"Int",
"Nat.cast",
"Int.instMonoid",
"Int.instMul",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"instAddNat",
"instNatCastInt",
"OfNat.ofNat",
"Int.negOnePow",
"instHMu... | true |
_private.Lean.Meta.Constructions.CtorElim.0.Lean.mkCtorElimType._sparseCasesOn_1 | Lean.Meta.Constructions.CtorElim | [
"Lean.ConstantInfo.recInfo",
"Lean.ConstantInfo.defnInfo",
"Lean.ConstructorVal",
"Nat.ne_of_beq_eq_false",
"Lean.QuotVal",
"Lean.ConstantInfo.inductInfo",
"Lean.ConstantInfo.opaqueInfo",
"Nat.shiftRight",
"Lean.ConstantInfo.thmInfo",
"Nat.hasNotBit",
"Lean.ConstantInfo.rec",
"instOfNatNat",
... | false |
_private.Lean.Elab.DocString.Builtin.0.Lean.Doc.NoInfo.noConfusionType | Lean.Elab.DocString.Builtin | [
"_private.Lean.Elab.DocString.Builtin.0.Lean.Doc.NoInfo"
] | true |
Matrix.fromBlocks_diagonal | Mathlib.Data.Matrix.Block | [
"Matrix.fromBlocks",
"False",
"Sum.ctorIdx",
"congrArg",
"Sum.inr.injEq",
"Matrix",
"instDecidableEqSum",
"False.elim",
"noConfusion_of_Nat",
"Sum.casesOn",
"Sum",
"Sum.inl",
"Sum.inl.injEq",
"Sum.inr",
"True",
"eq_self",
"of_eq_true",
"Zero.toOfNat0",
"Eq.refl",
"ite_congr",
... | true |
Submodule.isOrtho_sSup_left._simp_1 | Mathlib.Analysis.InnerProductSpace.Orthogonal | [
"InnerProductSpace.toNormedSpace",
"Submodule",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"NormedSpace.toModule",
"Membership.mem",
"NormedField.toField",
"CompleteLattice.toConditionallyCompleteLattice",
"Field.toSemifield",
"Submodule.IsOrtho",
"RCLike.toDenselyNormedField",... | false |
CategoryTheory.SplitEpi.casesOn | Mathlib.CategoryTheory.EpiMono | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.SplitEpi.mk",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.SplitEpi.rec",
"CategoryTheory.SplitEpi",
"Eq",
"CategoryTheory.Category"
] | false |
mulEquivIsoCommGroupIso._proof_1 | Mathlib.Algebra.Category.Grp.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Monoid.toMulOneClass",
"CommGrpCat.instCategory",
"CategoryTheory.CategoryStruct.id",
"CommGrpCat.str",
"TypeCat.ofHom",
"id",
"MulOne.toMul",
"CategoryTheory.Iso",
"DivInvMonoid.toMonoid",
"CategoryTheory.Iso.commGroupIsoToMulEquiv",
... | false |
MeasureTheory.Measure.ae_prod_iff_ae_ae | Mathlib.MeasureTheory.Measure.Prod | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"MeasurableSet",
"Compl.compl",
"Filter.Eventually",
"setOf",
"Prod.mk",
"MeasurableSet.compl",
"Set.instCompl",
"MeasurableSpace",
"Iff",
"MeasureTheory.SFinite",
"MeasureTheory.Measure.prod",
"MeasureTheory.Measure.measure_prod_null",
"Prod"... | true |
Std.HashMap.getKeyD_eq_getD_getKey? | Std.Data.HashMap.Lemmas | [
"Std.DHashMap.getKeyD_eq_getD_getKey?",
"Option.getD",
"Std.HashMap",
"LawfulHashable",
"EquivBEq",
"Std.HashMap.getKeyD",
"Std.HashMap.getKey?",
"Hashable",
"Std.HashMap.inner",
"BEq",
"Eq"
] | true |
CategoryTheory.Limits.hasColimitsOfSize_thinSkeleton | Mathlib.CategoryTheory.Limits.Skeleton | [
"CategoryTheory.ThinSkeleton.fromThinSkeleton_isEquivalence",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.ThinSkeleton.fromThinSkeleton",
"CategoryTheory.Limits.HasColimitsOfSize",
"Preorder.smallCategory",
"CategoryTheory.hasColimits_of_hasColimits_createsColimits",
"CategoryTheory.ThinSk... | true |
_private.Mathlib.Util.Notation3.0.Mathlib.Notation3.exprToMatcher.match_10 | Mathlib.Util.Notation3 | [
"Lean.TSyntax",
"MProd.casesOn",
"Lean.Expr",
"MProd.mk",
"List.cons",
"MProd",
"Lean.SyntaxNodeKind",
"Lean.Name.mkStr1",
"List.nil"
] | false |
