name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
PowerSeries.coeff_invUnitsSub | Mathlib.RingTheory.PowerSeries.WellKnown | [
"Semiring.toModule",
"AddGroupWithOne.toAddMonoidWithOne",
"LinearMap.instFunLike",
"Units",
"PowerSeries.coeff",
"PowerSeries.coeff_mk",
"instOfNatNat",
"MvPowerSeries.instModule",
"divp",
"LinearMap",
"MvPowerSeries.instAddCommMonoid",
"Monoid.toPow",
"NonUnitalNonAssocSemiring.toAddCommMo... | true |
CategoryTheory.Abelian.Ext.covariantSequence_exact | Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences | [
"CategoryTheory.Abelian.toPreadditive",
"AddCommGrpCat.instCategory",
"CategoryTheory.Abelian.Ext.postcomp",
"CategoryTheory.Abelian.Ext.instAddCommGroup",
"CategoryTheory.ShortComplex.mk",
"AddMonoid.toAddZeroClass",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.A... | true |
Lean.Elab.Term.Do.DoIfView._sizeOf_inst | Lean.Elab.Do.Legacy | [
"Lean.Elab.Term.Do.DoIfView",
"Lean.Elab.Term.Do.DoIfView._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
Lean.Meta.Grind.AC.ProofM.State.mk._flat_ctor | Lean.Meta.Tactic.Grind.AC.Proof | [
"UInt64",
"Lean.Meta.Grind.AC.instHashableSeq_lean",
"Lean.Grind.AC.Expr",
"Lean.Meta.Grind.AC.ProofM.State",
"Lean.Expr",
"Lean.Meta.Grind.AC.instHashableExpr_lean",
"Std.HashMap",
"instHashableNat",
"instBEqOfDecidableEq",
"Lean.Grind.AC.instBEqSeq",
"Lean.Meta.Grind.AC.ProofM.State.mk",
"Le... | false |
Sum.Lex.rec | Init.Data.Sum.Basic | [
"Sum",
"Sum.inl",
"Sum.Lex.inl",
"Sum.inr",
"Sum.Lex.sep",
"Sum.Lex.inr",
"Sum.Lex"
] | false |
Quiver.Arborescence.rec | Mathlib.Combinatorics.Quiver.Arborescence | [
"Quiver.Arborescence",
"Unique",
"Quiver.Path",
"Quiver",
"Quiver.Arborescence.mk"
] | false |
Aesop.extractProof | Aesop.Tree.ExtractProof | [
"Aesop.BaseM",
"Lean.Core.instMonadLiftIOCoreM",
"IO.instMonadLiftSTRealWorldBaseIO",
"ReaderT",
"Aesop.Goal",
"Lean.Meta.State",
"instMonadLiftT",
"IO",
"ST.Ref.get",
"Lean.Meta.MetaM",
"IO.RealWorld",
"liftM",
"ReaderT.instMonadLift",
"Aesop.GoalRef",
"Unit",
"ST",
"Lean.Core.CoreM... | true |
List.findSome?_replicate | Init.Data.List.Find | [
"List.replicate",
"False",
"congrArg",
"Nat.add_eq_zero_iff._simp_1",
"Option.some",
"Membership.mem",
"id",
"List.findSome?.match_1",
"Ne",
"instOfNatNat",
"ite_cond_eq_true",
"Nat.casesAuxOn",
"Option.none",
"List",
"instHAdd",
"And",
"Unit",
"List.mem_replicate._simp_1",
"List... | true |
SetLike.gsemiring._proof_10 | Mathlib.Algebra.DirectSum.Internal | [
"SetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddSubmonoidClass",
"AddZeroClass.toAddZero",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Nat.cast",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
... | false |
_private.Lean.Server.CodeActions.Basic.0.Lean.Server.handleCodeAction.match_1 | Lean.Server.CodeActions.Basic | [
"Lean.Server.CodeActionProvider",
"Prod.mk",
"Lean.Name",
"Prod",
"Prod.casesOn"
] | false |
Std.Iterators.Types.Drop.mk.noConfusion | Std.Data.Iterators.Combinators.Monadic.Drop | [
"id",
"heq_of_eq",
"Std.Iterators.Types.Drop",
"Nat",
"Eq.refl",
"HEq",
"Std.IterM",
"Std.Iterators.Types.Drop.mk",
"Eq",
"Std.Iterators.Types.Drop.noConfusion"
] | false |
