name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Analysis.CStarAlgebra.Unitary.Connected.0.expUnitary_argSelfAdjoint._simp_1_1 | Mathlib.Analysis.CStarAlgebra.Unitary.Connected | [
"NormedCommRing.toSeminormedCommRing",
"Complex.exp_eq_exp_ℂ",
"NormedSpace.exp",
"Complex.instNormedField",
"IsTopologicalDivisionRing.toIsTopologicalRing",
"PseudoMetricSpace.toUniformSpace",
"NormedDivisionRing.toDivisionRing",
"NormedField.toNormedDivisionRing",
"Complex.exp",
"SeminormedCommR... | false |
Lean.Parser.instCoeParserParserAliasValue | Lean.Parser.Extension | [
"Lean.Parser.ParserAliasValue",
"Lean.Parser.Parser",
"Coe.mk",
"Lean.Parser.AliasValue.const",
"Coe"
] | true |
OpenPartialHomeomorph.trans._proof_2 | Mathlib.Topology.OpenPartialHomeomorph.Composition | [
"OpenPartialHomeomorph.open_source",
"congrArg",
"PartialEquiv.target",
"OpenPartialHomeomorph.restrOpen",
"Set.instInter",
"Inter.inter",
"Set.inter_comm",
"TopologicalSpace",
"True",
"eq_self",
"of_eq_true",
"PartialEquiv.source",
"congrFun'",
"OpenPartialHomeomorph.open_target",
"Open... | false |
isClosed_sUnion | Mathlib.Topology.AlexandrovDiscrete | [
"Set.sUnion",
"alexandrovDiscrete_iff_isClosed",
"Membership.mem",
"inferInstance",
"IsClosed",
"TopologicalSpace",
"AlexandrovDiscrete",
"Iff.mp",
"Set.instMembership",
"Set"
] | true |
CategoryTheory.Functor.whiskeringRight._proof_6 | Mathlib.CategoryTheory.Whiskering | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.whiskeringRight._proof_4",
"CategoryTheory.Functor.whiskeringRight._proof_5",
"CategoryTheory.Functor.mk",
"CategoryTheory.Functor.categor... | false |
String.Slice.Pattern.Model.Char.isLongestMatch_iff | Init.Data.String.Lemmas.Pattern.Char | [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"String.Slice",
"Exists",
"id",
"String.Slice.Pos.next",
"Ne",
"String.Slice.startPos",
"String.Slice.endPos",
"And",
"Iff",
"String.Slice.Pattern.Model.isLongestMatch_iff_isMatch",
"String.Slice.Pattern.Model.IsLongestMatch",
"propext",
"String.Slice.P... | true |
Std.Sat.AIG.RefVec.map.go_decl_eq._unary | Std.Sat.AIG.RefVecOperator.Map | [
"Std.Sat.AIG.RefVec.get",
"Eq.mpr",
"Lean.Omega.LinearCombo.coordinate_eval_6",
"Std.Sat.AIG.Entrypoint.aig",
"Std.Sat.AIG.Decl",
"False",
"Decidable.casesOn",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Std.Sat.AIG.RefVec.map._proof_2",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le... | false |
BooleanSubalgebra.rec | Mathlib.Order.BooleanSubalgebra | [
"Sublattice",
"BooleanAlgebra",
"BooleanSubalgebra",
"Compl.compl",
"Sublattice.carrier",
"Membership.mem",
"BooleanAlgebra.toCompl",
"Bot.bot",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanSubalgebra.mk",
"BooleanAlgebra.toBiheytingAlgebra",
"CoheytingAlgebra.toGeneralizedCoheytingAlgebra",... | false |
Nat.log_monotone | Mathlib.Data.Nat.Log | [
"Eq.mpr",
"Nat.zero_le",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"Monotone",
"Preorder.toLE",
"id",
"instOfNatNat",
"LE.le",
"Or.casesOn",
"Nat.le_log_of_pow_le",
"instHAdd",
"le_or_gt",
"HAdd.hAdd",
"Nat.instPreorder",
"Nat",
"LT.lt",
"Nat.log_of_left_le_one",
... | true |
Lean.Lsp.instFromJsonSemanticTokenModifier | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.instFromJsonSemanticTokenModifier.fromJson",
"Lean.Lsp.SemanticTokenModifier",
"Lean.FromJson",
"Lean.FromJson.mk"
] | true |
StarMulEquiv.ext_iff | Mathlib.Algebra.Star.MonoidHom | [
"StarMulEquiv",
"HEq.refl",
"Mul",
"Eq.casesOn",
"StarMulEquiv.instEquivLike",
"Iff",
"StarMulEquiv.ext",
"Star",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
Qq.QuotedDefEq | Qq.Typ | [
"Lean.Expr.sort",
"Lean.Level",
"Qq.Quoted",
"Qq.QuotedDefEq.unsafeIntro"
] | true |
gc_sdiff_sup | Mathlib.Order.Heyting.Basic | [
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"GeneralizedCoheytingAlgebra",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"SDiff.sdiff",
