name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Matrix.IsAdjMatrix.apply_diag | Mathlib.Combinatorics.SimpleGraph.AdjMatrix | [
"One",
"Matrix",
"Matrix.IsAdjMatrix",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Zero"
] | true |
Ordnode.repr._f | Mathlib.Data.Ordmap.Ordnode | [
"Ordnode.below",
"Ordnode",
"Std.Format.paren",
"Std.Format.joinSep",
"Ordnode.node",
"List.cons",
"Unit",
"Ordnode.size.match_1",
"Nat",
"Ordnode.nil",
"Std.Format",
"Std.instToFormatFormat",
"Repr",
"Repr.reprPrec",
"Std.Format.text",
"List.nil"
] | false |
Real.sin_arctan_lt_zero | Mathlib.Analysis.SpecialFunctions.Trigonometric.Arctan | [
"Real",
"Preorder.toLT",
"Real.arctan",
"Real.instZero",
"congrArg",
"PartialOrder.toPreorder",
"StrictMono.lt_iff_lt",
"Real.instLT",
"Real.sin_zero",
"Eq.mp",
"Real.arctan_zero",
"Iff",
"LT.lt",
"Real.sin_arctan_strictMono",
"Zero.toOfNat0",
"congrFun'",
"OfNat.ofNat",
"LinearOrd... | true |
SSet.N.eq_iff | Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices | [
"SSet.N.instPreorder",
"SSet.S.subcomplex",
"Opposite",
"instReflLe",
"congrArg",
"and_self",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Std.le_refl._simp_1",
"SSet.N.instPartialOrder",
"SSet",
"_private.Mathlib.AlgebraicTopology.SimplicialSet.NonDegenerateSimplices.0.SSet.N.eq_iff._simp_1_2... | true |
Aesop.NormalizationState.isNormal | Aesop.Tree.Data | [
"Lean.Meta.SavedState",
"_private.Aesop.Tree.Data.0.Aesop.NormalizationState.isNormal.match_1",
"Lean.MVarId",
"Aesop.NormalizationState",
"Aesop.DisplayRuleName",
"Array",
"Bool.true",
"Unit",
"Bool",
"Prod",
"Bool.false",
"Aesop.Script.LazyStep",
"Option"
] | true |
String.Slice.posGT_le_iff | Init.Data.String.Lemmas.FindPos | [
"Eq.mpr",
"String.instLTRaw",
"String.instLEPos_1",
"String.Slice.posGT_eq_posGE._proof_1",
"congrArg",
"String.Slice.Pos.offset",
"Iff.rfl",
"String.Slice.rawEndPos",
"String.Slice",
"id",
"String.Slice.posGE_le_iff",
"String.Pos.Raw.inc",
"LE.le",
"String.Pos.Raw",
"Iff",
"String.Sli... | true |
Zero.ctorIdx | Init.Prelude | [
"Nat",
"Zero"
] | false |
Matrix.toLpLinAlgEquiv_symm_apply | Mathlib.Analysis.Normed.Lp.Matrix | [
"WithLp",
"Pi.Function.module",
"LinearEquiv.symm",
"CommRing",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"instSMulOfMul",
"IsScalarTower.right",
"AlgEquiv.symm",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Matrix",
"Module.End.instSemiring",
"Function.smulCommClass"... | true |
Cardinal.lt_one_iff | Mathlib.SetTheory.Cardinal.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Preorder.toLT",
"Cardinal.instOne",
"Order.succ",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"OrderBot.toBot",
"AddMonoid.toAddZeroClass",
"Cardinal.commSemiring",
"PartialOrder.toPreorder",
"Cardinal.instNoMaxOrder",
"Preorder.toLE",
"Ca... | true |
Lean.Elab.TerminationBy.synthetic | Lean.Elab.PreDefinition.TerminationHint | [
"Lean.Elab.TerminationBy",
"Bool"
] | true |
BoundedContinuousFunction.coe_nsmulRec._f | Mathlib.Topology.ContinuousMap.Bounded.Basic | [
"Eq.mpr",
"Nat.instMulZeroClass",
"instHSMul",
"PseudoMetricSpace.toBornology",
"AddMonoid.toAddSemigroup",
"BoundedContinuousFunction.instAdd",
"congrArg",
"SMulWithZero.toSMulZeroClass",
"_private.Mathlib.Topology.ContinuousMap.Bounded.Basic.0.BoundedContinuousFunction.coe_nsmulRec.match_1_1",
"... | false |
Mathlib.Tactic.BicategoryLike.Mor₂.comp.sizeOf_spec | Mathlib.Tactic.CategoryTheory.Coherence.Datatypes | [
"Mathlib.Tactic.BicategoryLike.Mor₂",
"Option._sizeOf_inst",
"Mathlib.Tactic.BicategoryLike.Mor₁._sizeOf_inst",
"Mathlib.Tactic.BicategoryLike.IsoLift._sizeOf_inst",
"Lean.Expr",
"Mathlib.Tactic.BicategoryLike.Mor₂._sizeOf_inst",
"instOfNatNat",
"Mathlib.Tactic.BicategoryLike.Mor₁",
"Mathlib.Tactic.... | true |
_private.Lean.Meta.Sym.InstantiateS.0.Lean.Meta.Sym.instantiateRevRangeS._proof_1 | Lean.Meta.Sym.InstantiateS | [
"HSub.hSub",