Witt._aux_Mathlib_RingTheory_WittVector_StructurePolynomial___unexpand_wittPolynomial_2 | Mathlib.RingTheory.WittVector.StructurePolynomial | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.matchesIdent",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.T... | false |
EuclideanGeometry.side_angle_side | Mathlib.Geometry.Euclidean.Congruence | [
"Real.instIsOrderedRing",
"Eq.mpr",
"Real.partialOrder",
"Real",
"HMul.hMul",
"pow_two",
"Real.cos",
"Monoid.toMulOneClass",
"Real.instRCLike",
"congrArg",
"Real.instSub",
"Nat.instAtLeastTwoHAddOfNat",
"dist_nonneg",
"HSub.hSub",
"Real.semiring",
"id",
"MulOne.toMul",
"EMetricSpac... | true |
LinearMap.submoduleOf_span_singleton_of_mem | Mathlib.LinearAlgebra.Span.Basic | [
"SMulMemClass.smul_mem",
"Eq.mpr",
"Submodule",
"instHSMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"_private.Mathlib.LinearAlgebra.Span.Basic.0.LinearMap.submoduleOf_span_singleton_of_mem._simp_1_1",
"Submodule.addCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Subtype... | true |
Real.arsinh_lt_arsinh | Mathlib.Analysis.SpecialFunctions.Arsinh | [
"OrderIso.lt_iff_lt",
"Real.instLE",
"Real",
"Real.instLT",
"Real.sinhOrderIso",
"Real.arsinh",
"OrderIso.symm",
"Iff",
"LT.lt",
"Real.instPreorder"
] | true |
CategoryTheory.Limits.WalkingMulticospan.functorExt.congr_simp | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"CategoryTheory.Limits.MulticospanShape.snd",
"CategoryTheory.Functor",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingMulticospan.instSmallCategory",
"CategoryTheory.Limits.WalkingMul... | true |
MonoidHom.coe_mgraph | Mathlib.Algebra.Group.Graph | [
"Monoid",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"setOf",
"Prod.instMulOneClass",
"Prod.fst",
"MulOneClass.toMulOne",
"SetLike.coe",
"Eq.refl",
"Submonoid.instSetLike",
"Prod",
"Eq",
"Prod.snd",
"DFunLike.coe",
"MonoidHom.mgraph",
"Submonoid",
"Set"
] | true |
Set.sub_mem_Ioc_iff_right | Mathlib.Algebra.Order.Interval.Set.Group | [
"Set.Ioc",
"Preorder.toLT",
"AddCommGroup.toAddCommMonoid",
"instIsLeftCancelAddOfAddLeftReflectLE",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddZeroClass.toAddZero",
"PartialOrder",
"AddCommGroup",
"... | true |
CategoryTheory.SimplicialObject.Splitting.IndexSet.mk_fst | Mathlib.AlgebraicTopology.SimplicialObject.Split | [
"Opposite",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.SimplicialObject.Splitting.IndexSet.mk",
"Subtype",
"Sigma.fst",
"Opposite.op",
"SimplexCategory",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"SimplexCategory.smallCategory",
... | true |
_private.Mathlib.Data.Nat.MaxPowDiv.0.Nat.maxPowDvdDiv.go_spec._simp_1_4 | Mathlib.Data.Nat.MaxPowDiv | [
"HMul.hMul",
"instMulNat",
"Nat.mul_assoc",
"Nat",
"Eq.symm",
"Eq",
"instHMul"
] | false |
Int.gcd_eq_natAbs_left | Init.Data.Int.Gcd | [
"Iff.mpr",
"Int.gcd",
"Dvd.dvd",
"Int",
"Int.instDvd",
"Nat",
"Int.natAbs",
"Int.gcd_eq_natAbs_left_iff_dvd",
"Eq"
] | true |
hasFDerivAt_tsum_of_isPreconnected | Mathlib.Analysis.Calculus.SmoothSeries | [
"HasFDerivAt",
"SummationFilter.mk",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toNormedAddCommGroup",
"Real.instLE",
"Real",
"CompleteSpace",