"Max.max",
"GeneralizedCoheytingAlgebra.toLattice",
"sdiff_le_iff",
"GeneralizedCoheytingAlgebra.toSDiff",
"Lattice.toSemilatticeInf",
"... | true |
intervalIntegral.norm_integral_min_max | Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic | [
"Norm.norm",
"SeminormedAddGroup.toNorm",
"NegZeroClass.toNeg",
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"congrArg",
"inf_of_le_left",
"Real.instSemilatticeSup",
"PartialOrder.toPreorder",
"intervalIntegral",
"Preorder.toLE",
"inf_of_le_right",
"SubtractionMonoid.toSubNegZeroMonoid"... | true |
MvPolynomial.IsWeightedHomogeneous | Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous | [
"Finsupp.instAddZeroClass",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"Finsupp.weight",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"AddZeroClass.toAddZero",
"Ne",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddCommM... | true |
Behrend.ceil_lt_mul | Mathlib.Combinatorics.Additive.AP.Three.Behrend | [
"NormedCommRing.toNormedRing",
"Int.cast",
"Real.instNNRatCast",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real.instLE",
"Real",
"NNRatCast.toOfScientific",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Mathlib.Meta.NormNum.IsNat.to_isNNRat",
... | true |
_private.Mathlib.Data.List.Defs.0.List.length_mapAccumr.match_1_1 | Mathlib.Data.List.Defs | [
"List.cons",
"List",
"List.casesOn",
"Prod",
"List.nil"
] | false |
Lean.Doc.CodeBlockSuggestion.casesOn | Lean.Elab.DocString | [
"String",
"Lean.Doc.CodeBlockSuggestion.mk",
"Lean.Doc.CodeBlockSuggestion.rec",
"Lean.Doc.CodeBlockSuggestion",
"Lean.Name",
"Option"
] | false |
_private.Lean.Elab.Match.0.Lean.Elab.Term.elabNoMatch.loop._sunfold | Lean.Elab.Match | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Array.push",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.SourceInfo",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.MonadQuotation.toMonadRef",
"... | false |
PowerSeries.hasEvalIdeal.eq_1 | Mathlib.RingTheory.PowerSeries.Evaluation | [
"PowerSeries.hasEvalIdeal._proof_1",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"PowerSeries.HasEval.mul_left",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"PowerSeries.HasEval.zero",
"AddMonoid.toAddZeroClass",
"setOf",
"AddZeroClass.toAddZe... | true |
CategoryTheory.ObjectProperty.limitsClosure_top | Mathlib.CategoryTheory.ObjectProperty.LimitsClosure | [
"CategoryTheory.ObjectProperty.instIsClosedUnderLimitsOfShapeTop",
"CategoryTheory.ObjectProperty.limitsClosure",
"CategoryTheory.ObjectProperty.limitsClosure_eq_self",
"BooleanAlgebra.toTop",
"CategoryTheory.ObjectProperty.instIsClosedUnderIsomorphismsTop",
"CategoryTheory.Category.toCategoryStruct",
"... | true |
Mathlib.Tactic.Order.ToInt.toInt_nlt_toInt | Mathlib.Tactic.Order.ToInt | [
"Eq.mpr",
"Preorder.toLT",
"Mathlib.Tactic.Order.ToInt.toInt_le_toInt",
"congrArg",
"Int.instLinearOrder",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"id",
"Int",
"LE.le",
"Int.instLTInt",
"not_lt._simp_1",
"I... | true |
Rep.quotientToInvariantsFunctor._proof_4 | Mathlib.RepresentationTheory.Invariants | [
"Rep.invariantsFunctor",
"Submodule",
"Rep.V",
"Representation.invariantsEquivIntertwiningMap._proof_10",
"CommRing",
"Representation",
"MonoidHom.instFunLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AddCommGro... | false |
BitVec.getLsbD_reverse | Init.Data.BitVec.Lemmas | [
"Eq.mpr",
"BitVec.setWidth",
"Nat.recAux",
"instDecidableTrue",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.getLsbD_reverse._simp_1_4",
"BitVec.getMsbD",
"congrArg",
"BitVec.getLsbD_of_ge",
"Decidable.decide.congr_simp",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.getLsbD_reverse._proof_1_5",
"HSu... | true |
