name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.mkAndN._sunfold | Lean.Expr | [
"Lean.Expr",
"Lean.Level",
"Lean.mkAndN",
"Lean.mkConst",
"List",
"Unit",
"Lean.mkAnd",
"Lean.Name.mkStr1",
"_private.Lean.Expr.0.Lean.mkAndN.match_1",
"List.nil"
] | false |
Int8.toInt.eq_1 | Init.Data.SInt.Lemmas | [
"Int8",
"Int8.toInt",
"instOfNatNat",
"Int",
"Nat",
"Int8.toBitVec",
"Eq.refl",
"BitVec.toInt",
"OfNat.ofNat",
"Eq"
] | true |
_private.Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms.0.SimplexCategoryGenRel.IsAdmissible.cons._proof_1_2 | Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms | [
"False",
"eq_false",
"Lean.Grind.iff_eq",
"SimplexCategoryGenRel.isAdmissible_singleton_iff",
"Classical.byContradiction",
"Eq.mp",
"id",
"LE.le",
"instLENat",
"List.cons",
"Iff",
"Nat",
"True",
"eq_true",
"SimplexCategoryGenRel.IsAdmissible",
"Eq.symm",
"Eq",
"Not",
"Eq.trans",
... | false |
_private.Mathlib.RingTheory.Coalgebra.CoassocSimps.0.CoassocSimps.«_aux_Mathlib_RingTheory_Coalgebra_CoassocSimps___delab_app__private_Mathlib_RingTheory_Coalgebra_CoassocSimps_0_CoassocSimps_termρ⁻¹_1» | Mathlib.RingTheory.Coalgebra.CoassocSimps | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Mathlib.Notation3.MatchState.empty",
"Mathlib.Notation3.withHeadRefIfTagAppFns",
"Mathlib.Notation3.matchApp",
"Lean.PrettyPrinter.Delaborator.instMonadReaderOfSubExprDelabM",
"Lean.SourceInfo",
"Lean.PrettyPrinter.Delaborator.Contex... | false |
CategoryTheory.ShortComplex.rightHomology_ext | Mathlib.Algebra.Homology.ShortComplex.RightHomology | [
"CategoryTheory.ShortComplex.opcycles",
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.ShortComplex.rightHomology",
"Quiver.Hom",
"_private.Mathlib.Algebra.Homology.ShortComplex.RightHomology.0.CategoryTheory.ShortComplex.rightHomology_ext._... | true |
seqCompactSpace_iff | Mathlib.Topology.Defs.Sequences | [
"Set.univ",
"SeqCompactSpace.casesOn",
"TopologicalSpace",
"Iff",
"SeqCompactSpace.mk",
"Iff.intro",
"SeqCompactSpace",
"IsSeqCompact"
] | true |
Lean.Meta.Grind.Arith.CommRing.DiseqCnstr.noConfusion | Lean.Meta.Tactic.Grind.Arith.CommRing.Types | [
"Lean.Meta.Grind.Arith.CommRing.SemiringExpr",
"Lean.Meta.Grind.Arith.CommRing.DiseqCnstr.casesOn",
"Lean.Expr",
"Lean.Meta.Grind.Arith.CommRing.PolyDerivation",
"Lean.Meta.Grind.Arith.CommRing.DiseqCnstr.noConfusionType",
"Lean.Meta.Grind.Arith.CommRing.RingExpr",
"Eq.ndrec",
"Eq.refl",
"Prod",
"... | false |
Lean.JsonRpc.instInhabitedMessageDirection | Lean.Data.JsonRpc | [
"Lean.JsonRpc.instInhabitedMessageDirection.default",
"Inhabited",
"Lean.JsonRpc.MessageDirection",
"Inhabited.mk"
] | true |
Real.HolderConjugate.div_conj_eq_sub_one | Mathlib.Data.Real.ConjExponents | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"AddGroup.toSubtractionMonoid",
"Mathlib.Tactic.FieldSimp.zpow'_one",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
... | true |
IntermediateField.relrank_dvd_of_le_left | Mathlib.FieldTheory.Relrank | [
"IntermediateField.instPartialOrder",
"Dvd.dvd",
"Cardinal",
"CommSemiring.toNonUnitalCommSemiring",
"IntermediateField",
"Cardinal.commSemiring",
"PartialOrder.toPreorder",
"semigroupDvd",
"NonUnitalCommSemiring.toCommSemigroup",
"dvd_of_mul_left_eq",
"Algebra",
"Preorder.toLE",
"SemigroupW... | true |
AffineMap.pi_ext_nonempty | Mathlib.LinearAlgebra.AffineSpace.AffineMap | [
"Eq.mpr",
"Inhabited.default",
"AffineMap.instFunLike",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Pi.single_zero",
"Finite",
"Pi.module",
"Lean.Elab.Tactic.nonempty_to_inhabited",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"id",
"addGroupIsAddTorsor",
"Pi.instZero",
"SubtractionMonoid... | true |
Std.DHashMap.Raw.Const.equiv_of_beq | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"congrArg",
"Std.DHashMap.Raw.Const.beq",
"Std.DHashMap.Raw",
"LawfulBEq",
"id",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"Std.DHashMap.Internal.Raw₀.Const.beq",