_private.Std.Data.DTreeMap.Internal.Balancing.0.Std.DTreeMap.Internal.Impl.balanceL!_eq_balance!._proof_1_7 | Std.Data.DTreeMap.Internal.Balancing | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"HMul.hMul",
"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.eval",
... | false |
AdjoinRoot.instDistribSMulOfIsScalarTower | Mathlib.RingTheory.AdjoinRoot | [
"AdjoinRoot.instSMulAdjoinRoot",
"CommRing",
"instSMulOfMul",
"AdjoinRoot",
"CommSemiring.toSemiring",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"AddZeroClass.toAddZero",
"DistribSMul.mk",
"DistribSMul.toSMulZeroClass",
"SMulZeroClass.mk",
"Polynomial... | true |
smul_sub | Mathlib.Algebra.GroupWithZero.Action.Defs | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"instHSMul",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"AddZeroClass.toAddZero",
"id",
"smul_neg",
"DistribSMul.toSMulZeroClass",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZero... | true |
Filter.map_prod_eq_map₂ | Mathlib.Order.Filter.NAry | [
"Filter.instMembership",
"Eq.mpr",
"Filter.map₂.eq_1",
"SProd.sprod",
"congrArg",
"Filter.map",
"Function.uncurry_def",
"setOf",
"Membership.mem",
"Exists",
"id",
"HasSubset.Subset",
"Filter.copy_eq",
"Prod.fst",
"And",
"Set.image2",
"Filter.map₂._proof_5",
"Eq.refl",
"Filter.map... | true |
LinearMap.IsProj.submodule_eq_bot_iff | Mathlib.LinearAlgebra.Projection | [
"LinearMap.IsProj.map_mem",
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"LinearMap.IsProj.range",
"LinearMap.ext",
"congrArg",
"LinearMap.range_zero",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Submodule.mem_bot._simp_1",
"Membership.mem",
"AddZeroClass.toAddZero",
"LinearMa... | true |
cfcHom_comp | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"StarAlgHom.toAlgHom",
"DFunLike.congr_fun",
"AlgHom.toMonoidHom'._proof_2",
"cfcHom_eq_of_continuous_of_map_id",
"cfcHom_continuous",
"spectrum",
"Ring.toNonAssocRing",
"congrArg",
"CommSemiring.toSemiring",
"IsTopologicalSemiring",
"HEq.refl",
"AlgHom",
"ContinuousStar",
"ContinuousMap",... | true |
CFC.abs_eq_zero_iff | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Abs | [
"Eq.mpr",
"IsSelfAdjoint",
"Real.partialOrder",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"instSMulOfMul",
"HMul.hMul",
"star_mul_self_nonneg._simp_1",
"NormedSpace",
"IsTopologicalRing.toIsTopologicalSemiring",
"congrArg",
"CFC.sqrt",
"DistribMulAction.t... | true |
Cardinal.continuum_ne_zero | Mathlib.SetTheory.Cardinal.Continuum | [
"Cardinal",
"PartialOrder.toPreorder",
"Ne",
"Cardinal.continuum_pos",
"LT.lt.ne'",
"Cardinal.continuum",
"Cardinal.partialOrder",
"Zero.toOfNat0",
"OfNat.ofNat",
"Cardinal.instZero"
] | true |
FreeAlgebra.instSemiring | Mathlib.Algebra.FreeAlgebra | [
"FreeAlgebra.instSemiring._proof_1",
"NonAssocSemiring.toAddCommMonoidWithOne",
"FreeAlgebra.instSemiring._proof_2",
"AddMonoid.toAddSemigroup",
"CommSemiring.toSemiring",
"FreeAlgebra.instSemiring._proof_8",
"FreeAlgebra.instSemiring._proof_10",
"AddMonoid.mk",
"FreeAlgebra.Pre.ofScalar",
"FreeAl... | true |
CategoryTheory.Limits.LimitPresentation.casesOn | Mathlib.CategoryTheory.Limits.Presentation | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.LimitPresentation",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.LimitPresentation.mk",
"CategoryTheory.Limits.IsLimit",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.F... | false |
Multiset.nodup_of_le | Mathlib.Data.Multiset.Defs | [
"Multiset.Nodup",