IsSymmetricAlgebra.lift_eq | Mathlib.LinearAlgebra.SymmetricAlgebra.Basic | [
"SymmetricAlgebra.lift_ι_apply",
"TensorAlgebra.SymRel",
"Equiv.instEquivLike",
"AlgEquiv.symm",
"SymmetricAlgebra",
"congrArg",
"IsSymmetricAlgebra.lift",
"CommSemiring.toSemiring",
"AlgHom",
"IsSymmetricAlgebra",
"AlgHom.funLike",
"LinearMap.instFunLike",
"Algebra",
"SymmetricAlgebra.lif... | true |
HahnSeries.instLinearOrderLex | Mathlib.RingTheory.HahnSeries.Lex | [
"HahnSeries.instLinearOrderLex._proof_2",
"Preorder.toLT",
"Max.mk",
"Lex",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ord.mk",
"Min.mk",
"HahnSeries.instLinearOrderLex._proof_3",
"SemilatticeInf.toPartialOrder",
"decidableEqOfDecidableLE",
"DistribLattice.toLattice",
"Hah... | true |
LinearIsometryEquiv._sizeOf_inst | Mathlib.Analysis.Normed.Operator.LinearIsometry | [
"SeminormedAddCommGroup",
"AddCommGroup.toAddCommMonoid",
"RingHom",
"RingHomInvPair",
"SeminormedAddCommGroup.toAddCommGroup",
"SizeOf.mk",
"LinearIsometryEquiv",
"Semiring",
"SizeOf",
"Module",
"Semiring.toNonAssocSemiring",
"LinearIsometryEquiv._sizeOf_1"
] | false |
_private.Mathlib.Algebra.BigOperators.Intervals.0.Fin.sum_Icc_sub._proof_1_11 | Mathlib.Algebra.BigOperators.Intervals | [
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Int.Linear.norm_le",
"Lean.Grind.CommRing.Expr.var",
"Lean.Grind.ToInt.toInt",
"Lean.Grind.Order.le_eq_true_of_le_k",
"PartialOrder.toPreorder",
"Nat.ToInt.add_c... | false |
MulOpposite.op_le_op._simp_2 | Mathlib.Algebra.Order.Group.Opposite | [
"MulOpposite",
"Preorder.toLE",
"LE.le",
"MulOpposite.op_le_op",
"propext",
"MulOpposite.instPreorder",
"Eq",
"Preorder",
"MulOpposite.op"
] | false |
Lean.Parser.Term.showTermElabImpl._regBuiltin.Lean.Parser.Term.showTermElabImpl.formatter_9 | Lean.Parser.Term | [
"Lean.PrettyPrinter.Formatter",
"Lean.Name.mkStr5",
"IO",
"Unit",
"Lean.Parser.Term.showTermElabImpl.formatter",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
Std.TreeSet._sizeOf_inst | Std.Data.TreeSet.Basic | [
"Std.TreeSet",
"Ordering",
"Std.TreeSet._auto_1",
"Std.TreeSet._sizeOf_1",
"autoParam",
"SizeOf.mk",
"SizeOf"
] | false |
ContinuousMap.instNorm | Mathlib.Topology.ContinuousMap.Compact | [
"SeminormedAddCommGroup",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"Norm",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"CompactSpace",
"TopologicalSpace",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"Semino... | true |
neg_sub_neg | Mathlib.Algebra.Group.Basic | [
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"AddZeroClass.toAddZero",
"neg_neg",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubtractionMonoid.toSubNegMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionComm... | true |
LineDeriv.iteratedLineDerivOp_fin_zero | Mathlib.Analysis.Distribution.DerivNotation | [
"instOfNatNat",
"LineDeriv.iteratedLineDerivOp",
"LineDeriv",
"Nat",
"OfNat.ofNat",
"Fin",
"Eq",
"rfl"
] | true |
_private.Mathlib.LinearAlgebra.Span.Defs.0.Submodule.mem_sSup_of_directed._simp_1_1 | Mathlib.LinearAlgebra.Span.Defs | [
"Membership.mem",
"Exists",
"Set.Elem",
"SetCoe.exists",
"Subtype.mk",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
MeasureTheory.«_aux_Mathlib_MeasureTheory_Integral_Bochner_Basic___macroRules_MeasureTheory_term∫_,_∂__1» | Mathlib.MeasureTheory.Integral.Bochner.Basic | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax... | false |
Std.DTreeMap.get?_inter_of_not_mem_left | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap.instInter",
"Std.DTreeMap",
"congrArg",
"Ord.mk",
"Membership.mem",
"Ordering",
"Eq.mp",
"Std.DTreeMap.contains_eq_false_iff_not_mem",
"Std.DTreeMap.inner",
"Std.DTreeMap.get?",
"Std.TransCmp",
"Inter.inter",
"Std.DTreeMap.instMembership",
"Option.none",
"Std.LawfulEqCmp",
... | true |
MeasureTheory.Integrable.comp_snd_iff | Mathlib.MeasureTheory.Integral.Prod | [