"Std.DHashMap.Raw.Equiv",
"Subtype.mk",
"Std.DHashMap.Internal.Raw.Const.beq_eq",
... | true |
RootPairing.rec | Mathlib.LinearAlgebra.RootSystem.Defs | [
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Equiv.instEquivLike",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass... | false |
MeasurableEquiv.prodCongr.eq_1 | Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace | [
"MeasurableEquiv.toEquiv",
"MeasurableEquiv.prodCongr._proof_2",
"MeasurableEquiv.prodCongr._proof_4",
"MeasurableEquiv.prodCongr",
"MeasurableSpace",
"MeasurableEquiv.mk",
"Eq.refl",
"Prod",
"Equiv.prodCongr",
"MeasurableEquiv",
"Eq",
"Prod.instMeasurableSpace"
] | true |
RingCon.instCompleteLattice._proof_2 | Mathlib.RingTheory.Congruence.Basic | [
"RingCon.toCon",
"HMul.hMul",
"Mul",
"RingCon",
"RingCon.mul",
"Setoid",
"And",
"And.right",
"Con.toSetoid",
"And.left",
"And.intro",
"Min.min",
"Add",
"Setoid.r",
"instHMul",
"Setoid.instMin_mathlib"
] | false |
SSet.IsStrictSegal.mk | Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | [
"SSet.Path",
"Opposite",
"SSet.IsStrictSegal.mk",
"SSet",
"SimplexCategory.mk",
"Opposite.op",
"Nat",
"CategoryTheory.types",
"SimplexCategory",
"Function.Bijective",
"CategoryTheory.Category.opposite",
"SSet.IsStrictSegal",
"SimplexCategory.smallCategory",
"SSet.spine",
"CategoryTheory.... | true |
SSet.StrictSegalCore.concat | Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.ConcreteCategory.hom",
"Quiver.Hom.op",
"TypeCat.instFunLikeFun",
"instOfNatNat",
"SSet",
"CategoryTheory.Functor.map",
"instHAdd",
"SimplexCategory.const",
"TypeCat.Fun",
"HAdd.hAdd",
"SimplexCategory.mk",
"Opposite.op"... | true |
Lean.PrettyPrinter.Delaborator.TopDownAnalyze.Context.rec | Lean.PrettyPrinter.Delaborator.TopDownAnalyze | [
"Lean.PrettyPrinter.Delaborator.TopDownAnalyze.Context",
"Bool",
"Lean.PrettyPrinter.Delaborator.TopDownAnalyze.Context.mk",
"Lean.SubExpr"
] | false |
_private.Mathlib.FieldTheory.KrullTopology.0.IntermediateField.map_fixingSubgroup._simp_1_1 | Mathlib.FieldTheory.KrullTopology | [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"Group",
"Membership.mem",
"DivInvMonoid.toMonoid",
"Subgroup",
"Subgroup.mem_comap",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"propext",
"Eq",
"DFunLike.coe",
"Subgroup.comap",
"SetLike.instMembership",
"Subgroup.ins... | false |
Aesop.Nanos.instDecidableRelLt | Aesop.Nanos | [
"Aesop.Nanos.mk",
"Aesop.Nanos",
"DecidableRel",
"Decidable",
"Aesop.Nanos.instDecidableRelLt.match_1",
"Nat",
"LT.lt",
"Nat.decLt",
"Aesop.Nanos.instLT"
] | true |
Equiv.boolEquivPUnitSumPUnit._proof_1 | Mathlib.Logic.Equiv.Sum | [
"Sum",
"Sum.inl",
"Bool.true",
"Bool.casesOn",
"Sum.inr",
"PUnit",
"Bool",
"Eq.ndrec",
"Eq.refl",
"PUnit.unit",
"Eq.symm",
"Bool.false",
"Eq",
"Sum.elim"
] | false |
Antivary.of_inv_right | Mathlib.Algebra.Order.Monovary | [
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Monovary",
"IsOrderedMonoid",
"Antivary",
"PartialOrder.toPreorder",
"Pi.instInv",
"DivisionMonoid.toDivInvOneMonoid",
"PartialOrder",
"CommGroup",
"CommGroup.toDivisionCommMonoid",
"Inv.inv",
"Iff.mp",
"InvOneClass.t... | true |
CategoryTheory.PreservesPullbacksOfInclusions.rec | Mathlib.CategoryTheory.Extensive | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.PreservesLimit",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limits.coprod.inl",
"CategoryTheory.Limits.WalkingPair",... | false |
_private.Mathlib.Analysis.Convex.Between.0.sbtw_neg_iff._simp_1_1 | Mathlib.Analysis.Convex.Between | [
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"SubNegMonoid",
"AddZeroClass.toAddZero",
"SubNegMonoid.toSub",
"AddZero.toZero",
"instHSub",
"SubNegMonoid.toNeg",
"Zero.toOfNat0",
"SubNegMonoid.toAddMonoid",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Neg.neg",
"zero_sub"
] | false |
RatFunc.liftRingHom_ofFractionRing_algebraMap | Mathlib.FieldTheory.RatFunc.Basic | [