"_private.Lean.Meta.Sym.InstantiateS.0.Lean.Meta.Sym.instantiateRevRangeS._proof_4",
"GE.ge",
"Lean.Expr",
"instSubNat",
"instOfNatNat",
"instLENat",
"Array",
"GT.gt",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"Nat.decLt",
"instAdd... | false |
Manifold.«_aux_Mathlib_Geometry_Manifold_ContMDiffMap___macroRules_Manifold_termC^_⟮_,_;_⟯_1» | Mathlib.Geometry.Manifold.ContMDiffMap | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.node5",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSynta... | false |
GradedMonoid.GSMul.rec | Mathlib.Algebra.GradedMulAction | [
"GradedMonoid.GSMul",
"GradedMonoid.GSMul.mk",
"VAdd",
"HVAdd.hVAdd",
"instHVAdd"
] | false |
Std.Time.TimeZone.TZif.TZifV2._sizeOf_inst | Std.Time.Zoned.Database.TzIf | [
"Std.Time.TimeZone.TZif.TZifV2",
"SizeOf.mk",
"Std.Time.TimeZone.TZif.TZifV2._sizeOf_1",
"SizeOf"
] | false |
PresheafOfModules.evaluationJointlyReflectsLimits | Mathlib.Algebra.Category.ModuleCat.Presheaf.Limits | [
"PresheafOfModules.evaluation",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.IsLimit.mk",
"CategoryTheory.Limits.Cone",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"Presh... | true |
_private.Mathlib.RingTheory.Spectrum.Prime.Topology.0.PrimeSpectrum.localization_away_comap_range._simp_1_3 | Mathlib.RingTheory.Spectrum.Prime.Topology | [
"Set.singleton_subset_iff",
"Membership.mem",
"Set.instSingletonSet",
"HasSubset.Subset",
"propext",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Set.instHasSubset",
"Set"
] | false |
Submodule.equivMapOfInjective._proof_4 | Mathlib.Algebra.Module.Submodule.Map | [
"Submodule",
"Equiv.right_inv",
"LinearMap.instFunLike",
"Equiv.Set.image",
"RingHom",
"Set.Elem",
"Equiv.toFun",
"LinearMap",
"AddCommMonoid",
"SetLike.coe",
"Submodule.setLike",
"Function.RightInverse",
"Semiring",
"Set.image",
"Function.Injective",
"Module",
"Semiring.toNonAssocSe... | false |
Mathlib.PrintSorries.State.mk.inj | Mathlib.Util.PrintSorries | [
"Lean.MessageData",
"Mathlib.PrintSorries.State",
"Lean.NameSet",
"Lean.Expr.instBEq",
"Std.HashSet",
"Lean.Expr",
"Array",
"Mathlib.PrintSorries.State.mk",
"And",
"And.intro",
"Lean.Expr.instHashable",
"Mathlib.PrintSorries.State.mk.noConfusion",
"Eq"
] | true |
NonUnitalStarSubalgebra.toNonUnitalSubring_injective | Mathlib.Algebra.Star.NonUnitalSubalgebra | [
"NonUnitalSubring.instSetLike",
"Eq.mpr",
"CommRing",
"NonUnitalStarSubalgebra.ext",
"congrArg",
"CommSemiring.toSemiring",
"Iff.rfl",
"NonUnitalSubring",
"Membership.mem",
"NonUnitalRing.toNonUnitalNonAssocRing",
"NonUnitalStarSubalgebra.mem_toNonUnitalSubring",
"id",
"NonUnitalNonAssocRing... | true |
Lean.ErrorExplanation.Metadata.removedVersion? | Lean.ErrorExplanation | [
"String",
"Lean.ErrorExplanation.Metadata",
"Option"
] | true |
CategoryTheory.sheafificationNatIso | Mathlib.CategoryTheory.Sites.Sheafification | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.Iso",
"CategoryTheory.presheafToSheaf",
"CategoryTheory.sheafificationNatIso._proof_3",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.HasWea... | true |
RelIso.sumLexComplRight_symm_apply | Mathlib.Order.Hom.Lex | [
"Sum.swap",
"Equiv.instEquivLike",
"DecidableRel",
"Sum",
"Equiv",
"Subtype",
"Subrel",
"Std.Trichotomous",
"IsTrans",
"RelIso",
"RelIso.instFunLike",
"RelIso.sumLexComplRight",
"Equiv.sumCompl",
"Eq",
"DFunLike.coe",
"Not",
"rfl",
"Sum.Lex",
"EquivLike.toFunLike"
] | true |
CategoryTheory.instIsAddModHomNegOfHom | Mathlib.CategoryTheory.Monoidal.Mod | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Iso.comp_inv_eq",
"CategoryTheory.AddModObj",
"CategoryTheory.AddModObj.vadd",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHomRight_in... | true |
CategoryTheory.ShortComplex.RightHomologyMapData.comp_φQ | Mathlib.Algebra.Homology.ShortComplex.RightHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.RightHomologyData",