"MeasureTheory.Measure",
"MeasureTheory.Integrable.comp_snd",
"PseudoMetricSpace.toUniformSpace",
"MeasureTheory.Integrable",
"MeasureTheory.Integrable.of_comp_snd",
"SeminormedAddGroup.toContinuousENorm",
"Ne",
"MeasureTheory.Measure.instZero",
"MeasurableSpace",
"SeminormedAddCommGroup.toSeminor... | true |
Multiset.chooseX | Mathlib.Data.Multiset.Basic | [
"Multiset.chooseX._proof_2",
"Multiset.chooseX._proof_1",
"Quotient.recOn",
"Membership.mem",
"Multiset",
"Subtype",
"Quotient.mk",
"Multiset.instMembership",
"List",
"And",
"DecidablePred",
"ExistsUnique",
"List.chooseX",
"List.isSetoid"
] | true |
ExtremallyDisconnected.open_closure | Mathlib.Topology.ExtremallyDisconnected | [
"TopologicalSpace",
"closure",
"IsOpen",
"ExtremallyDisconnected",
"Set"
] | true |
_private.Mathlib.Tactic.Linter.EmptyLine.0.Mathlib.Linter.EmptyLine.emptyLineLinter.match_1 | Mathlib.Tactic.Linter.EmptyLine | [
"Unit.unit",
"Lean.MessageSeverity.ctorIdx",
"Nat.hasNotBit",
"Lean.MessageSeverity",
"Unit",
"Lean.MessageSeverity.information",
"_private.Mathlib.Tactic.Linter.EmptyLine.0.Mathlib.Linter.EmptyLine.emptyLineLinter._sparseCasesOn_1"
] | false |
Lean.Lsp.FileEvent | Lean.Data.Lsp.Workspace | [
"Lean.Lsp.FileEvent.mk"
] | true |
IsometryEquiv.divRight_toEquiv | Mathlib.Topology.MetricSpace.IsometricSMul | [
"MulOpposite",
"IsometryEquiv.toEquiv",
"IsIsometricSMul",
"Group",
"Equiv",
"DivInvMonoid.toMonoid",
"Equiv.divRight",
"PseudoEMetricSpace",
"Group.toDivInvMonoid",
"Monoid.toOppositeMulAction",
"MulOpposite.instMonoid",
"Monoid.toSemigroup",
"Eq.refl",
"SemigroupAction.toSMul",
"MulAct... | true |
CategoryTheory.Limits.isoBiprodZero_inv | Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.isoBiprodZero",
"CategoryTheory.Limits.HasBinaryBiproduct",
"CategoryTheory.Limits.biprod",
"CategoryTheory.Limits.biprod.fst",
"CategoryTheory.Limits.IsZero",
"Eq.refl",
"Categ... | true |
Matroid.isRkFinite_iff_exists_isBasis' | Mathlib.Combinatorics.Matroid.Rank.Finite | [
"Matroid.IsBasis'",
"Set.Finite",
"Exists",
"Matroid.IsRkFinite.exists_finite_isBasis'",
"And",
"Iff",
"Matroid.IsBasis'.isRkFinite_of_finite",
"Iff.intro",
"Matroid",
"_private.Mathlib.Combinatorics.Matroid.Rank.Finite.0.Matroid.isRkFinite_iff_exists_isBasis'.match_1_1",
"Matroid.IsRkFinite",
... | true |
Std.Tactic.BVDecide.BVExpr.bitblast.OverflowInput.casesOn | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Carry | [
"Std.Tactic.BVDecide.BVExpr.bitblast.OverflowInput.mk",
"Std.Tactic.BVDecide.BVExpr.bitblast.OverflowInput",
"Std.Sat.AIG.BinaryRefVec",
"Std.Tactic.BVDecide.BVExpr.bitblast.OverflowInput.rec",
"Std.Sat.AIG.Ref",
"Std.Sat.AIG",
"Nat",
"Hashable",
"DecidableEq"
] | false |
Std.DHashMap.Internal.Raw₀.wfImp_insertMany | Std.Data.DHashMap.Internal.WF | [
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.WF.insert₀",
"Std.DHashMap.Internal.Raw.WF.out",
"Std.DHashMap.Raw",
"instOfNatNat",
"Std.DHashMap.Internal.Raw.WFImp",
"Id",
"LawfulHashable",
"EquivBEq",
"Std.DHashMap.Internal.Raw₀.insert",
"ForIn",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"... | true |
Field.Emb.Cardinal.succEquiv._proof_7 | Mathlib.FieldTheory.CardinalEmb | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"Cardinal",
"CommSemiring.toSemiring",
"IntermediateField",
"IsScalarTower",
"IntermediateField.toField",
"PartialOrder.toPreorder",
"Algebra",
"Algebra.toSMul",
"Function.comp",
"Membersh... | false |
RelHom.id_apply | Mathlib.Order.RelIso.Basic | [
"RelHom.instFunLike",
"RelHom",
"Eq.refl",
"RelHom.id",
"Eq",
"DFunLike.coe"
] | true |
Cardinal.nat_le_lift_iff._simp_1 | Mathlib.SetTheory.Cardinal.Order | [
"Cardinal",
"Cardinal.lift",
"LE.le",
"Nat.cast",
"Cardinal.instLE",
"Nat",
"propext",
"Cardinal.nat_le_lift_iff",
"Eq",
"Cardinal.instNatCast"
] | false |