"Eq.mpr",
"RingHom.instRingHomClass",
"MulOne.toOne",
"CommRing",
"Localization.mk",
"instHDiv",
"DivisionCommMonoid.toDivisionMonoid",
"Algebra.algebraMap",
"OreLocalization.instAlgebra",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"AddGroupWi... | true |
Std.Sat.AIG.mkGateCached.go._proof_1 | Std.Sat.AIG.Cached | [
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.Cache",
"Std.Sat.AIG.BinaryInput",
"instOfNatNat",
"Std.Sat.AIG.IsDAG",
"Array",
"GetElem.getElem",
"Std.Sat.AIG.BinaryInput.lhs",
"Std.Sat.AIG.Ref.hgate",
"Array.instGetElemNatLtSize",
"Nat",
"LT.lt",
"Std.Sat.AIG.Ref.gate",
"Hashable",
"instLTNat",
"S... | false |
List.card_toFinset | Mathlib.Data.Finset.Card | [
"List.dedup",
"List.toFinset",
"List",
"Nat",
"Finset.card",
"Eq",
"List.length",
"rfl",
"DecidableEq"
] | true |
WittVector.IsocrystalHom._sizeOf_1 | Mathlib.RingTheory.WittVector.Isocrystal | [
"WittVector.IsocrystalHom.rec",
"WittVector.IsocrystalHom",
"WittVector.Isocrystal",
"PerfectRing",
"CommRing",
"Nat.Prime",
"WittVector.FractionRing.frobenius",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"WittVector.instCommRing",
"Co... | false |
Std.Http.Method.rebind.sizeOf_spec | Std.Internal.Http.Data.Method | [
"Std.Http.Method",
"instOfNatNat",
"Std.Http.Method.rebind",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"Std.Http.Method._sizeOf_inst",
"OfNat.ofNat",
"Eq"
] | true |
Polynomial.Monic.eq_one_of_isUnit | Mathlib.Algebra.Polynomial.Monic | [
"Nontrivial",
"MulOne.toOne",
"Polynomial.instOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"Polynomial.Monic.natDegree_eq_zero",
"AddMonoid.toAddZeroClass",
"eq_iff_true_of_subsingleton._simp_1",
"IsUnit",
"Exists",
"AddZeroClass.toAddZero",
"Eq.mp",
"MulOne.toMul",
"right_ne_z... | true |
Matroid.emptyOn_isBase_iff._simp_1 | Mathlib.Combinatorics.Matroid.Constructions | [
"Matroid.IsBase",
"Matroid.emptyOn",
"Matroid.emptyOn_isBase_iff",
"propext",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Set"
] | false |
Lean.Meta.Grind.Arith.CommRing.EqCnstr.simplify | Lean.Meta.Tactic.Grind.Arith.CommRing.EqCnstr | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.Meta.Grind.GrindM",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.Grind.Arith.CommRing.EqCnstr.denoteExpr",
"Lean.indentD",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.Arith.CommRing.RingM",
"Lean.Met... | true |
cfc_star_id | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"Eq.mpr",
"Ring.toNonAssocRing",
"congrArg",
"CommSemiring.toSemiring",
"cfc",
"IsTopologicalSemiring",
"ContinuousStar",
"_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital.0._auto_374",
"cfc_id'",
"PseudoMetricSpace.toUniformSpace",
"Algebra",
"id",
"NonUnitalNonAss... | true |
_private.Mathlib.Order.RelSeries.0.RelSeries.append_assoc._simp_1_1 | Mathlib.Order.RelSeries | [
"instHAdd",
"HAdd.hAdd",
"Nat",
"propext",
"instAddNat",
"Eq",
"Nat.add_left_inj"
] | false |
Function.Surjective.distribMulActionLeft | Mathlib.Algebra.GroupWithZero.Action.End | [
"Monoid",
"instHSMul",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"DistribMulAction.toDistribSMul",
"Function.Surjective.distribMulActionLeft._proof_1",
"SMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"DistribMulAction.mk",
"Fun... | true |
CategoryTheory.StructuredArrow.map₂IsoPreEquivalenceInverseCompProj._proof_2 | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"Categor... | false |
WithTop.toDual_symm | Mathlib.Order.WithBot | [
"WithBot",
"WithTop.toDual",
"Equiv",
"WithBot.ofDual",
"OrderDual",
"Equiv.symm",
"Eq",
"rfl",
"WithTop"
] | true |
StarSubalgebra.topologicalClosure._proof_2 | Mathlib.Topology.Algebra.StarSubalgebra | [
"MulOne.toOne",
"StarSubalgebra.toSubalgebra",
"CommSemiring.toSemiring",
"Submonoid.toSubsemigroup",
"Algebra",
"Algebra.toSMul",
"Membership.mem",
"MulOne.toMul",
"Subalgebra.toSubsemiring",