"Multiset.leInductionOn",
"PartialOrder.toPreorder",
"Preorder.toLE",
"List.Nodup.sublist",
"Multiset",
"LE.le",
"List",
"Multiset.instPartialOrder"
] | true |
Pi.normedAddGroup | Mathlib.Analysis.Normed.Group.Constructions | [
"SeminormedAddGroup.toNorm",
"SeminormedAddGroup.toAddGroup",
"NormedAddGroup.mk",
"Pi.normedAddGroup._proof_2",
"SeminormedAddGroup",
"NormedAddGroup.toSeminormedAddGroup",
"Fintype",
"SeminormedAddGroup.toPseudoMetricSpace",
"Pi.normedAddGroup._proof_1",
"Pi.seminormedAddGroup",
"MetricSpace.m... | true |
CFC.rpow_eq_rpow_prod | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic | [
"CFC.rpow_eq_rpow_prod._auto_1",
"IsSelfAdjoint",
"Real.partialOrder",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CFC.rpow_eq_rpow_prod._auto_3",
"instStarRingReal",
"Ring.toNonAssocRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"CommSemiring.toSemiring",
"PartialOrder.toPreo... | true |
Batteries.ByteSubarray.mk.injEq | Batteries.Data.ByteSlice | [
"Eq.propIntro",
"Batteries.ByteSubarray",
"Lean.injEq_helper",
"LE.le",
"instLENat",
"And",
"Nat",
"Batteries.ByteSubarray.mk",
"Eq.ndrec",
"Eq.refl",
"ByteArray",
"Eq",
"ByteArray.size",
"Batteries.ByteSubarray.mk.inj"
] | true |
AddSubsemigroup.gciMapComap.eq_1 | Mathlib.Algebra.Group.Subsemigroup.Operations | [
"GaloisConnection.toGaloisCoinsertion",
"AddHom",
"PartialOrder.toPreorder",
"AddSubsemigroup.comap",
"AddHom.funLike",
"AddSubsemigroup.instPartialOrder",
"AddSubsemigroup.gciMapComap._proof_1",
"AddSubsemigroup",
"Eq.refl",
"Function.Injective",
"Eq",
"DFunLike.coe",
"Add",
"AddSubsemigr... | true |
AddMonCat.instCategory | Mathlib.Algebra.Category.MonCat.Basic | [
"Quiver.mk",
"CategoryTheory.CategoryStruct.mk",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Category.mk",
"_private.Mathlib.Algebra.Category.MonCat.Basic.0.AddMonCat.Hom.mk",
"AddMonCat.Hom",
"AddMonoidHom.id",
"AddZeroClass.toAddZero",
"AddMonCat.str",
"AddMonCat",
"AddMonCat.Hom.hom'",
"Add... | true |
Matroid.Matroidᵣ.ofMatroid._flat_ctor | Mathlib.Combinatorics.Matroid.Minor.Restrict | [
"Matroid.Matroidᵣ",
"Matroid.Matroidᵣ.ofMatroid",
"Matroid"
] | false |
OrderIso.essSup_apply._auto_5 | Mathlib.MeasureTheory.Function.EssSup | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Stream'.get_interleave_right | Mathlib.Data.Stream.Init | [
"Stream'.interleave",
"HMul.hMul",
"Nat.brecOn",
"instMulNat",
"Stream'.get_interleave_right._f",
"instOfNatNat",
"Stream'",
"instHAdd",
"Stream'.get",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Eq",
"instHMul"
] | true |
«term_ᵒᵖ» | Mathlib.Data.Opposite | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
AddSubgroupClass.toAddGroup._proof_4 | Mathlib.Algebra.Group.Subgroup.Defs | [
"SetLike",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"instHSMul",
"Membership.mem",
"Subtype",
"AddSubgroupClass.instZSMul._proof_1",
"SubtractionMonoid.toSubNegZeroMonoid",
"Int",
"AddSubgroupClass.toNegMemClass",
"SubNegZeroMonoid.toNegZeroClass",
"Nat.cast",
"autoParam",
"Su... | false |
Std.DHashMap.Const.getKey?_unitOfList_of_mem | Std.Data.DHashMap.Lemmas | [
"List.Pairwise",
"Std.DHashMap.Const.unitOfList",
"Option.some",
"Membership.mem",
"Std.DHashMap.Internal.Raw₀.Const.getKey?_insertManyIfNewUnit_emptyWithCapacity_list_of_mem",
"LawfulHashable",
"Bool.true",
"List",
"BEq.beq",
"Unit",
"EquivBEq",
"List.instMembership",
"Std.DHashMap.getKey?"... | true |
UniformConvergenceCLM.piEquivL._proof_2 | Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM | [
"instHSMul",
"Pi.addCommMonoid",
"Pi.topologicalSpace",
"UniformConvergenceCLM.instAddCommGroup",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Pi.module",
"AddMonoid.toAddZeroClass",
"ContinuousLinearMap.pi",
"AddCommGroup.toAddGroup",
"RingHom",
"NormedField.toField",
... | false |
CategoryTheory.Comonad.coalgebraPreadditive_homGroup_zero_f | Mathlib.CategoryTheory.Preadditive.EilenbergMoore | [
"CategoryTheory.Comonad",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"CategoryTheory.Comonad.Coalgebra.Hom.f",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"CategoryTh... | true |
_private.Mathlib.Analysis.Normed.Field.Approximation.0.Polynomial.exists_roots_norm_sub_lt_of_norm_coeff_sub_lt._simp_1_7 | Mathlib.Analysis.Normed.Field.Approximation | [
"map_sub",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"SubtractionMonoid.toSubNegMonoid",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"SubtractionMonoid",
"SubNegMonoid.toAddMonoid",
"Eq.symm",
"Eq",
"DFunLike.coe"... | false |
Function.Injective.addGroupWithOne._proof_3 | Mathlib.Algebra.Ring.InjSurj | [
"instHSMul",
"AddGroupWithOne.toAddGroup",
"SMul",
"Function.swap",
"AddGroupWithOne.toAddMonoidWithOne",
"AddMonoid.toNSMul",
"AddGroup.toSubNegMonoid",
"Nat",
"AddGroupWithOne",
"HSMul.hSMul",
"AddMonoidWithOne.toAddMonoid",
"SubNegMonoid.toAddMonoid",
"Eq"
] | false |
CategoryTheory.Grp.instMonoidalCategory._proof_1 | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Grp.instMonoidalCategoryStruct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Mon.Hom.hom",
"CategoryTheory.Grp.instCategory",
"CategoryTheory.MonoidalCategory.tensorHom_def",
"CategoryTheory.... | false |
_private.Lean.Data.Options.0.Lean.getOptionDecl._sparseCasesOn_1 | Lean.Data.Options | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
Decidable.imp_or | Init.PropLemmas | [
"Eq.mpr",
"False",
"congrArg",
"true_or",
"Iff.rfl",
"Decidable",
"id",
"iff_false_intro",
"imp_iff_right",
"dite",
"false_imp_iff",
"Iff",
"True",
"propext",
"Or",
"Eq",
"Not"
] | true |
Module.End.genEigenspace_inf_le_add | Mathlib.LinearAlgebra.Eigenspace.Basic | [
"Module.End.instRing",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"CommRing",
"instHSMul",
"Nat.choose",
"Module.End.instMonoid",
"instSMulOfMul",
"Pi.addCommMonoid",
"instAddMonoidWithOneENat",
"HMul.hMul",
"SemilinearMapClass.distribMulActionSemiHomClass",
"AddMono... | true |
ProbabilityTheory.gaussianReal_map_div_const | Mathlib.Probability.Distributions.Gaussian.Real | [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real.instIsOrderedRing",
"Eq.mpr",
"NNReal.instCommSemiring",
"Real.partialOrder",
"Real.instLE",
"Real",
"DivInvMonoid.toInv",
"MeasureTheory.Measure",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsOrderedRing.toP... | true |
ProofWidgets.ExprWithCtx.noConfusionType | ProofWidgets.Compat | [
"Lean.Expr",
"Lean.Elab.ContextInfo",
"ProofWidgets.ExprWithCtx.casesOn",
"ProofWidgets.ExprWithCtx",
"Lean.LocalInstances",
"Eq",
"Lean.LocalContext"
] | false |
Real.one_lt_cosh | Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | [
"AddGroup.toSubtractionMonoid",
"Real",
"_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp.0.Real.one_lt_cosh._simp_1_1",
"Real.lattice",
"Real.instZero",
"abs",
"congrArg",
"Real.instLT",
"Eq.rec",
"Real.instAddGroup",
"Ne",
"SubtractionMonoid.toSubNegZeroMonoid",
"Real.cosh... | true |