MvPFunctor.WPath._sizeOf_inst | Mathlib.Data.PFunctor.Multivariate.W | [
"MvPFunctor",
"PFunctor.W",
"instOfNatNat",
"MvPFunctor.WPath._sizeOf_1",
"instHAdd",
"HAdd.hAdd",
"MvPFunctor.WPath",
"SizeOf.mk",
"Nat",
"MvPFunctor.last",
"instAddNat",
"SizeOf",
"OfNat.ofNat",
"Fin2"
] | false |
CategoryTheory.Pi.laxMonoidalPi._proof_10 | Mathlib.CategoryTheory.Pi.Monoidal | [
"CategoryTheory.Functor.LaxMonoidal.right_unitality",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pi.monoidalCategory",
"congrArg",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"Categor... | false |
EuclideanGeometry.Sphere.IsDiameter.midpoint_eq_center | Mathlib.Geometry.Euclidean.Sphere.Basic | [
"Real",
"NormedSpace",
"invertibleTwo",
"Real.instRCLike",
"NormedSpace.toModule",
"EuclideanGeometry.Sphere",
"Real.instRing",
"EuclideanGeometry.Sphere.IsDiameter",
"Field.toSemifield",
"EuclideanGeometry.Sphere.center",
"NormedAddTorsor.toAddTorsor",
"Semifield.toDivisionSemiring",
"Metri... | true |
Dilation.ratio_comp' | Mathlib.Topology.MetricSpace.Dilation | [
"Eq.mpr",
"Semigroup.toMul",
"ENNReal.ofNNReal",
"Dilation.funLike",
"HMul.hMul",
"Dilation.comp",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"ENNReal.coe_inj",
"Exists",
"Dilation.edist_eq",
"SemigroupWithZero.toSemigroup",
"ENNReal.mul_left_inj",
"Eq... | true |
Nat.count_le_cardinal | Mathlib.SetTheory.Cardinal.NatCount | [
"Eq.mpr",
"Cardinal.mk_subtype_mono",
"Cardinal",
"Nat.CountSet.fintype",
"congrArg",
"Nat.count_eq_card_fintype",
"setOf",
"Cardinal.mk",
"Membership.mem",
"Set.Elem",
"Fintype.card",
"id",
"Subtype",
"LE.le",
"Cardinal.mk_fintype",
"Nat.cast",
"Cardinal.instLE",
"And",
"And.rig... | true |
Aesop.GoalUnsafe.noConfusion | Aesop.Tree.Data | [
"Aesop.GoalData",
"Aesop.RappUnsafe",
"Aesop.GoalUnsafe.casesOn",
"Aesop.MVarClusterUnsafe",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Aesop.GoalUnsafe",
"Aesop.GoalUnsafe.noConfusionType"
] | false |
_private.Mathlib.Tactic.CategoryTheory.Elementwise.0.Mathlib.Tactic.Elementwise.initFn.match_1._@.Mathlib.Tactic.CategoryTheory.Elementwise.3754623819._hygCtx._hyg.2 | Mathlib.Tactic.CategoryTheory.Elementwise | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Prod.mk",
"Lean.Level",
"_private.Mathlib.Tactic.CategoryTheory.Elementwise.0.Mathlib.Tactic.Elementwise.elementwiseExpr.extractCatInstance._sparseCasesOn_9",
"Prod",
"Prod.casesOn",
"Option"
] | false |
_private.Lean.Meta.Sym.Pattern.0.Lean.Meta.Sym.DefEqM.Context._sizeOf_1 | Lean.Meta.Sym.Pattern | [
"Lean.MVarId",
"instOfNatNat",
"_private.Lean.Meta.Sym.Pattern.0.Lean.Meta.Sym.DefEqM.Context",
"Array._sizeOf_inst",
"Array",
"Lean.MVarId._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Bool",
"instAddNat",
"instSizeOfNat",
"OfNat.ofNat",
"Bool._sizeOf_inst",
"_priva... | false |
_private.Mathlib.AlgebraicGeometry.Cover.Open.0.AlgebraicGeometry.Scheme.OpenCover.ext_elem._simp_1_2 | Mathlib.AlgebraicGeometry.Cover.Open | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
Std.DHashMap.Internal.Raw₀.contains_diff_eq_false_of_contains_eq_false_left | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.Internal.List.containsKey_of_perm",
"Bool.not",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.DHashMap.Internal.Raw.WF.out",
"congrArg",
"List.map",
"List.contains",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw₀.contains_eq_containsKey",
"id",
"Sigma.fst... | true |
SpecialLinearGroup.instGroup._proof_10 | Mathlib.LinearAlgebra.SpecialLinearGroup | [
"LinearEquiv.det",
"Semigroup.toMul",
"CommRing",
"DivInvMonoid.toInv",
"SpecialLinearGroup.coe_zpow",
"MonoidHom.instFunLike",
"SpecialLinearGroup.instGroup._proof_9",
"HMul.hMul",
"SpecialLinearGroup.coe_one",
"SpecialLinearGroup.instPowInt",
"MonoidHom",
"Monoid.toMulOneClass",
"CommSemir... | false |