"StarSubalgebra",
"NonAssocSemiring.toMulZeroOneClass",
"Subsemiring.toSubmonoid",
"StarAddMonoid.t... | false |
Digraph.mk.sizeOf_spec | Mathlib.Combinatorics.Digraph.Basic | [
"Digraph",
"Digraph.mk",
"instOfNatNat",
"Digraph._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"SizeOf",
"OfNat.ofNat",
"Eq"
] | true |
CategoryTheory.ShiftMkCore.assoc_hom_app._autoParam | Mathlib.CategoryTheory.Shift.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
SMulPosReflectLE.lift | Mathlib.Algebra.Order.Module.Defs | [
"instHSMul",
"Preorder.toLT",
"congrArg",
"SMulPosReflectLE.mk",
"SMul",
"Preorder.toLE",
"Eq.mp",
"LE.le",
"lt_iff_lt_of_le_iff_le'",
"Iff",
"le_of_smul_le_smul_right",
"congr",
"LT.lt",
"propext",
"Zero.toOfNat0",
"HSMul.hSMul",
"congrFun'",
"OfNat.ofNat",
"Eq.symm",
"Eq",
... | true |
Nat.smallSchroder | Mathlib.Combinatorics.Enumerative.Schroder | [
"Nat.largeSchroder",
"instHDiv",
"Nat.smallSchroder.match_1",
"HDiv.hDiv",
"instOfNatNat",
"Unit",
"Nat",
"Nat.instDiv",
"OfNat.ofNat"
] | true |
CategoryTheory.prod.leftUnitor_isEquivalence | Mathlib.CategoryTheory.Products.Unitor | [
"CategoryTheory.prod.leftUnitor",
"CategoryTheory.prod.leftUnitorEquivalence",
"CategoryTheory.Equivalence.isEquivalence_functor",
"CategoryTheory.discreteCategory",
"PUnit",
"CategoryTheory.prod'",
"CategoryTheory.Functor.IsEquivalence",
"Prod",
"CategoryTheory.Category",
"CategoryTheory.Discrete... | true |
εNFA.ctorIdx | Mathlib.Computability.EpsilonNFA | [
"Nat",
"εNFA"
] | false |
DirectSum.decompose_one | Mathlib.RingTheory.GradedAlgebra.Basic | [
"GradedRing.toGradedMonoid",
"SetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"SetLike.gOne",
"MulOne.toOne",
"DirectSum.decomposeRingEquiv",
"Equiv.instEquivLike",
"AddMonoid.toAddSemigroup",
"RingEquiv.instEquivLike",
"AddMonoid.toAddZeroClass",
"RingEquiv.instRingEquivClass",
"Membersh... | true |
Std.TreeMap.Raw.contains_map | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.contains",
"Std.TreeMap.Raw.WF.out",
"Ordering",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw.map",
"Std.TreeMap.Raw",
"Std.DTreeMap.Raw.contains_map",
"Bool",
"Eq"
] | true |
Lean.Meta.RecursorUnivLevelPos.ctorElim | Lean.Meta.RecursorInfo | [
"Lean.Meta.RecursorUnivLevelPos.motive",
"Lean.Meta.RecursorUnivLevelPos",
"Lean.Meta.RecursorUnivLevelPos.casesOn",
"Nat",
"Lean.Meta.RecursorUnivLevelPos.majorType",
"Eq.ndrec",
"Lean.Meta.RecursorUnivLevelPos.ctorIdx",
"PULift.down",
"Eq",
"Lean.Meta.RecursorUnivLevelPos.ctorElimType"
] | false |
Associated.dvd_iff_dvd_left | Mathlib.Algebra.GroupWithZero.Associated | [
"Monoid",
"Units.val",
"Dvd.dvd",
"HMul.hMul",
"Monoid.toMulOneClass",
"semigroupDvd",
"Units.mul_right_dvd",
"Units",
"Eq.rec",
"MulOne.toMul",
"_private.Mathlib.Algebra.GroupWithZero.Associated.0.Associated.dvd_iff_dvd_left.match_1_1",
"MulOneClass.toMulOne",
"Iff",
"Associated",
"Mono... | true |
hasStrictFDerivAt_zero | Mathlib.Analysis.Calculus.FDeriv.Const | [
"AddCommGroup.toAddCommMonoid",
"NormedField.toField",
"AddCommGroup",
"Pi.instZero",
"ContinuousLinearMap.zero",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Field.toSemifield",
"ContinuousLinearMap",
"TopologicalSpace"... | true |
_private.Std.Time.Format.Basic.0.Std.Time.GenericFormat.DateBuilder.m._default | Std.Time.Format.Basic | [
"id",
"Option.none",
"Std.Time.Minute.Ordinal",
"Option"
] | false |
_private.Mathlib.Order.Interval.Set.LinearOrder.0.Set.Ioc_union_Ioc_union_Ioc_cycle._proof_1_1 | Mathlib.Order.Interval.Set.LinearOrder | [
"instLawfulOrderLT_mathlib",
"Lean.Grind.of_eq_eq_true",
"Set.mem_union",
"Lean.Grind.eq_false_of_not_eq_true",
"Set.ext",
"Set.Ioc",
"of_eq_false",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Lean.Grind.not_not",
"eq_false",
"Lean.Grind.iff... | false |
Lean.Lsp.instToJsonDocumentChange.match_1 | Lean.Data.Lsp.Basic | [
"Lean.Lsp.DeleteFile",
"Lean.Lsp.DocumentChange.rename",