"CategoryTheory.ShortComplex.RightHomologyMapData.comp",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.ShortCo... | true |
WithSeminorms.hasBasis_ball | Mathlib.Analysis.LocallyConvex.WithSeminorms | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instVAddOfAdd",
"Real.instZero",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Filter.map",
"HEq.refl",
"Finset",
"AddMonoid.toAddZeroClass",
"Real.instLT",
"Seminor... | true |
List.sortedLE_ofFn_iff | Mathlib.Data.List.Sort | [
"_private.Mathlib.Data.List.Sort.0.List.sortedLE_ofFn_iff._simp_1_3",
"List.get_ofFn",
"congrArg",
"List.get",
"List.SortedLE",
"PartialOrder.toPreorder",
"Monotone",
"List.ofFn",
"List.length_ofFn",
"Preorder.toLE",
"Eq.rec",
"Fin.mk",
"LE.le",
"instLENat",
"instLEFin",
"iff_self",
... | true |
Rel.edgeDensity.congr_simp | Mathlib.Combinatorics.SimpleGraph.Density | [
"instSubsingletonDecidable",
"Finset",
"Rat",
"Decidable",
"Eq.rec",
"Rel.edgeDensity",
"Pi.instSubsingleton",
"DecidablePred",
"Eq.ndrec",
"Eq.refl",
"Subsingleton.elim",
"Eq"
] | true |
CategoryTheory.CostructuredArrow.toOverCompYoneda._proof_1 | Mathlib.CategoryTheory.Comma.Presheaf.Basic | [
"CategoryTheory.Functor.op",
"CategoryTheory.CostructuredArrow.toOverCompOverEquivPresheafCostructuredArrow",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Equivalence.fullyFaithfulFunctor",
"CategoryTheory.Functo... | false |
Lean.IR.LogEntry | Lean.Compiler.IR.CompilerM | [
"Lean.IR.LogEntry.message",
"Lean.IR.LogEntry.step"
] | true |
Differentiable.continuous | Mathlib.Analysis.Calculus.FDeriv.Basic | [
"Differentiable",
"Iff.mpr",
"NormedCommRing.toSeminormedCommRing",
"Continuous",
"ContinuousSMul",
"ContinuousAt",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"DifferentiableAt.con... | true |
Int64.sub_mul | Init.Data.SInt.Lemmas | [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"HSub.hSub",
"id",
"Int64",
"instHSub",
"instSubInt64",
"Eq.refl",
"Int64.mul_sub",
"Eq",
"instMulInt64",
"Int64.mul_comm",
"instHMul"
] | true |
OrderHom.gfp_le | Mathlib.Order.FixedPoints | [
"OrderHom.gfp",
"ChainCompletePartialOrder.instOfCompleteLattice",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"OrderHom.instPreorder",
"LE.le",
"ChainCompletePartialOrder.toPartialOrder",
"OrderHom.instFunLike",
"CompleteLattice.toCompleteSemilatticeSup",
"sSup_le",
"CompleteLattice"... | true |
_private.Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic.0.Algebra.finite_iff_isIntegral_and_finiteType.match_1_1 | Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic | [
"CommRing",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.IsIntegral",
"Algebra.FiniteType",
"And.casesOn",
"And",
"CommRing.toCommSemiring",
"And.intro",
"CommRing.toRing"
] | false |
Lean.Compiler.LCNF.instInhabitedLetDecl | Lean.Compiler.LCNF.Basic | [
"Lean.Compiler.LCNF.Purity",
"Inhabited",
"Lean.Compiler.LCNF.LetDecl",
"Inhabited.mk",
"Lean.Compiler.LCNF.instInhabitedLetDecl.default"
] | true |
Lean.Parser.Tactic.mcasesPatAlts | Std.Tactic.Do.Syntax | [
"instOfNatNat",
"Lean.ParserDescr.nodeWithAntiquot",
"Lean.ParserDescr",
"Lean.ParserDescr.sepBy1",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | true |
Nucleus.mem_toSublocale | Mathlib.Order.Sublocale | [
"Nucleus",
"Iff.rfl",
"Membership.mem",
"Exists",
"Sublocale.instSetLike",
"CompleteLattice.toConditionallyCompleteLattice",
"Nucleus.toSublocale",
"Nucleus.instFunLike",
"Iff",
"Order.Frame.toCompleteLattice",
"ConditionallyCompleteLattice.toLattice",
"Order.Frame",
"Eq",
"DFunLike.coe",
... | true |
CategoryTheory.LaxFunctor.mk.noConfusion | Mathlib.CategoryTheory.Bicategory.Functor.Lax | [
"CategoryTheory.LaxFunctor.map₂_rightUnitor._autoParam",
"CategoryTheory.LaxFunctor.noConfusion",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Bicategory.rightUnitor",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Bicategory.whiskerRight",
"id",