CategoryTheory.ShortComplex.HomologyData.ofEpiMonoFactorisation.rightHomologyData._proof_7 | Mathlib.Algebra.Homology.ShortComplex.Abelian | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.opcycles",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.Epi",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limit... | false |
Std.Do.PostShape.pure.sizeOf_spec | Std.Do.PostCond | [
"Std.Do.PostShape._sizeOf_inst",
"Std.Do.PostShape",
"Std.Do.PostShape.pure",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
_private.Mathlib.Algebra.Order.Group.Pointwise.Interval.0.Set.preimage_mul_const_Icc_of_neg._simp_1_1 | Mathlib.Algebra.Order.Group.Pointwise.Interval | [
"Set.Ici",
"Set.instInter",
"Inter.inter",
"Set.Icc",
"Set.Iic",
"Eq.symm",
"Eq",
"Preorder",
"Set.Ici_inter_Iic",
"Set"
] | false |
_private.Mathlib.Analysis.InnerProductSpace.Semisimple.0.LinearMap.IsSymmetric.isFinitelySemisimple._simp_1_1 | Mathlib.Analysis.InnerProductSpace.Semisimple | [
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"OrderBot",
"disjoint_iff",
"SemilatticeInf.toPartialOrder",
"Bot.bot",
"SemilatticeInf.toMin",
"SemilatticeInf",
"propext",
"Eq",
"Min.min"
] | false |
_private.Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree.0.WeierstrassCurve.natDegree_preΨ'_pos._simp_1_1 | Mathlib.AlgebraicGeometry.EllipticCurve.DivisionPolynomial.Degree | [
"instHDiv",
"HDiv.hDiv",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.div_pos_iff",
"And",
"Nat",
"LT.lt",
"Nat.instDiv",
"propext",
"instLTNat",
"OfNat.ofNat",
"Eq"
] | false |
_private.Lean.Meta.AppBuilder.0.Lean.Meta.mkEqTrans?.match_1 | Lean.Meta.AppBuilder | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Lean.Expr",
"Option.none",
"Unit",
"Option"
] | false |
Std.ExtTreeMap.getD_ofList_of_mem | Std.Data.ExtTreeMap.Lemmas | [
"List.Pairwise",
"Std.ExtTreeMap.ofList",
"Membership.mem",
"Ordering",
"Std.ExtTreeMap.getD",
"Ordering.eq",
"Prod.mk",
"Std.TransCmp",
"Prod.fst",
"List",
"List.instMembership",
"Prod",
"Std.ExtDTreeMap.Const.getD_ofList_of_mem",
"Eq",
"Not"
] | true |
_private.Mathlib.Dynamics.OmegaLimit.0.mem_omegaLimit_iff_frequently₂._simp_1_2 | Mathlib.Dynamics.OmegaLimit | [
"Set.instInter",
"Inter.inter",
"Set.Nonempty",
"Set.preimage",
"propext",
"Set.image",
"Eq",
"Set.image_inter_nonempty_iff",
"Set"
] | false |
ENat.toENNReal_ne_top._simp_1 | Mathlib.Data.Real.ENatENNReal | [
"ENat.toENNReal_ne_top",
"instTopENat",
"ENat.toENNReal",
"Ne",
"ENat",
"ENNReal",
"propext",
"instTopENNReal",
"Top.top",
"Eq"
] | false |
Matroid.loopless_iff | Mathlib.Combinatorics.Matroid.Loop | [
"Matroid.Loopless.casesOn",
"Matroid.Loopless",
"Iff",
"Matroid.Loopless.mk",
"Iff.intro",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Matroid",
"Matroid.loops",
"Set"
] | true |
FirstOrder.Language.BoundedFormula.sumElim_comp_relabelAux | Mathlib.ModelTheory.Syntax | [
"Fin.natAdd",
"Equiv.instEquivLike",
"Sum.map",
"Fin.castAdd",
"Function.comp",
"Sum.casesOn",
"Sum",
"FirstOrder.Language.BoundedFormula.relabelAux",
"id",
"Equiv",
"Sum.inl",
"funext",
"instHAdd",
"HAdd.hAdd",
"Nat",
"eq_self",
"finSumFinEquiv",
"of_eq_true",
"instAddNat",
"E... | true |
_private.Init.System.FilePath.0.System.instHashableFilePath.hash.match_1 | Init.System.FilePath | [
"String",
"System.FilePath.casesOn",
"System.FilePath.mk",
"System.FilePath"
] | false |
Finset.inf'._proof_1 | Mathlib.Data.Finset.Lattice.Fold | [
"Eq.mpr",
"False",
"Classical.not_not._simp_1",
"congrArg",
"Finset",
"WithTop.coe_ne_top._simp_1",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Function.comp",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"id",
"Ne",
"WithTop.some",
"funext",
"SemilatticeInf",
"Ord... | false |
Filter.div_mem_div | Mathlib.Order.Filter.Pointwise | [
"Filter.instMembership",
"Filter.image2_mem_map₂",
"instHDiv",
"Filter.instDiv",
"Membership.mem",