"NormedSpace.toIsBoundedSMul",
"Set.Ici",
"NormedSpace",
"ContinuousLinearMap.topologicalSpace",
"FrechetUrysohnSpace.t... | true |
Lean.Parser.Term.doNested._regBuiltin.Lean.Parser.Term.doNested.parenthesizer_11 | Lean.Parser.Do | [
"Lean.Parser.Term.doNested.parenthesizer",
"Lean.Name.mkStr5",
"IO",
"Lean.PrettyPrinter.Parenthesizer",
"Lean.PrettyPrinter.parenthesizerAttribute",
"Unit",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
Lean.Meta.GeneralizeIndicesSubgoal.mk.noConfusion | Lean.Meta.Tactic.Cases | [
"Lean.Meta.GeneralizeIndicesSubgoal.noConfusion",
"Lean.MVarId",
"id",
"Lean.FVarId",
"Array",
"Lean.Meta.GeneralizeIndicesSubgoal.mk",
"Nat",
"Lean.Meta.GeneralizeIndicesSubgoal",
"Eq"
] | false |
UniformEquiv.uniformContinuous | Mathlib.Topology.UniformSpace.Equiv | [
"UniformContinuous",
"UniformSpace",
"UniformEquiv.instEquivLike",
"UniformEquiv.uniformContinuous_toFun",
"DFunLike.coe",
"UniformEquiv",
"EquivLike.toFunLike"
] | true |
OpenPartialHomeomorph.prod_eq_prod_of_nonempty' | Mathlib.Topology.OpenPartialHomeomorph.Constructions | [
"Eq.mpr",
"congrArg",
"Iff.rfl",
"OpenPartialHomeomorph.prod_eq_prod_of_nonempty",
"instTopologicalSpaceProd",
"id",
"eq_comm",
"TopologicalSpace",
"And",
"Iff",
"Set.Nonempty",
"propext",
"PartialEquiv.source",
"Prod",
"OpenPartialHomeomorph.prod",
"OpenPartialHomeomorph.toPartialEqui... | true |
Metric.hausdorffDist_le_of_infDist | Mathlib.Topology.MetricSpace.HausdorffDistance | [
"Metric.hausdorffDist_empty'",
"Eq.mpr",
"Metric.hausdorffDist",
"Real.instLE",
"Real",
"Real.instZero",
"ENNReal.ofReal",
"congrArg",
"Metric.hausdorffEDist_le_of_infEDist",
"Metric.infDist",
"Membership.mem",
"Metric.hausdorffDist_empty",
"Eq.mp",
"id",
"Metric.infEDist_ne_top",
"LE.... | true |
unique_uniformity_of_compact | Mathlib.Topology.UniformSpace.Compact | [
"UniformSpace",
"Eq.mpr",
"Filter.instSupSet",
"congrArg",
"iSup",
"uniformity",
"instTopologicalSpaceProd",
"nhds",
"id",
"Prod.mk",
"compactSpace_uniformity",
"CompactSpace",
"UniformSpace.ext",
"TopologicalSpace",
"Eq.refl",
"Prod",
"UniformSpace.toTopologicalSpace",
"Eq",
"Fi... | true |
Nat.coprime_sub_self_left._simp_1 | Mathlib.Data.Nat.GCD.Basic | [
"Nat.Coprime",
"HSub.hSub",
"instSubNat",
"LE.le",
"instLENat",
"instHSub",
"Nat",
"propext",
"Nat.coprime_sub_self_left",
"Eq"
] | false |
PrimeSpectrum.zariskiTopology | Mathlib.RingTheory.Spectrum.Prime.Topology | [
"PrimeSpectrum.zeroLocus",
"PrimeSpectrum.zariskiTopology._proof_4",
"CommSemiring",
"TopologicalSpace",
"PrimeSpectrum",
"Set.range",
"PrimeSpectrum.zariskiTopology._proof_3",
"PrimeSpectrum.zariskiTopology._proof_2",
"TopologicalSpace.ofClosed",
"Set"
] | true |
CategoryTheory.Functor.Monoidal.map_leftUnitor_inv_assoc | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.Monoidal.map_leftUnitor_inv",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategoryStruct.leftUnitor",
"CategoryTheory.Functor.LaxMonoi... | true |
_private.Mathlib.MeasureTheory.Constructions.BorelSpace.Order.0.AEMeasurable.isLUB._simp_1_2 | Mathlib.MeasureTheory.Constructions.BorelSpace.Order | [
"Preorder.toLE",
"IsBot",
"IsLUB",
"propext",
"Set.instEmptyCollection",
"isLUB_empty_iff",