"Lean.Lsp.CreateFile",
"Lean.Lsp.RenameFile",
"Lean.Lsp.DocumentChange",
"Lean.Lsp.DocumentChange.edit",
"Lean.Lsp.DocumentChange.delete",
"Lean.Lsp.TextDocumentEdit",
"Lean.Lsp.DocumentChange.create",
"Lean.Lsp.DocumentChange.casesOn"
] | false |
Booleanisation.instSemilatticeInf._proof_3 | Mathlib.Order.Booleanisation | [
"Booleanisation.instInf",
"Iff.mpr",
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"Booleanisation",
"Preorder.toLE",
"Booleanisation.instSemilatticeInf.match_1",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"le_sdiff",
"SemilatticeInf.toMin",
"LE.le",
"Boo... | false |
Lean.AxiomVal.casesOn | Lean.Declaration | [
"Lean.ConstantVal",
"Lean.AxiomVal.mk",
"Lean.AxiomVal.rec",
"Bool",
"Lean.AxiomVal"
] | false |
Monoid.CoprodI.Word.consRecOn._proof_3 | Mathlib.GroupTheory.CoprodI | [
"List.head?",
"Monoid",
"Eq.mpr",
"Monoid.CoprodI.Word.fstIdx",
"MulOne.toOne",
"Monoid.CoprodI.Word.consRecOn._simp_5",
"Monoid.toMulOneClass",
"congrArg",
"Option.instMembership",
"Monoid.CoprodI.Word.consRecOn._proof_1",
"List.mem_cons_of_mem",
"Option.some",
"Membership.mem",
"Exists",... | false |
ChainComplex.toSingle₀Equiv._proof_6 | Mathlib.Algebra.Homology.Single | [
"CategoryTheory.Limits.HasZeroMorphisms",
"ChainComplex",
"HomologicalComplex.instCategory",
"ChainComplex.toSingle₀Equiv._proof_1",
"HomologicalComplex.mkHomToSingle",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HomologicalComp... | false |
_private.Std.Sat.CNF.RelabelFin.0.Std.Sat.CNF.Clause.of_maxLiteral_eq_some._simp_1_3 | Std.Sat.CNF.RelabelFin | [
"List.map",
"Membership.mem",
"Exists",
"List",
"And",
"List.instMembership",
"propext",
"List.mem_map",
"Eq"
] | false |
CategoryTheory.Quiv.equivOfIso._proof_2 | Mathlib.CategoryTheory.Category.Quiv | [
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.Quiv.str'",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso",
"CategoryTheory.Quiv.category",
"CategoryTheory.Bundled.α",
"CategoryTheory.Quiv",
"CategoryTheory.CategoryStruct.comp",
"Quiver",
"Prefunctor.congr_obj",
"CategoryTheory.Catego... | false |
Irrational.of_pow | Mathlib.NumberTheory.Real.Irrational | [
"Irrational.of_pow._f",
"Real",
"Nat.brecOn",
"Monoid.toPow",
"Real.instMonoid",
"Irrational",
"HPow.hPow",
"Nat",
"instHPow"
] | true |
Matrix.frobenius_norm_replicateCol | Mathlib.Analysis.Matrix.Normed | [
"WithLp",
"PiLp.instNorm",
"Norm.norm",
"Inhabited.default",
"Real.instPow",
"Real",
"DivInvMonoid.toInv",
"instHSMul",
"instHDiv",
"SeminormedAddCommGroup",
"Finset.univ",
"Real.instAddMonoid",
"congrArg",
"Matrix",
"Finset",
"Nat.instMonoid",
"Real.instDivInvMonoid",
"Unique",
... | true |
Algebra.leftMulMatrix_complex | Mathlib.RingTheory.Complex | [
"Complex.mul_im",
"Finsupp.instFunLike",
"Eq.mpr",
"Complex.instAlgebraOfReal",
"instNeZeroNatHAdd_1",
"Real",
"Fintype.elems",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Complex.mul_re",
"Semiring.toModule",
"Equiv.instEquivLike",
"Finsupp.module",
"HMul.hMul",
"CommRing.toNonUnita... | true |
NumberField.InfinitePlace.mult_isComplex | Mathlib.NumberTheory.NumberField.InfinitePlace.Basic | [
"Iff.mpr",
"Eq.mpr",
"congrArg",
"NumberField.InfinitePlace.IsComplex",
"NumberField.InfinitePlace.mult",
"Classical.propDecidable",
"id",
"Subtype",
"instOfNatNat",
"NumberField.InfinitePlace.IsReal",
"NumberField.InfinitePlace.mult.eq_1",
"Nat",
"Subtype.prop",
"NumberField.InfinitePlace... | true |
Std.HashSet.contains_toList | Std.Data.HashSet.Lemmas | [
"List.contains",
"Std.HashSet.toList",
"Std.HashSet",
"LawfulHashable",
"Unit",
"EquivBEq",
"Std.HashSet.inner",
"Std.HashSet.contains",
"Std.HashMap.contains_keys",
"Bool",
"Hashable",
"BEq",
"Eq"
] | true |
_private.Mathlib.Topology.Baire.Lemmas.0.dense_of_mem_residual.match_1_1 | Mathlib.Topology.Baire.Lemmas | [
"Exists",
"Dense",
"HasSubset.Subset",
"And.casesOn",
"TopologicalSpace",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"IsGδ",