"HDiv.hDiv",
"Div",
"Set.div",
"Filter",
"Set"
] | true |
Lean.FuzzyMatching.CharType.separator.elim | Lean.Data.FuzzyMatching | [
"PULift.up",
"Lean.FuzzyMatching.CharType",
"Lean.FuzzyMatching.CharType.ctorIdx",
"Nat",
"Lean.FuzzyMatching.CharType.ctorElim",
"Eq.symm",
"Eq",
"Lean.FuzzyMatching.CharType.separator"
] | false |
MeasureTheory.pdf.eq_of_map_eq_withDensity' | Mathlib.Probability.Density | [
"MeasureTheory.ae",
"MeasureTheory.Measure.withDensity",
"MeasureTheory.Measure",
"Measurable.aemeasurable",
"AEMeasurable",
"MeasureTheory.SigmaFinite",
"ENNReal.measurableSpace",
"Eq.rec",
"MeasureTheory.measurable_pdf",
"Filter.EventuallyEq",
"MeasureTheory.map_eq_withDensity_pdf",
"Measure... | true |
_private.Mathlib.Computability.TuringMachine.ToPartrec.0.Option.getD.match_1.splitter | Mathlib.Computability.TuringMachine.ToPartrec | [
"Option.getD.match_1",
"Option.some",
"Option.none",
"Unit",
"Option"
] | true |
mabs_div_lt_of_one_le_of_lt | Mathlib.Algebra.Order.Group.Abs | [
"instIsRightCancelMulOfMulRightReflectLE",
"IsLeftCancelMul.mulLeftReflectLE_of_mulLeftReflectLT",
"Eq.mpr",
"IsOrderedMonoid.toIsOrderedCancelMonoid",
"Preorder.toLT",
"instHDiv",
"InvOneClass.toOne",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"CommMonoid.toCommSemigroup",
"DivInvOneMo... | true |
lebesgue_number_of_compact_open | Mathlib.Topology.UniformSpace.Compact | [
"Filter.instMembership",
"Iff.mpr",
"UniformSpace",
"Filter.HasBasis.mem_iff",
"SetRel",
"uniformity",
"instTopologicalSpaceProd",
"Membership.mem",
"Exists",
"id",
"HasSubset.Subset",
"UniformSpace.ball",
"And",
"And.intro",
"_private.Mathlib.Topology.UniformSpace.Compact.0.lebesgue_num... | true |
Array.mergeDedupWith.go._unary._proof_2 | Batteries.Data.Array.Merge | [
"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",
"Array.push",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"InvImage",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_... | false |
Submodule.smul_le_smul | Mathlib.Algebra.Algebra.Operations | [
"Submodule",
"Submodule.instAddCommMonoidWithOne",
"SetSemiring.down",
"instHSMul",
"Equiv.instEquivLike",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"SetSemiring.instIdemSemiringOfMonoid",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"... | true |
MeasureTheory.measureReal_abs_dual_gt_le_integral_charFunDual | Mathlib.MeasureTheory.Measure.IntegralCharFun | [
"instInnerProductSpaceRealComplex",
"MeasurableSet.preimage",
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"instClosedIicTopology",
"Real.instLE",
"Real",
"Algebra.to_smulCommClass",
"instHSMul",
"MeasureTheory.Measure",
"NonUnitalCommRing.... | true |
finRotate_last | Mathlib.Logic.Equiv.Fin.Rotate | [
"instNeZeroNatHAdd_1",
"Equiv.instEquivLike",
"Fin.instOfNat",
"instOfNatNat",
"finRotate",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Equiv.Perm",
"Nat",
"Fin.last",
"finRotate_last'",
"instAddNat",
"OfNat.ofNat",
"Fin",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
Finset.instAddTorsorForall | Mathlib.LinearAlgebra.AffineSpace.Combination | [
"Pi.addGroup",
"AddGroupWithOne.toAddGroup",
"addGroupIsAddTorsor",
"Pi.instAddTorsor",
"AddTorsor",
"Ring",
"Ring.toAddGroupWithOne"
] | true |
Std.Sat.AIG.RefVec.IfInput.rec | Std.Sat.AIG.If | [
"Std.Sat.AIG.RefVec.IfInput",
"Std.Sat.AIG.Ref",
"Std.Sat.AIG",
"Nat",
"Std.Sat.AIG.RefVec.IfInput.mk",
"Hashable",
"Std.Sat.AIG.RefVec",
"DecidableEq"
] | false |
InnerProductSpace.canonicalCovariantTensor.congr_simp | Mathlib.Analysis.Distribution.DerivNotation | [
"InnerProductSpace.toNormedSpace",
"Real",
"Real.instRCLike",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"InnerProductSpace.canonicalCovariantTensor",
"FiniteDimensional",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"Real.instDivisionRing",
"TensorProduct",