"Catego... | false |
ULift.div | Mathlib.Algebra.Group.ULift | [
"instHDiv",
"ULift",
"HDiv.hDiv",
"Div",
"Div.mk",
"ULift.up",
"ULift.down"
] | true |
LinearIsometryEquiv.symm_conjStarAlgEquiv | Mathlib.Analysis.InnerProductSpace.Adjoint | [
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"CompleteSpace",
"NormedSpace.toIsBoundedSMul",
"LinearIsometryEquiv.symm",
"ContinuousLinearMap.instStarId",
"UniformContinuousConstSMul.to_continuousConstSMul",
"LinearIsometryEquiv.conjStarAlgEquiv",
"DistribMulAction.toDis... | true |
CategoryTheory.Functor.prod._proof_2 | Mathlib.CategoryTheory.Products.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.prod",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Prod.mkHom",
"CategoryTheory.CategoryStruct.id",
"Prod.mk",
"CategoryTheory.Functor.map",
"Prod.fst",
"CategoryTheory.Functor.map_id",
"congr",
"CategoryTheory... | false |
MeasureTheory.lintegral_lintegral_symm | Mathlib.MeasureTheory.Measure.Prod | [
"MeasureTheory.Measure",
"AEMeasurable",
"AEMeasurable.prod_swap",
"ENNReal.measurableSpace",
"Prod.mk",
"Prod.fst",
"MeasurableSpace",
"MeasureTheory.SFinite",
"MeasureTheory.Measure.prod",
"ENNReal",
"MeasureTheory.lintegral_prod_symm",
"Prod.swap",
"Function.uncurry",
"Prod",
"Eq.symm... | true |
CompactlySupportedContinuousMap._sizeOf_1 | Mathlib.Topology.ContinuousMap.CompactlySupported | [
"ContinuousMap._sizeOf_inst",
"CompactlySupportedContinuousMap",
"ContinuousMap",
"instOfNatNat",
"TopologicalSpace",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"CompactlySupportedContinuousMap.rec",
"instAddNat",
"ContinuousMap.toFun",
"SizeOf",
"OfNat.ofNat",
"HasCompactSupport",... | false |
Mathlib.Tactic.BicategoryCoherence.LiftHom.recOn | Mathlib.Tactic.CategoryTheory.BicategoryCoherence | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.FreeBicategory.of",
"Mathlib.Tactic.BicategoryCoherence.LiftHom",
"CategoryTheory.Bicategory.toCategoryStruct",
"Mathlib.Tactic.BicategoryCoherence.LiftHom.mk",
"CategoryTheory.FreeBicategory.quiver",
"CategoryTheory.Bicategory",
... | false |
StarMemClass.rec | Mathlib.Algebra.Star.Basic | [
"SetLike",
"Membership.mem",
"Star",
"StarMemClass",
"StarMemClass.mk",
"SetLike.instMembership",
"Star.star"
] | false |
Std.IterM.stepSize | Std.Data.Iterators.Combinators.Monadic.StepSize | [
"HSub.hSub",
"instSubNat",
"Std.IterM.mk",
"instOfNatNat",
"Std.Iterator",
"Std.Iterators.Types.StepSizeIterator",
"instHSub",
"Nat",
"Std.IterM",
"Std.IteratorAccess",
"OfNat.ofNat",
"Monad",
"Std.Iterators.Types.StepSizeIterator.mk"
] | true |
_private.Init.Data.BitVec.Bitblast.0.BitVec.ult_eq_not_carry._proof_1_6 | Init.Data.BitVec.Bitblast | [
"instPowNat",
"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",
"Lean.Omega.Int.ofNat_sub_sub",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_di... | false |
ContMDiffVAdd.mk._flat_ctor | Mathlib.Geometry.Manifold.Algebra.SMul | [
"Prod.normedSpace",
"Prod.normedAddCommGroup",
"NormedSpace",
"ContMDiff",
"instTopologicalSpaceProd",
"VAdd",
"instTopologicalSpaceModelProd",
"Prod.fst",
"HVAdd.hVAdd",
"TopologicalSpace",
"ModelWithCorners",
"ContMDiffVAdd",
"ContMDiffVAdd.mk",
"ENat",
"instHVAdd",
"NontriviallyNorm... | false |
ContinuousMap.Homotopy.extend_one | Mathlib.Topology.Homotopy.Basic | [
"Real",
"Real.instZero",
"Real.instZeroLEOneClass",
"instReflLe",
"congrArg",
"and_self",
"ContinuousMap",
"PseudoMetricSpace.toUniformSpace",
"Preorder.toLE",
"Std.le_refl._simp_1",
"ContinuousMap.Homotopy.curry",
"Membership.mem",
"Set.Elem",
"zero_le_one._simp_1",
"LE.le",
"Subtype.... | true |
MeasureTheory.exists_subordinate_pairwise_disjoint | Mathlib.MeasureTheory.Measure.NullMeasurable | [
"MeasureTheory.ae",
"MeasurableSet.diff",
"Set.diff_subset",
"MeasureTheory.Measure",
"Filter.EventuallyEq.trans",
"ChainCompletePartialOrder.instOfCompleteLattice",
"MeasurableSet",
"MeasureTheory.exists_null_pairwise_disjoint_diff",