Set.Ioo.coe_mul._simp_1 | Mathlib.Algebra.Order.Interval.Set.Instances | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Membership.mem",
"PartialOrder",
"Set.Elem",
"Set.Ioo.instMul",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"instDistribOfSemiring",
"AddMonoidWithOne.toOne",
"Distrib.toMul",
"Semiring"... | false |
Std.PRange.UpwardEnumerable.succMany_add | Init.Data.Range.Polymorphic.UpwardEnumerable | [
"Std.PRange.UpwardEnumerable",
"congrArg",
"Option.bind",
"Option.get.congr_simp",
"id",
"Std.PRange.UpwardEnumerable.succMany",
"Bool.true",
"instHAdd",
"Std.PRange.InfinitelyUpwardEnumerable",
"Std.PRange.UpwardEnumerable.succMany?",
"Option.get",
"HAdd.hAdd",
"Nat",
"Option.isSome_of_is... | true |
Set.not_isChain_of_chainHeight_lt_encard | Mathlib.Order.Height | [
"Set.chainHeight",
"le_refl",
"False",
"Set.encard",
"Preorder.toLT",
"instPreorderENat",
"id",
"HasSubset.Subset",
"lt_imp_lt_of_le_of_le",
"lt_self_iff_false",
"ENat",
"LT.lt",
"IsChain",
"Iff.mp",
"Set.encard_le_chainHeight_of_isChain",
"instLTENat",
"Not",
"Set.instHasSubset",
... | true |
CategoryTheory.GrothendieckTopology.Point.instLiftingFunctorOppositeSheafPresheafToSheafWPresheafFiberSheafFiber | Mathlib.CategoryTheory.Sites.Point.Skyscraper | [
"CategoryTheory.GrothendieckTopology.Point.presheafToSheafCompSheafFiberIso",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.GrothendieckTopology.Point",
"CategoryTheory.Limits.HasProducts",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.HasColimitsOfSize",
"CategoryTheory.presheafTo... | true |
CategoryTheory.MonoidalSingleObj.instMonoidalEndMonoidalStarEndMonoidalStarFunctor._proof_4 | Mathlib.CategoryTheory.Bicategory.SingleObj | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.instBicategoryMonoidalSingleObj",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalSingleObj.endMonoidalStarFunctor",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalSingleObj",
... | false |
_private.Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree.0.WeierstrassCurve.natDegree_coeff_preΨ' | Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | [
"WeierstrassCurve.coeff_Ψ₂Sq",
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"apply_ite₂",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Polynomial.instOne",
"CommRing",
"_private.Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree.0.WeierstrassCurve.expCoeff_rec",
"HMul.hMul",... | true |
_private.Lean.Message.0.Lean.errorNameOfKind?._sparseCasesOn_1 | Lean.Message | [
"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 |
Function.Odd | Mathlib.Algebra.Group.EvenFunction | [
"Neg",
"Eq",
"Neg.neg"
] | true |
_private.Mathlib.RingTheory.AdicCompletion.Exactness.0.AdicCompletion.map_surjective._simp_1_5 | Mathlib.RingTheory.AdicCompletion.Exactness | [
"Submodule",
"Submodule.Quotient.instZeroQuotient",
"AddCommGroup.toAddCommMonoid",
"Submodule.Quotient.mk",
"Submodule.hasQuotient",
"Membership.mem",
"AddCommGroup",
"HasQuotient.Quotient",
"Submodule.setLike",
"propext",
"Zero.toOfNat0",
"Module",
"OfNat.ofNat",
"Ring.toSemiring",
"Eq... | false |
Std.Internal.List.getKey?._unsafe_rec | Std.Data.Internal.List.Associative | [
"cond",
"Option.some",
"Option.none",
"List",
"BEq.beq",
"Unit",
"Std.Internal.List.getKey?._unsafe_rec",
"BEq",
"Sigma",
"Option",
"_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.getEntry?.match_1"
] | false |
AList.mem_union._simp_1 | Mathlib.Data.List.AList | [
"Membership.mem",
"AList.mem_union",
"AList",
"propext",
"Or",