"EmptyCollection.emptyCollection",
"Eq",
"Preorder",
"Set"
] | false |
IntermediateField.normalClosure_def' | Mathlib.FieldTheory.Normal.Closure | [
"IntermediateField.instPartialOrder",
"IntermediateField.isScalarTower_mid'",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"_private.Mathlib.FieldTheory.Normal.Closure.0.IntermediateField.normalClosure_def'.match_1_3",
"Subsemiring.instSetLike",
"instSMulOfMul",
"IsScalarTower.right",
"CommRing.to... | true |
Lean.Meta.instHashableOrigin.match_1 | Lean.Meta.Tactic.Simp.SimpTheorems | [
"Lean.Meta.Origin.decl",
"Nat.hasNotBit",
"Lean.Meta.Origin.ctorIdx",
"Lean.Meta.instBEqOrigin._sparseCasesOn_1",
"Bool.true",
"Bool.casesOn",
"Bool",
"Lean.Name",
"Lean.Meta.Origin",
"Bool.false"
] | false |
Lean.Meta.Grind.ActionResult._sizeOf_inst | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.ActionResult._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Lean.Meta.Grind.ActionResult"
] | false |
Bitraversable.bitraverse | Mathlib.Control.Bitraversable.Basic | [
"Bitraversable",
"Applicative"
] | true |
Lean.Meta.Grind.AC.getTermOpIds | Lean.Meta.Tactic.Grind.AC.Util | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Sym.ExprPtr.mk",
"Lean.Meta.Grind.Goal",
"StateRefT'.instAlternativeOfMonad",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.Sym.Context",
"Option.getD",
"ReaderT.instMonad",
"Lean.Meta.Grind.Context",
"Lean.Meta.Grind.AC.State.exprToOpIds",
... | true |
Associates.prod_le | Mathlib.RingTheory.UniqueFactorizationDomain.FactorSet | [
"Nontrivial",
"CommMonoidWithZero.toCommMonoid",
"WithTop.instPreorder",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Irreducible",
"Multiset",
"Eq.mp",
"Subtype",
"UniqueFactorizationMonoid",
"CommMonoidWithZero.toMonoidWithZero",
"LE.le",
"Associates.factors_mono",
"Associa... | true |
Lean.JsonRpc.ErrorCode.methodNotFound.sizeOf_spec | Lean.Data.JsonRpc | [
"Lean.JsonRpc.ErrorCode",
"instOfNatNat",
"Nat",
"Lean.JsonRpc.ErrorCode._sizeOf_inst",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.JsonRpc.ErrorCode.methodNotFound"
] | true |
linearIndepOn_zero_iff._simp_1 | Mathlib.LinearAlgebra.LinearIndependent.Defs | [
"Nontrivial",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Pi.instZero",
"AddCommMonoid",
"AddZero.toZero",
"linearIndepOn_zero_iff",
"propext",
"Set.instEmptyCollection",
"Semiring",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"EmptyCollection.emptyCollection",
"Module",
"Of... | false |
UniqueFactorizationMonoid.toNormalizedGCDMonoid._proof_6 | Mathlib.RingTheory.UniqueFactorizationDomain.GCDMonoid | [
"Associates.mk",
"NormalizationMonoid",
"MonoidWithZeroHom.funLike",
"Associates.normalize_out",
"UniqueFactorizationMonoid",
"CommMonoidWithZero.toMonoidWithZero",
"Associates.instMax",
"MonoidWithZeroHom",
"MonoidWithZero.toMulZeroOneClass",
"Associates",
"Max.max",
"CommMonoidWithZero",
"... | false |
Stream'.nil_append_stream | Mathlib.Data.Stream.Init | [
"Stream'",
"Stream'.appendStream'",
"Eq",
"rfl",
"List.nil"
] | true |
Lean.Linter.initFn._@.Lean.Linter.UnusedVariables.3334728626._hygCtx._hyg.2 | Lean.Linter.UnusedVariables | [
"IO.mkRef",
"instMonadLiftT",
"IO",
"EIO",
"liftM",