"Function.onFun",
"CompleteBooleanAlgebra.toCompleteDistribLatt... | true |
RightCancelMonoid.Nat.card_submonoidPowers | Mathlib.GroupTheory.OrderOfElement | [
"Iff.mpr",
"Eq.mpr",
"Fintype.card_fin",
"Monoid.toMulOneClass",
"congrArg",
"Nat.card_eq_zero_of_infinite",
"Classical.propDecidable",
"Membership.mem",
"Set.Elem",
"Fintype.card",
"id",
"Subtype",
"Nat.card",
"RightCancelMonoid.infinite_powers",
"instOfNatNat",
"finEquivPowers",
"R... | true |
_private.Mathlib.Algebra.Lie.Ideal.0.LieIdeal.comap._simp_2 | Mathlib.Algebra.Lie.Ideal | [
"AddSubsemigroup.instSetLike",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddSubmonoid.toAddSubsemigroup",
"AddSubmonoid",
"AddZeroClass",
"AddSubsemigroup",
"propext",
"AddZero.toAdd",
"AddSubmonoid.instSetLike",
"Eq",
"SetLike.instMembership",
"AddSubmonoid.mem_toSubsemigroup"
] | false |
Mul.recOn | Init.Prelude | [
"Mul.mk",
"Mul",
"Mul.rec"
] | false |
SubmoduleClass.module'._proof_2 | Mathlib.Algebra.Module.Submodule.Defs | [
"SetLike",
"MulOne.toOne",
"instHSMul",
"Monoid.toMulOneClass",
"congrArg",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"SMul",
"AddMonoid.toAddZeroClass",
"SMulMemClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Subtype",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"one... | false |
_private.Mathlib.NumberTheory.Divisors.0.Nat.pairwise_divisorsAntidiagonalList_snd._simp_1_4 | Mathlib.NumberTheory.Divisors | [
"Prod.mk",
"propext",
"Prod.forall",
"Prod",
"Eq"
] | false |
_private.Lean.Compiler.LCNF.DeclHash.0.Lean.Compiler.LCNF.instHashableSignature.hash.match_1 | Lean.Compiler.LCNF.DeclHash | [
"Lean.Compiler.LCNF.Signature.casesOn",
"Lean.Compiler.LCNF.Signature",
"Lean.Expr",
"Lean.Compiler.LCNF.Purity",
"Array",
"List",
"Bool",
"Lean.Name",
"Lean.Compiler.LCNF.Param",
"Lean.Compiler.LCNF.Signature.mk"
] | false |
USize.lt_of_le_of_lt | Init.Data.UInt.Lemmas | [
"Eq.mpr",
"instLEUSize",
"Nat.lt_of_le_of_lt",
"id",
"_private.Init.Data.UInt.Lemmas.0.USize.lt_of_le_of_lt._simp_1_2",
"LE.le",
"instLENat",
"USize.toNat",
"implies_congr",
"Nat",
"LT.lt",
"_private.Init.Data.UInt.Lemmas.0.USize.lt_of_le_of_lt._simp_1_1",
"instLTUSize",
"instLTNat",
"Eq... | true |
Lean.Elab.Term.StructInst.SourcesView.noConfusionType | Lean.Elab.StructInst | [
"Lean.Elab.Term.StructInst.SourcesView",
"Lean.Elab.Term.StructInst.SourcesView.casesOn",
"Lean.Syntax",
"Array",
"Eq",
"Option",
"Lean.Elab.Term.StructInst.ExplicitSourceView"
] | false |
CategoryTheory.monoidalCategoryMop._proof_11 | Mathlib.CategoryTheory.Monoidal.Opposite | [
"CategoryTheory.MonoidalOpposite.mop",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.MonoidalOpposite.unmop",
"CategoryTheory.MonoidalCategory.whiskerLeftIso",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.MonoidalOpposite",
"Quiver.Hom",
"CategoryTheory.MonoidalCate... | false |
ZSpan.fract_eq_self | Mathlib.Algebra.Module.ZLattice.Basic | [
"NormedCommRing.toNormedRing",
"Finsupp.instFunLike",
"Preorder.toLT",
"Semiring.toModule",
"NormedRing.toRing",
"Finsupp.module",
"NormedSpace",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"_private.Mathlib.Algebra.Module.ZLattice.Basic.0.ZSpan.fract_eq_self._simp_1_1",
"Int.fract",
"LinearOr... | true |
groupHomology.inhomogeneousChains.d._proof_4 | Mathlib.RepresentationTheory.Homological.GroupHomology.Basic | [
"Finsupp.smulZeroClass",
"Rep.V",
"CommRing",
"Finsupp.smulCommClass",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"AddMonoid.toAddZeroClass",
"Group",
"Rep.hV1",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"DistribSMul.t... | false |
instDecidableIsValidUTF8 | Init.Data.String.Basic | [
"decidable_of_iff",
"Decidable",
"ByteArray.validateUTF8_eq_true_iff",
"instDecidableEqBool",
"Bool.true",
"Bool",
"ByteArray.validateUTF8",
"ByteArray",
"Eq",
"ByteArray.IsValidUTF8"
] | true |