"Set.instHasSubset",
"Set"
] | false |
Ideal.Quotient.ring._aux_23 | Mathlib.RingTheory.Ideal.Quotient.Defs | [
"Int.cast",
"AddMonoid.toAddSemigroup",
"AddGroupWithOne.toAddMonoidWithOne",
"RingCon.toQuotient",
"Ideal.IsTwoSided",
"Int",
"AddGroupWithOne.toIntCast",
"Ideal",
"instDistribOfSemiring",
"HasQuotient.Quotient",
"AddSemigroup.toAdd",
"Distrib.toMul",
"Ideal.instHasQuotient",
"Ideal.Quoti... | false |
String.Pos.Raw.isValidUTF8_extract_iff | Init.Data.String.Basic | [
"Iff.mpr",
"Eq.mpr",
"String.instLTRaw",
"_private.Init.Data.String.Basic.0.String.Pos.Raw.isValidUTF8_extract_iff.match_1_7",
"String.Pos.Raw.IsValid.isValidUTF8_extract_zero",
"trivial",
"ByteArray.IsValidUTF8.append",
"congrArg",
"String",
"Std.IsLinearPreorder.toIsPreorder",
"ByteArray.IsVal... | true |
MeasureTheory.Measure.LebesgueDecomposition.zero_mem_measurableLE | Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | [
"ENNReal.instCanonicallyOrderedAdd",
"MeasureTheory.lintegral_const",
"MeasureTheory.Measure",
"HMul.hMul",
"MeasurableSet",
"congrArg",
"CommSemiring.toSemiring",
"instIsBotZeroClass",
"zero_le._simp_1",
"Set.univ",
"MulZeroClass.zero_mul",
"AddMonoid.toAddZeroClass",
"Measurable",
"Measu... | true |
_private.Mathlib.Tactic.Translate.TagUnfoldBoundary.0.Mathlib.Tactic.Translate.CastKind | Mathlib.Tactic.Translate.TagUnfoldBoundary | [
"_private.Mathlib.Tactic.Translate.TagUnfoldBoundary.0.Mathlib.Tactic.Translate.CastKind.refoldFun",
"_private.Mathlib.Tactic.Translate.TagUnfoldBoundary.0.Mathlib.Tactic.Translate.CastKind.eq",
"_private.Mathlib.Tactic.Translate.TagUnfoldBoundary.0.Mathlib.Tactic.Translate.CastKind.unfoldFun"
] | true |
MvPolynomial.homEquiv._proof_1 | Mathlib.Algebra.MvPolynomial.CommRing | [
"Finsupp.instAddZeroClass",
"Nat.instMulZeroClass",
"CommRing",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"MvPolynomial.X",
"Nat.instAddMonoid",
"RingHom",
"MvPolynomial.eval₂_X",
"Function.comp",
"MvPolynomial.eval₂Hom",
"Int",
"CommRing.toNonAssocCommRing",
"Co... | false |
LawfulMonadStateOf.get_bind_map_set | Batteries.Control.LawfulMonadState | [
"Pure.pure",
"LawfulMonadStateOf",
"MonadStateOf",
"congrArg",
"Monad.toApplicative",
"MonadState.get",
"LawfulMonadStateOf.toLawfulMonad",
"Applicative.toPure",
"funext",
"PUnit",
"True",
"eq_self",
"instMonadStateOfMonadStateOf",
"of_eq_true",
"Applicative.toFunctor",
"Monad.toBind",... | true |
ergodic_vadd_of_denseRange_nsmul | Mathlib.Dynamics.Ergodic.Action.OfMinimal | [
"Iff.mpr",
"Eq.mpr",
"Ergodic",
"instHSMul",
"MeasureTheory.Measure",
"MeasurableSet",
"AddMonoid.toAddSemigroup",
"R1Space",
"congrArg",
"MeasurableVAdd.toMeasurableConstVAdd",
"Ergodic.mk",
"MeasurableSet.nullMeasurableSet",
"ErgodicVAdd.toVAddInvariantMeasure",
"MeasureTheory.measurePre... | true |
FiniteField.frobeniusAlgEquivOfAlgebraic | Mathlib.FieldTheory.Finite.Basic | [
"MulEquiv.instEquivLike",
"Monoid.toMulOneClass",
"AlgHom",
"Algebra",
"Field.toDivisionRing",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"DivisionRing.toRing",
"Algebra.IsAlgebraic",
"AlgHom.End",
"Field.toSemifield",
"Field.toCommRing",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Co... | true |
List.rtakeWhile_concat | Mathlib.Data.List.DropRight | [
"Eq.mpr",
"congrArg",
"List.filter.match_1",
"id",
"instDecidableEqBool",
"if_pos",
"List.reverse_singleton",
"dite",
"List.cons",
"Bool.true",
"List.reverse_cons",
"instHAppendOfAppend",
"List",
"Unit",
"congr",
"True",
"Bool.of_not_eq_true",
"eq_self",
"List.reverse",
"Bool",... | true |
Module.Basis.ofIsCoprimeDifferentIdeal | Mathlib.RingTheory.DedekindDomain.LinearDisjoint | [
"Submodule",
"IsIntegralClosure",
"IsDomain",
"IntermediateField.isScalarTower_mid'",
"FractionRing.field",
"IsDedekindDomain.toIsDomain",
"CommRing",
"Lattice.toSemilatticeSup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraM... | true |