"List.toArray",
"Array",
"Lean.Linter.IgnoreFunction",
"IO.Error",
"IO.Ref",
"instMonadLiftTOfMonadLift",
"BaseIO",
"instMonadLiftBaseIOEIO",
"List.nil"
] | false |
Int16.toInt64_toISize | Init.Data.SInt.Lemmas | [
"Int16",
"Int64.toInt",
"congrArg",
"ISize.toInt_toInt64",
"Int64",
"Int",
"congr",
"True",
"eq_self",
"Int16.toInt_toInt64",
"Int16.toInt",
"of_eq_true",
"Int16.toISize",
"Int16.toInt64",
"ISize.toInt64",
"Eq",
"Int64.toInt.inj",
"Int16.toInt_toISize",
"Eq.trans",
"ISize.toInt... | true |
_private.Init.Data.Int.Gcd.0.Int.gcd_eq_one_iff._simp_1_1 | Init.Data.Int.Gcd | [
"Int.gcd",
"Dvd.dvd",
"Int",
"Nat.cast",
"Int.instDvd",
"And",
"Nat",
"Int.gcd_eq_iff",
"propext",
"instNatCastInt",
"Eq"
] | false |
pow_three' | Mathlib.Algebra.Group.Defs | [
"Monoid",
"Eq.mpr",
"HMul.hMul",
"pow_two",
"Monoid.toMulOneClass",
"congrArg",
"pow_succ",
"id",
"MulOne.toMul",
"instOfNatNat",
"Monoid.toPow",
"instHAdd",
"MulOneClass.toMulOne",
"HPow.hPow",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq.refl",
"instHPow",
"OfNat.ofNat",
"Eq",
"... | true |
Matrix.vecMul_eq_sum | Mathlib.Data.Matrix.Mul | [
"instHSMul",
"instSMulOfMul",
"Pi.addCommMonoid",
"HMul.hMul",
"Finset.univ",
"Matrix",
"Matrix.vecMul",
"Function.hasSMul",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Fintype",
"Distrib.toMul",
"NonUnitalNonAssocSemiring.toDistrib",
"HSMul.hSMul",
"Finset.sum_fn",
"NonUnitalNonAssocS... | true |
_private.Mathlib.Topology.Sheaves.PUnit.0.TopCat.Presheaf.isSheaf_iff_isTerminal_of_indiscrete.match_1_1 | Mathlib.Topology.Sheaves.PUnit | [
"Lattice.toSemilatticeSup",
"Opposite",
"TopologicalSpace.Opens.instPartialOrder",
"CategoryTheory.Limits.IsTerminal",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"Preorder.toLE",
"TopCat.Presheaf",
"Preorder.smallCategory",
"Bot.bot",
"Nonempty.intro",
"TopCat.str... | false |
_private.Lean.Server.Completion.SyntheticCompletion.0.Lean.Server.Completion.findOutermostContextInfo?.go._sparseCasesOn_1 | Lean.Server.Completion.SyntheticCompletion | [
"Lean.Elab.CommandContextInfo",
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Lean.Elab.PartialContextInfo.rec",
"Lean.Elab.PartialContextInfo",
"Lean.Expr",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Elab.PartialContextInfo.ctorIdx",
"Array",
"Lean.Elab.PartialContextInfo.parentDeclCtx",
"Nat.land... | false |
_private.Lean.Data.Json.Printer.0.Lean.Json.needEscape.go.eq_def | Lean.Data.Json.Printer | [
"Eq.mpr",
"ByteArray.get",
"_private.Lean.Data.Json.Printer.0.Lean.Json.needEscape.go._proof_3",
"Nat.lt_of_lt_of_eq",
"UInt8.instOfNat",
"instSubsingletonDecidable",
"congrArg",
"String",
"InvImage",
"HSub.hSub",
"Decidable",
"WellFounded.Nat.fix",
"String.utf8ByteSize",
"instDecidableEqU... | true |
MeasureTheory.Content.outerMeasure_eq_iInf | Mathlib.MeasureTheory.Measure.Content | [
"iInf",
"R1Space",
"MeasureTheory.OuterMeasure",
"MeasureTheory.Content",
"HasSubset.Subset",
"MeasureTheory.Content.innerContent_bot",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"MeasureTheory.inducedOuterMeasure_eq_iInf",
"TopologicalSpace",
"MeasureTheory.Content.outerMe... | true |