Matroid.IsBasis'.eRk_eq_encard | Mathlib.Combinatorics.Matroid.Rank.ENat | [
"Eq.mpr",
"Set.encard",
"Matroid.Indep.eRk_eq_encard",
"congrArg",
"Matroid.IsBasis'",
"id",
"Matroid.IsBasis'.indep",
"ENat",
"Matroid.eRk",
"Matroid.IsBasis'.eRk_eq_eRk",
"Eq.refl",
"Eq.symm",
"Eq",
"Matroid",
"Set"
] | true |
AddOpposite.coe_symm_opAddEquiv | Mathlib.Algebra.Group.Equiv.Opposite | [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddOpposite",
"AddOpposite.instAdd",
"AddCommMonoid",
"AddOpposite.opAddEquiv",
"AddEquiv",
"AddZero.toAdd",
"AddOpposite.unop",
"AddCommMonoid.toAddMonoid",
"AddEquiv.instEquivLike",
"Eq",
"DFunLike.coe",
"rfl",
"AddEquiv.symm",
"... | true |
LocalSubring.exists_le_valuationSubring | Mathlib.RingTheory.Valuation.LocalSubring | [
"Iff.mpr",
"LocalSubring.isLocalRing",
"SubmonoidClass.instIsDedekindFiniteMonoidSubtypeMem",
"NonAssocSemiring.toAddCommMonoidWithOne",
"_private.Mathlib.RingTheory.Valuation.LocalSubring.0.LocalSubring.exists_le_valuationSubring.match_1_1",
"RingHom.instRingHomClass",
"MulOne.toOne",
"LocalSubring.m... | true |
AddMonCat.forget_createsLimit._proof_6 | Mathlib.Algebra.Category.MonCat.Limits | [
"Eq.mpr",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"Subtype.mk.congr_simp",
"CategoryTheory.Limits.Cone",
"AddMonCat.instConcreteCategoryAddMonoidHomCarrier",
"AddMonoidHom.instAddMonoidHomClass",
"Equiv.instEquivLike",
"CategoryTheory.Limits.Types.Small.limitCone",
"AddMonoid.toA... | false |
Complex.tan | Mathlib.Analysis.Complex.Trigonometric | [
"instHDiv",
"Complex.cos",
"Complex.sin",
"Complex.instDivInvMonoid",
"HDiv.hDiv",
"DivInvMonoid.toDiv",
"Complex"
] | true |
isMinOn_Iic_of_deriv | Mathlib.Analysis.Calculus.DerivativeTest | [
"Real.instIsOrderedRing",
"IsOrderedModule.toPosSMulMono",
"Real.partialOrder",
"Real.instLE",
"Real",
"Set.Ioi",
"Preorder.toLT",
"convex_Iic",
"Semiring.toModule",
"Set.nonempty_Ioi._simp_1",
"MulZeroClass.toMul",
"Real.denselyNormedField",
"instNoMaxOrderOfNontrivial",
"Real.instZero",
... | true |
Finset.sup_eq_bot_of_isEmpty | Mathlib.Data.Finset.Lattice.Fold | [
"Eq.mpr",
"congrArg",
"Finset",
"False.elim",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"Membership.mem",
"id",
"Bot.bot",
"IsEmpty",
"Finset.instSetLike",
"propext",
"Finset.sup",
"SemilatticeSup.toPartialOrder",
"IsEmpty.false",
"Eq",
"Semilattic... | true |
QuasiconcaveOn.convex_gt | Mathlib.Analysis.Convex.Quasiconvex | [
"OrderDual.toDual",
"QuasiconvexOn.convex_lt",
"Preorder.toLT",
"Equiv.instEquivLike",
"LinearOrder",
"SMul",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Function.comp",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"PartialOrder",
"DistribLattice.toLattice",
"Equiv",
"A... | true |
Nat.prod_divisors_prime_pow | Mathlib.NumberTheory.Divisors | [
"Nat.divisors_prime_pow",
"Nat.Prime",
"congrArg",
"Finset",
"Nat.instMonoid",
"Finset.map",
"Membership.mem",
"Function.Embedding.mk",
"instOfNatNat",
"Finset.prod_congr",
"Function.Embedding",
"Finset.prod",
"Monoid.toPow",
"Finset.range",
"Nat.divisors",
"instHAdd",
"HPow.hPow",
... | true |
_private.Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic.0.IsStrictlyPositive.sqrt._proof_1_8 | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic | [
"_private.Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic.0.IsStrictlyPositive.sqrt._proof_1_3",
"IsSelfAdjoint",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"Ring.toNonAssocRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"_private.Mathlib... | false |
Equiv.semilatticeInf | Mathlib.Order.Lattice | [
"Preorder.toLT",
"Equiv.instEquivLike",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"Equiv.semilatticeInf._proof_2",
"PartialOrder",
"Equiv.min",
"Equiv",
"SemilatticeInf.toMin",
"Min",
"Function.Injective.semilatticeInf",
"SemilatticeInf",
"Equiv.partialOr... | true |
StrictMonoOn.add | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"Preorder.toLT",