CategoryTheory.MonoidalCategory.DayFunctor.equiv._proof_1 | Mathlib.CategoryTheory.Monoidal.DayConvolution.DayFunctor | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.MonoidalCategory.DayFunctor.instCategory",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"id",
"CategoryTheory.MonoidalCategory.DayFunctor",
... | false |
OreLocalization.instMonoidWithZero._proof_2 | Mathlib.RingTheory.OreLocalization.Basic | [
"Eq.mpr",
"Semigroup.toMul",
"HMul.hMul",
"MulZeroClass.toMul",
"Monoid.toMulOneClass",
"congrArg",
"OreLocalization.OreSet",
"OreLocalization",
"OreLocalization.ind",
"OreLocalization.mul_div_one",
"Membership.mem",
"id",
"MulOne.toMul",
"Subtype",
"MulZeroClass.mul_zero",
"MulZeroOne... | false |
Lean.Elab.HeaderProcessedSnapshot.mk.sizeOf_spec | Lean.Elab.DefView | [
"Lean.Elab.DefViewElabHeaderData._sizeOf_inst",
"Lean.Elab.BodyProcessedSnapshot",
"Option._sizeOf_inst",
"Lean.Language.SnapshotTree",
"Lean.Elab.Tactic.TacticParsedSnapshot._sizeOf_inst",
"Lean.Syntax._sizeOf_inst",
"Lean.Elab.BodyProcessedSnapshot._sizeOf_inst",
"Lean.Syntax",
"Lean.Elab.Tactic.T... | true |
String.Slice.Pattern.Model.NoSuffixPatternModel | Init.Data.String.Lemmas.Pattern.Basic | [
"String.Slice.Pattern.Model.NoSuffixPatternModel.mk",
"String.Slice.Pattern.Model.PatternModel"
] | true |
CliffordAlgebra.foldr'Aux._proof_1 | Mathlib.LinearAlgebra.CliffordAlgebra.Fold | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"instAlgebraCliffordAlgebra",
"QuadraticForm",
"AddCommGroup",
"Algebra.toModule",
"smulCommClass_self",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"CommRing.toCommSemiring",
"CommMonoid.toMonoid",
"N... | false |
_private.Init.Data.Dyadic.Basic.0.Rat.toDyadic.match_1.splitter | Init.Data.Dyadic.Basic | [
"Rat.toDyadic.match_1",
"Int.ofNat",
"Int",
"Nat",
"Int.negSucc"
] | true |
BitVec.reduceDiv | Lean.Meta.Tactic.Simp.BuiltinSimprocs.BitVec | [
"instHDiv",
"BitVec",
"HDiv.hDiv",
"BitVec.reduceBin",
"instOfNatNat",
"BitVec.instDiv",
"Nat",
"Lean.Meta.Simp.DSimproc",
"Lean.Name.mkStr2",
"OfNat.ofNat"
] | true |
Std.Iter.toArray.eq_1 | Init.Data.Iterators.Lemmas.Combinators.FlatMap | [
"Std.IterM.toArray",
"Id.run",
"Std.Iter.toIterM",
"Id",
"Std.Iter.toArray",
"Std.Iterator",
"Array",
"Std.Iter",
"Eq.refl",
"Id.instMonad",
"Eq"
] | true |
Nat.minFac_eq | Mathlib.Data.Nat.Prime.Defs | [
"Dvd.dvd",
"Nat.decidable_dvd",
"Nat.minFac",
"instOfNatNat",
"Nat.minFacAux",
"Nat.instDvd",
"Nat",
"OfNat.ofNat",
"Eq",
"rfl",
"ite"
] | true |
_private.Init.Data.BitVec.Lemmas.0.BitVec.toInt_ushiftRight_of_lt._proof_1_5 | Init.Data.BitVec.Lemmas | [
"instPowNat",
"Nat.lt_of_not_le",
"Int.instDiv",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"instHDiv",
"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.ofNat_sub_dich... | false |
Real.iteratedDerivWithin_cos_Icc | Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | [
"uniqueDiffOn_Icc",
"Real",
"ENat.instNatCast",
"Real.denselyNormedField",
"Real.cos",
"iteratedDerivWithin",
"iteratedDerivWithin_eq_iteratedDeriv",
"Real.instLT",
"Membership.mem",
"Real.normedAddCommGroup",
"Nat.cast",
"Real.contDiff_cos",
"Set.Icc",
"Nat",
"ENat",
"LT.lt",
"WithT... | true |
Algebra.Generators.Hom.mk.inj | Mathlib.RingTheory.Extension.Generators | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Algebra.Generators.Ring",
"MvPolynomial.aeval",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoidAlgebra.algebra",
"Finsupp.instAddMonoid",
"Algebra",
"Nat.instAddMonoid",
"RingHom",
"... | true |
Lean.PrettyPrinter.Parenthesizer.categoryParser.parenthesizer.match_1 | Lean.PrettyPrinter.Parenthesizer | [
"Lean.PrettyPrinter.Parenthesizer.categoryParser.parenthesizer._sparseCasesOn_1",
"Nat.hasNotBit",
"Lean.PrettyPrinter.CategoryParenthesizer",
"List.cons",
"List",
"List.ctorIdx"
] | false |
Lean.Meta.Grind.propagateDIte | Lean.Meta.Tactic.Grind.Propagate | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Simp.Result.getProof",