"AList.instUnion",
"Union.union",
"AList.instMembership",
"Eq",
"DecidableEq"
] | false |
map_inv_natCast_smul | Mathlib.Algebra.Module.Basic | [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"inv_smul_smul₀",
"instHSMul",
"GroupWithZero.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"SMulWithZero.toSMulZeroClass",
"DistribMulAction.toDistribSMul",
"inv_zero",
"smul_inv_smul₀",
... | true |
_private.Lean.Linter.Omit.0.Lean.Linter.omit._sparseCasesOn_1 | Lean.Linter.Omit | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
_private.Lean.Meta.Sym.SymM.0.Lean.Meta.Sym.expandReportIssueMacro | Lean.Meta.Sym.SymM | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"String",
"Lean.SourceInfo",
"Lean.Syntax.node5",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr3",
"ReaderT.instMonad",
"Lean.TSyntax.... | true |
ContinuousAt.finInit | Mathlib.Topology.Constructions | [
"Pi.topologicalSpace",
"ContinuousAt",
"nhds",
"Filter.Tendsto.finInit",
"instOfNatNat",
"Fin.init",
"TopologicalSpace",
"instHAdd",
"ContinuousAt.tendsto",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Fin.castSucc",
"OfNat.ofNat",
"Fin"
] | true |
_private.Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat.0.SSet.instIsDiscreteHomotopyCategoryObjTruncatedOfNatNatTruncationSimplexCategoryStdSimplexMk._proof_1 | Mathlib.AlgebraicTopology.SimplicialSet.HomotopyCat | [
"SSet.OneTruncation₂",
"Opposite",
"CategoryTheory.Cat.FreeRefl.instCategory",
"SSet.instUniqueHomOneTruncation₂ObjTruncatedOfNatNatTruncationSimplexCategoryStdSimplexMk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"SSet.Truncated",
"SSet.truncation",
... | false |
FreeMonoid.mem_symbols | Mathlib.Algebra.FreeMonoid.Symbols | [
"List.mem_toFinset",
"FreeMonoid.instMembership",
"FreeMonoid",
"Finset",
"Membership.mem",
"Iff",
"Finset.instSetLike",
"FreeMonoid.symbols",
"SetLike.instMembership",
"DecidableEq"
] | true |
Lean.Parser.Tactic.matchAlts.parenthesizer | Lean.Parser.Tactic | [
"Lean.Parser.Term.matchAlts.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"Lean.Parser.Tactic.matchRhs.parenthesizer"
] | true |
CategoryTheory.Functor.flip₂₃._proof_4 | Mathlib.CategoryTheory.Functor.CurryingThree | [
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.flipFunctor",
"CategoryTheory.Functor.map",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"of_eq_true",
"... | false |
Matroid.restrict_contract_eq_contract_restrict | Mathlib.Combinatorics.Matroid.Minor.Contract | [
"Eq.mpr",
"congrArg",
"Set.union_eq_self_of_subset_right",
"Set.instUnion",
"id",
"Set.diff_union_self",
"HasSubset.Subset",
"SDiff.sdiff",
"True",
"Set.disjoint_sdiff_right",
"eq_self",
"of_eq_true",
"congrFun'",
"Matroid.contract_restrict_eq_restrict_contract",
"Union.union",
"Matroi... | true |
Lean.FileMap.noConfusionType | Lean.Data.Position | [
"String",
"Lean.FileMap",
"String.Pos.Raw",
"Array",
"Lean.FileMap.casesOn",
"Eq"
] | false |
AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection | Mathlib.Geometry.Euclidean.SignedDist | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Submodule",
"ContinuousAffineMap.instModuleOfSMulCommClassOfContinuousConstSMul",
"Real",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toMod... | true |
Lean.Parser.Category.translateReorder | Mathlib.Tactic.Translate.Reorder | [
"Lean.Parser.Category.mk",
"Lean.Parser.Category"
] | true |
Stream'.mem_append_stream_left._f | Mathlib.Data.Stream.Init | [
"Membership.mem",
"List.eq_or_mem_of_mem_cons",