"AddRightStrictMono",
"Membership.mem",
"instHAdd",
"AddLeftStrictMono",
"add_lt_add_of_lt_of_lt",
"HAdd.hAdd",
"LT.lt",
"StrictMonoOn",
"Set.instMembership",
"Add",
"Preorder",
"Set"
] | true |
Submodule.mem_span_set | Mathlib.LinearAlgebra.Finsupp.LinearCombination | [
"Eq.mpr",
"Submodule",
"instHSMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"Finset",
"AddMonoid.toAddZeroClass",
"Finsupp.sum",
"Finsupp.support",
"Membership.mem",
"Exists",
"Eq.rec",
"AddZeroClass.toAddZero",
"id",
"DistribSMul.toSMulZeroClass",
"HasSubset.Subset",
"AddCommM... | true |
_private.Init.Data.Int.Gcd.0.Int.lcm_mul_right_dvd_mul_lcm._simp_1_1 | Init.Data.Int.Gcd | [
"Nat.lcm",
"Dvd.dvd",
"HMul.hMul",
"instMulNat",
"Nat.lcm_mul_right_dvd_mul_lcm",
"Nat.instDvd",
"Nat",
"True",
"eq_true",
"Eq",
"instHMul"
] | false |
MulOpposite.instCancelCommMonoid.eq_1 | Mathlib.Algebra.Group.Opposite | [
"CancelCommMonoid.toCommMonoid",
"CancelCommMonoid.mk",
"MulOpposite",
"Eq.refl",
"MulOpposite.instCancelCommMonoid._proof_1",
"MulOpposite.instCancelCommMonoid",
"Eq",
"MulOpposite.instCommMonoid",
"CancelCommMonoid"
] | true |
AdicCompletion.AdicCauchySequence.instAddCommGroup._proof_4 | Mathlib.RingTheory.AdicCompletion.Basic | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"Ideal",
"CommRing.toCommSemiring",
"Nat",
"AdicCompletion.AdicCauchySequence.instNeg",
"AdicCompletion.IsAdicCauchy",
"Module",
"Subtype.val",
"Eq",
"AdicCompletion.AdicCauchySequence",
"Neg.neg",
"rf... | false |
TrivSqZeroExt.isNilpotent_inr | Mathlib.RingTheory.DualNumber | [
"TrivSqZeroExt.inr",
"TrivSqZeroExt.instPowNatOfDistribMulActionMulOpposite",
"TrivSqZeroExt",
"HMul.hMul",
"pow_two",
"Monoid.toMulOneClass",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"MulOpposite",
"AddZeroClass.toAddZero",
"TrivSqZeroExt.inr_mul_inr",
"MulO... | true |
_private.Lean.Server.Logging.0.Lean.Server.Logging.LogEntry.recOn | Lean.Server.Logging | [
"Lean.JsonRpc.MessageKind",
"_private.Lean.Server.Logging.0.Lean.Server.Logging.LogEntry.rec",
"Lean.JsonRpc.Message",
"_private.Lean.Server.Logging.0.Lean.Server.Logging.LogEntry",
"Std.Time.ZonedDateTime",
"Lean.JsonRpc.MessageDirection",
"_private.Lean.Server.Logging.0.Lean.Server.Logging.LogEntry.mk... | false |
_private.Lean.Meta.Sym.Offset.0.Lean.Meta.Sym.toOffset._sparseCasesOn_1 | Lean.Meta.Sym.Offset | [
"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 |
Summable.tsum_of_nat_of_neg | Mathlib.Topology.Algebra.InfiniteSum.NatInt | [
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Int.instNegInt",
"Int",
"HasSum.of_nat_of_neg",
"Nat.cast",
"SummationFilter.instNeBotUnconditional",
"SubNegMonoid.toSub",
"TopologicalSpace",
"in... | true |
Lean.Elab.Command.CtorView.modifiers | Lean.Elab.MutualInductive | [
"Lean.Elab.Command.CtorView",
"Lean.Elab.Modifiers"
] | true |
Algebra.IsAlgebraic.mk._flat_ctor | Mathlib.RingTheory.Algebraic.Defs | [
"CommRing",
"IsAlgebraic",
"Algebra",
"Algebra.IsAlgebraic",
"Algebra.IsAlgebraic.mk",
"CommRing.toCommSemiring",
"Ring.toSemiring",
"Ring"
] | false |
CategoryTheory.Functor.LaxMonoidal.ofBifunctor.bottomMapᵣ | Mathlib.CategoryTheory.Monoidal.Multifunctor | [
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.MonoidalCategory.rightUnitorNatIso",
"C... | true |
Subarray.mkSlice_roi_eq_mkSlice_rco | Init.Data.Slice.Array.Lemmas | [
"Std.Rci.mk",
"Std.Rco.Sliceable.mkSlice",
"Subarray",
"instSliceableSubarrayNat_5",
"congrArg",
"instSliceableSubarrayNat_2",
"instOfNatNat",
"Std.Roi.mk",
"instHAdd",
"Std.Rci.Sliceable.mkSlice",
"HAdd.hAdd",
"Std.Slice.Internal.SubarrayData",
"Nat",
"instSliceableSubarrayNat_1",
"True... | true |
LinearEquiv.cast_symm_apply | Mathlib.Algebra.Module.Equiv.Defs | [
"LinearEquiv.symm",
"congrArg",
"cast",
"LinearEquiv.cast",
"AddCommMonoid",
"RingHomInvPair.ids",
"LinearEquiv",
"Semiring",
"LinearEquiv.instEquivLike",