"Unit.unit",
"Lean.Meta.Grind.Goal",
"StateRefT'.instAlternativeOfMonad",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.Simp.Result.expr",
"Lean.Meta.State",
"Lean.Meta.Grind.Propagator",
"instMonadLiftT",
"Lean.Meta.S... | true |
CategoryTheory.Bicategory.whiskerLeft_hom_inv_whiskerRight_assoc | Mathlib.CategoryTheory.Bicategory.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"Eq.mp",
"CategoryTheory.Bicategory.whiskerRight",
"id",
"CategoryTheory.Iso",
"CategoryTheory.Bicategory.toCategoryStruct",
"Mathlib.Tactic.Reassoc.eq_whisker... | true |
IsTensorProduct.equiv_apply | Mathlib.RingTheory.IsTensorProduct | [
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"LinearMap.instFunLike",
"IsTensorProduct.equiv",
"LinearMap.module",
"LinearMap",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
"IsTensorProduct",
"CommMonoid.toMonoid",
"RingHomInvPair.ids",
"LinearMap.addCommMonoid",
"Co... | true |
Lean.Elab.Term.Do.ToTerm.Context.mk.injEq | Lean.Elab.Do.Legacy | [
"Eq.propIntro",
"Lean.injEq_helper",
"Lean.Syntax",
"Lean.Elab.Term.Do.Var",
"Lean.Elab.Term.Do.ToTerm.Context.mk",
"Array",
"Lean.Elab.Term.Do.ToTerm.Context",
"And",
"Eq.ndrec",
"Eq.refl",
"Lean.Elab.Term.Do.ToTerm.Kind",
"Eq",
"Lean.Elab.Term.Do.ToTerm.Context.mk.inj"
] | true |
_private.Mathlib.InformationTheory.KullbackLeibler.Basic.0.InformationTheory.toReal_klDiv_smul_right._simp_1_4 | Mathlib.InformationTheory.KullbackLeibler.Basic | [
"False",
"eq_false",
"four_ne_zero",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
SemiNormedGrp.instCoeSortType | Mathlib.Analysis.Normed.Group.SemiNormedGrp | [
"SemiNormedGrp.carrier",
"CoeSort.mk",
"CoeSort",
"SemiNormedGrp"
] | true |
Mathlib.Meta.NormNum.isInt_add | Mathlib.Tactic.NormNum.Basic | [
"Int.cast",
"AddMonoid.toAddSemigroup",
"AddGroupWithOne.toAddMonoidWithOne",
"Int.cast_add",
"Distrib.toAdd",
"Int",
"AddGroupWithOne.toIntCast",
"instDistribOfSemiring",
"instHAdd",
"AddSemigroup.toAdd",
"Mathlib.Meta.NormNum.IsInt.mk",
"HAdd.hAdd",
"_private.Mathlib.Tactic.NormNum.Basic.0... | true |
_private.Mathlib.Topology.LocallyFinite.0.LocallyFinite.comp_injOn.match_1_1 | Mathlib.Topology.LocallyFinite | [
"Filter.instMembership",
"setOf",
"Set.Finite",
"Membership.mem",
"Exists",
"nhds",
"Set.instInter",
"Inter.inter",
"And.casesOn",
"TopologicalSpace",
"And",
"Set.Nonempty",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"Filter",
"Set"
] | false |
_private.Mathlib.Order.Cover.0.Pi.covBy_iff_exists_left_eq._simp_1_2 | Mathlib.Order.Cover | [
"eq_comm",
"propext",
"Eq"
] | false |
ZNum.pred | Mathlib.Data.Num.Basic | [
"PosNum.pred'",
"instOnePosNum",
"Num.toZNum",
"PosNum.succ",
"ZNum",
"Unit",
"One.toOfNat1",
"ZNum.zNeg.match_1",
"PosNum",
"ZNum.neg",
"OfNat.ofNat"
] | true |
MeasureTheory.Measure.addHaarMeasure_eq_iff | Mathlib.MeasureTheory.Measure.Haar.Basic | [
"Eq.mpr",
"MulOne.toOne",
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"IsScalarTower.right",
"TopologicalSpace.PositiveCompacts.instSetLike",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"SecondCountableTopology",
"MeasureTheory.SigmaFinite",
"AddMonoid.toAddZero... | true |
Composition.ones | Mathlib.Combinatorics.Enumerative.Composition | [
"List.replicate",
"Composition.mk",
"Membership.mem",
"instOfNatNat",
"Composition",
"List",
"Composition.ones._proof_2",
"List.instMembership",
"Nat",
"OfNat.ofNat",
"Composition.ones._proof_1"
] | true |
TopologicalSpace.Closeds.complOrderIso | Mathlib.Topology.Sets.Closeds | [
"OrderDual.instLE",
"OrderDual.toDual",
"TopologicalSpace.Closeds.complOrderIso._proof_2",
"Equiv.instEquivLike",
"RelIso.mk",
"OrderDual.ofDual",
"TopologicalSpace.Opens.instPartialOrder",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"Preorder.toLE",
"Function.comp",
"Equiv.mk",
"Eq... | true |
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