String.Slice.dropSuffix?_slice_of_isEmpty | Init.Data.String.Lemmas.Pattern.TakeDrop.String | [
"String.Slice.sliceTo_endPos",
"String.Slice.Pattern.BackwardSliceSearcher.instBackwardPattern",
"congrArg",
"String.Slice.skipSuffix?_slice_of_isEmpty",
"Option.some",
"String.Slice",
"String.Slice.dropSuffix?_eq_map_skipSuffix?",
"String.Slice.isEmpty",
"Bool.true",
"String.Slice.endPos",
"Opt... | true |
Finset.affineCombination_affineCombinationSingleWeights | Mathlib.LinearAlgebra.AffineSpace.Combination | [
"Pi.Function.module",
"Semiring.toModule",
"AffineMap.instFunLike",
"Finset.affineCombinationSingleWeights",
"AddCommGroup.toAddCommMonoid",
"Finset",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddCommGroup",
"Finset.instAddTorsorForall",
"AffineMap",
"Finset.affineCombination",
"Finset.i... | true |
GroupLike | Mathlib.RingTheory.Coalgebra.GroupLike | [
"Coalgebra",
"CommSemiring.toSemiring",
"AddCommMonoid",
"CommSemiring",
"GroupLike.mk",
"Module"
] | true |
CategoryTheory.WithInitial.ofCommaMorphism_app | Mathlib.CategoryTheory.WithTerminal.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"CategoryTheory.Comma",
"CategoryTheory.WithInitial.ofCommaMorphism",
"CategoryTheory.commaCa... | true |
Topology.IsEmbedding.isStrictMap | Mathlib.Topology.Maps.Strict.Basic | [
"Topology.IsStrictMap.id",
"Function.comp",
"TopologicalSpace",
"Topology.IsEmbedding.isStrictMap_iff",
"Iff.mp",
"Topology.IsEmbedding",
"Topology.IsStrictMap"
] | true |
CategoryTheory.MorphismProperty.Comma.mapLeftIso_inverse_map_left | Mathlib.CategoryTheory.MorphismProperty.Comma | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.Comma.instCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.comp",
"CategoryTheory.Iso",
"CategoryT... | true |
Matroid.IsBase.finite | Mathlib.Combinatorics.Matroid.Basic | [
"_private.Mathlib.Combinatorics.Matroid.Basic.0.Matroid.IsBase.finite.match_1_1",
"Set.Finite",
"Exists",
"Matroid.IsBase",
"And",
"And.right",
"And.left",
"Matroid.RankFinite.exists_finite_isBase",
"Matroid.RankFinite",
"Matroid",
"Matroid.IsBase.finite_of_finite",
"Set"
] | true |
Quotient.congr | Mathlib.Logic.Equiv.Defs | [
"Equiv.instEquivLike",
"Equiv",
"Setoid",
"Iff",
"Quotient",
"Quot.congr",
"DFunLike.coe",
"Setoid.r",
"EquivLike.toFunLike"
] | true |
Set.Ioo_eq_empty | Mathlib.Order.Interval.Set.Basic | [
"Iff.mpr",
"False",
"Preorder.toLT",
"_private.Mathlib.Order.Interval.Set.Basic.0.Set.Ioo_eq_empty.match_1_1",
"Membership.mem",
"Set.eq_empty_iff_forall_notMem",
"LT.lt",
"Set.instEmptyCollection",
"LT.lt.trans",
"EmptyCollection.emptyCollection",
"Eq",
"Set.instMembership",
"Not",
"Set.I... | true |
Submonoid.unop_toSubsemigroup | Mathlib.Algebra.Group.Submonoid.MulOpposite | [
"Submonoid.toSubsemigroup",
"MulOpposite",
"MulOne.toMul",
"MulOneClass.toMulOne",
"Subsemigroup.unop",
"Subsemigroup",
"MulOpposite.instMulOneClass",
"MulOneClass",
"Eq",
"Submonoid.unop",
"Submonoid",
"rfl"
] | true |
_private.Lean.Meta.ExprDefEq.0.Lean.Meta.isDefEqProj._sparseCasesOn_1 | Lean.Meta.ExprDefEq | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
Lean.PersistentHashMap.Node.rec_1 | Lean.Data.PersistentHashMap | [
"Lean.PersistentHashMap.Entry.entry",
"Lean.PersistentHashMap.Entry",