"Eq.refl",
"Module",
"Eq.symm",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
MeasureTheory.MemLp.integrable_enorm_pow | Mathlib.MeasureTheory.Function.L1Space.Integrable | [
"False",
"Real",
"MeasureTheory.Measure",
"congrArg",
"CommSemiring.toSemiring",
"ENNReal.instPowReal",
"ENNReal.instCharZero",
"AddMonoid.toAddZeroClass",
"ENNReal.rpow_natCast",
"MeasureTheory.Integrable",
"cast",
"AddZeroClass.toAddZero",
"Eq.mp",
"ENNReal.toReal_natCast",
"AddMonoidW... | true |
SkewMonoidAlgebra.liftNCRingHom._proof_1 | Mathlib.Algebra.SkewMonoidAlgebra.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"RingHomClass.toAddMonoidHomClass",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"RingHom.instFunLike",
"Semiring",
"AddMonoidWithOne.toAddMo... | false |
Nat.recOnPrimePow._proof_5 | Mathlib.Data.Nat.Factorization.Induction | [
"instPowNat",
"Finsupp.instFunLike",
"Nat.Prime.factorization_pos_of_dvd",
"Nat.instCanonicallyOrderedAdd",
"MulOne.toOne",
"False",
"Nat.instMulZeroClass",
"Preorder.toLT",
"instHDiv",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"HMul.hMul",
"eq_false",
"MulZeroClass.toMul",
"IsSt... | false |
CategoryTheory.LocalizerMorphism.RightResolution.mk_surjective | Mathlib.CategoryTheory.Localization.Resolution | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.LocalizerMorphism.RightResolution",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.LocalizerMorphism.RightResolution.w",
"Exists",
"CategoryTheory.LocalizerMorphism.RightResolution.X₁",
"CategoryTheory.LocalizerMorphism.RightR... | true |
AffineMap.map_midpoint | Mathlib.LinearAlgebra.AffineSpace.Midpoint | [
"AffineMap.instFunLike",
"AddCommGroup.toAddCommMonoid",
"Nat.instAtLeastTwoHAddOfNat",
"AffineMap.apply_lineMap",
"AddGroupWithOne.toAddMonoidWithOne",
"Invertible.invOf",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"AffineMap",
"midpoint._proof_1"... | true |
Std.DHashMap.getKey?_union_of_not_mem_right | Std.Data.DHashMap.Lemmas | [
"Std.DHashMap.instUnion",
"congrArg",
"Std.DHashMap.Raw",
"Membership.mem",
"Eq.mp",
"Std.DHashMap.instMembership",
"Std.DHashMap.wf",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"LawfulHashable",
"Subtype.mk",
"Std.DHashMap.contains",
"EquivBEq",
"Std.DHashMap.inner",
"Std.D... | true |
_private.Mathlib.RingTheory.Jacobson.Ideal.0.Ideal.IsLocal.mem_jacobson_or_exists_inv.match_1_3 | Mathlib.RingTheory.Jacobson.Ideal | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"Membership.mem",
"Exists",
"Set.instSingletonSet",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Ideal",
"And.casesOn",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddMonoidWi... | false |
Std.ExtDHashMap.Const.insertManyIfNewUnit_list_eq_empty_iff._simp_1 | Std.Data.ExtDHashMap.Lemmas | [
"instForInOfForIn'",
"Std.ExtDHashMap.instEmptyCollection",
"inferInstance",
"Id",
"Membership",
"LawfulHashable",
"Std.ExtDHashMap.Const.insertManyIfNewUnit_list_eq_empty_iff",
"List",
"And",
"Unit",
"EquivBEq",
"List.instMembership",
"propext",
"Std.ExtDHashMap",
"Id.instMonad",
"Has... | false |
Lean.Meta.DiagSummary.data._default | Lean.Meta.Diagnostics | [
"Lean.MessageData",
"id",
"List.toArray",
"Array",
"List.nil"
] | false |
Bundle.TotalSpace.recOn | Mathlib.Data.Bundle | [
"Bundle.TotalSpace.mk",
"Bundle.TotalSpace.rec",
"Bundle.TotalSpace"
] | false |
ENNReal.finsetSum_iSup | Mathlib.Data.ENNReal.BigOperators | [
"Eq.mpr",
"ENNReal.instAdd",
"Finset.sum_cons",
"ENNReal.instAddCommMonoid",
"Finset.cons_induction",
"Finset.cons",
"congrArg",
"iSup",
"Finset",
"covariant_swap_add_of_covariant_add",
"AddMonoid.toAddZeroClass",
"add_le_add",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem"... | true |
Lean.SubExpr.Pos.pushAppArg | Lean.SubExpr | [
"instOfNatNat",
"Lean.SubExpr.Pos",
"Lean.SubExpr.Pos.push",
"Nat",
"OfNat.ofNat"
] | true |
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