"NormedAddCommGroup... | true |
BitVec.not_lt_zero._simp_1 | Init.Data.BitVec.Lemmas | [
"False",
"eq_false",
"BitVec",
"instOfNatNat",
"BitVec.ofNat",
"instLTBitVec",
"Nat",
"LT.lt",
"BitVec.not_lt_zero",
"OfNat.ofNat",
"Eq"
] | false |
imp_false | Init.Core | [
"False",
"Iff.rfl",
"Iff",
"Not"
] | true |
CategoryTheory.categoryFree._proof_5 | Mathlib.Algebra.Category.ModuleCat.Adjunctions | [
"add_mul",
"Distrib.leftDistribClass",
"CategoryTheory.Category.assoc",
"Semigroup.toMul",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Finsupp.sum_single_index",
... | false |
_private.Mathlib.Data.Set.Prod.0.Set.compl_prod_eq_union._proof_1_1 | Mathlib.Data.Set.Prod | [
"Lean.Grind.of_eq_eq_true",
"Set.mem_union",
"Set.instSProd",
"Lean.Grind.eq_false_of_not_eq_true",
"Set.ext",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Lean.Grind.not_not",
"eq_false",
"Lean.Grind.iff_eq",
"SProd.sprod",
"congrArg",
"Compl.compl",
"Set.univ",
"False.elim",
"Clas... | false |
upperPolar_empty | Mathlib.Order.Concept | [
"Set.univ",
"False.elim",
"upperPolar",
"Set.eq_univ_of_forall",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Set"
] | true |
AlgebraicGeometry.Scheme.Modules.conjugateEquiv_pullbackId_hom | Mathlib.AlgebraicGeometry.Modules.Sheaf | [
"AlgebraicGeometry.Scheme.Modules.pullback",
"CategoryTheory.Functor",
"AlgebraicGeometry.Scheme.Modules.pushforward",
"AlgebraicGeometry.Scheme",
"Equiv.instEquivLike",
"AlgebraicGeometry.Scheme.Modules.instCategory",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuive... | true |
HomologicalComplex₂.toGradedObjectMap | Mathlib.Algebra.Homology.HomologicalBicomplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex₂.toGradedObject",
"HomologicalComplex₂.toGradedObject.match_1",
"HomologicalComplex",
"ComplexShape",
"CategoryTheory... | true |
Lean.Meta.useEtaStruct | Lean.Meta.Basic | [
"Pure.pure",
"Bool.not",
"Lean.Meta.State",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Applicative.toPure",
"_private.Lean.Meta.Basic.0.Lean.Meta.useEtaStruct.match_1",
"Bool.true",
"Unit",
"Lean.Core.CoreM",
"Lean.Meta.Config.etaStruct",
"Lean.Meta.instMonadMetaM",
"StateRefT'",
"Lean.Meta.EtaSt... | true |
CategoryTheory.Endofunctor.Algebra.functorOfNatTransId_inv_app_f | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Algebra",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Endofunctor.Algebra.a",
"CategoryTheory.Endofunctor.Algebra.func... | true |
SkewMonoidAlgebra.coeff_single | Mathlib.Algebra.SkewMonoidAlgebra.Basic | [
"congrArg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Pi.single",
"AddZero.toZero",
"True",
"eq_self",
"AddMonoid",
"of_eq_true",
"congrFun'",
"Finsupp.single_eq_pi_single",
"SkewMonoidAlgebra.single",
"Eq",
"Eq.trans",
"SkewMonoidAlgebra.coeff",
"DecidableEq"
] | true |
Filter.Germ.total | Mathlib.Order.Filter.FilterProduct | [
"Filter.Eventually",
"Filter.Eventually.of_forall",
"Filter.Germ.instLE",
"LE.le",
"Ultrafilter.eventually_or",
"total_of",
"LE",
"Filter.Germ.inductionOn₂",
"Filter.Germ",
"Iff.mp",
"Or",
"Std.Total.mk",
"Std.Total",
"Ultrafilter",
"Ultrafilter.toFilter"
] | true |
_private.Lean.Elab.Tactic.BVDecide.Frontend.BVDecide.Reflect.0.Lean.Elab.Tactic.BVDecide.Frontend.LemmaM.run.match_1 | Lean.Elab.Tactic.BVDecide.Frontend.BVDecide.Reflect | [
"Prod.mk",
"Lean.Elab.Tactic.BVDecide.Frontend.LemmaState",
"Prod",
"Prod.casesOn"
] | false |
EReal.sub_add_cancel_right | Mathlib.Data.EReal.Operations | [
"Eq.mpr",
"Real",
"Real.instSub",
"HSub.hSub",
"EReal.instNeg",
"EReal",
"instTopEReal",
"id",
"Real.instAddGroup",
"Bot.bot",
"SubNegZeroMonoid.toSubNegMonoid",
"instAddCommMonoidEReal",
"Real.instAdd",
"SubNegMonoid.toSub",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Real.instNeg",
"... | true |
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