"instOfNatNat",
"Stream'.mem_cons_of_mem",
"List.cons",
"Stream'",
"List",
"absurd",
"_private.Mathlib.Data.Stream.Init.0.Stream'.mem_append_stream_left.match_1_1",
"List.instMembership",
"Stream'.appendStream'",
"Stream'.instMembership",
"Stre... | false |
Lean.AttributeApplicationTime._sizeOf_1 | Lean.Attributes | [
"Lean.AttributeApplicationTime.rec",
"Lean.AttributeApplicationTime",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | false |
BoundedContinuousFunction.C | Mathlib.Topology.ContinuousMap.Bounded.Normed | [
"MulOne.toOne",
"RingHom.mk",
"NormedRing.toRing",
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"BoundedContinuousFunction.C._proof_3",
"CommSemiring.toSemiring",
"IsTopologicalSemiring.toContinuousMul",
"IsSemitopologicalRing.toIsSemitopologicalSemirin... | true |
_private.Mathlib.Data.Real.Basic.0.Real.neg | Mathlib.Data.Real.Basic | [
"Real",
"Real.wrapped._@.Mathlib.Data.Real.Basic.2451848184._hygCtx._hyg.8"
] | true |
NegMemClass.coe_neg | Mathlib.Algebra.Group.Subgroup.Defs | [
"SetLike",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Membership.mem",
"Subtype",
"SubtractionMonoid.toSubNegZeroMonoid",
"AddSubgroupClass.toNegMemClass",
"SubNegZeroMonoid.toNegZeroClass",
"AddGroup",
"AddGroup.toSubNegMonoid",
"AddSubgroupClass",
"Subtype.val",
"NegMemClass.ne... | true |
Pi.lex_le_iff_of_unique | Mathlib.Order.PiLex | [
"Eq.mpr",
"Inhabited.default",
"Preorder.toLT",
"Equiv.instEquivLike",
"_private.Mathlib.Order.PiLex.0.Pi.lex_le_iff_of_unique._simp_1_2",
"congrArg",
"Lex",
"LinearOrder",
"Unique",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"PartialOrder",
"DistribLattic... | true |
Std.DTreeMap.minKeyD_insertIfNew_of_isEmpty | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.isEmpty",
"Ord.mk",
"Ordering",
"Std.DTreeMap.inner",
"Std.DTreeMap.insertIfNew",
"Std.TransCmp",
"Bool.true",
"Std.DTreeMap.Internal.Impl.minKeyD_insertIfNew_of_isEmpty",
"Std.DTreeMap.wf",
"Bool",
"Std.DTreeMap.minKeyD",
"Eq"
] | true |
Int.natAbs_tmod | Init.Data.Int.DivMod.Lemmas | [
"Int.tmod",
"congrArg",
"Int.neg_tmod",
"id",
"Nat.instMod",
"instHMod",
"Int.instNegInt",
"Int.tmod_neg",
"Int",
"Nat.cast",
"iff_self",
"HMod.hMod",
"Iff",
"Nat",
"congr",
"True",
"Int.wlog_sign",
"Int.natAbs",
"of_eq_true",
"Eq.refl",
"congrFun'",
"instNatCastInt",
"In... | true |
DistLat.instCoeSortType | Mathlib.Order.Category.DistLat | [
"CoeSort.mk",
"CoeSort",
"DistLat.carrier",
"DistLat"
] | true |
Quiver.Hom.unop_op | Mathlib.CategoryTheory.Opposites | [
"Quiver.Hom",
"Quiver.Hom.op",
"Quiver.Hom.unop",
"Opposite.op",
"Quiver",
"Eq",
"Opposite.unop",
"rfl"
] | true |
CategoryTheory.Limits.BinaryCofan.IsColimit.unop._proof_4 | Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | [
"CategoryTheory.Limits.IsColimit.fac",
"CategoryTheory.Limits.BinaryCofan.inr",
"CategoryTheory.Functor",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.opposite",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Limits.BinaryFan... | false |
AlgebraicGeometry.LocallyRingedSpace.isUnit_res_toΓSpecMapBasicOpen | Mathlib.AlgebraicGeometry.GammaSpecAdjunction | [
"Monoid",
"CategoryTheory.Functor.op",
"AlgebraicGeometry.LocallyRingedSpace.toToΓSpecMapBasicOpen",
"Eq.mpr",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"Lattice.toSemilatticeSup",
"CommRingCat.Hom.hom",
"Opposite",
"AlgebraicGeometry.SheafedSpace",
"CommRingCat.carrier"... | true |
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