"Lean.PersistentHashMap.Entry.ref",
"Lean.PersistentHashMap.Node",
"Lean.PersistentHashMap.Entry.null",
"Lean.PersistentHashMap.Node.collision",
"Lean.PersistentHashMap.Node.entries",
"List.cons",
"Array",
"List",
"Nat",
"Ar... | false |
HasFDerivAtFilter.comp | Mathlib.Analysis.Calculus.FDeriv.Comp | [
"ContinuousLinearMap.comp",
"NormedCommRing.toSeminormedCommRing",
"Asymptotics.IsBigOTVS",
"Trans.trans",
"sub_add_sub_cancel",
"NormedSpace.toIsBoundedSMul",
"map_sub",
"SemilinearMapClass.distribMulActionSemiHomClass",
"NormedSpace",
"HasFDerivAtFilter.isBigOTVS_sub",
"congrArg",
"DistribMu... | true |
le_ciInf_add | Mathlib.Order.ConditionallyCompleteLattice.Group | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"iInf",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"ConditionallyCompleteLattice",
"Preorder.toLE",
"AddRightMono",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"LE.le",
"SubNegZeroMonoid.toNegZ... | true |
_private.Batteries.Data.String.Legacy.0.String.Pos.Raw.utf8GetAux.match_1.eq_2 | Batteries.Data.String.Legacy | [
"String.Pos.Raw.utf8GetAux.match_1",
"String.Pos.Raw",
"List.cons",
"List",
"Eq.refl",
"Char",
"Eq",
"List.nil"
] | true |
Submodule.isOpenQuotientMap_mkQL | Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Quotient | [
"Submodule",
"Submodule.Quotient.addCommMonoid",
"QuotientModule.Quotient.topologicalSpace",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"Submodule.isOpenQuotientMap_mkQ",
"Submodule.hasQuotient",
"AddCommGroup",
"Submodule.Quotient.module",
"ContinuousLinearMap",
"Topological... | true |
LinearMap.extendTo𝕜'_apply | Mathlib.Analysis.RCLike.Extend | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"Semiring.toModule",
"NormedRing.toRing",
"RCLike.toNormedAlgebra",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"AddMon... | true |
AlgebraicGeometry.Scheme.Hom.appIso | Mathlib.AlgebraicGeometry.OpenImmersion | [
"AlgebraicGeometry.Scheme.Hom.opensFunctor",
"AlgebraicGeometry.Scheme.Hom.toLRSHom",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"Opposite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Top... | true |
_private.Init.Data.List.Lemmas.0.List.getLast?_dropLast.match_1_5 | Init.Data.List.Lemmas | [
"False",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"instOfNatNat",
"Nat.le.step",
"List.cons",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat.le",
"Nat",
"LT.lt",
"List.casesOn",
"Eq.ndrec",
"Nat.ctorIdx",
"instAddNat",
"Eq.refl",
"HEq",
"Nat.le.refl",
"instLTNat",
"Nat.le.cas... | false |
CommGroup.monoidHomMonoidHomEquiv._proof_3 | Mathlib.GroupTheory.FiniteAbelian.Duality | [
"Iff.mpr",
"OneHom.mk.injEq",
"Eq.mpr",
"MonoidHom.instCommGroup",
"MulOne.toOne",
"MonoidHom.instFunLike",
"CommGroup.monoidHomMonoidHomEquiv._proof_2",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"CommGroup.card_monoidHom_of_hasEnoughRootsOfUnity",
"OneHom.mk",
"Finite",
"funext_iff... | false |
CategoryTheory.NatTrans.naturality_app_assoc | Mathlib.CategoryTheory.Functor.Category | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.Functor.map",
"CategoryTheory.NatTrans.naturality_app",
"congr"... | true |
Lean.Meta.FunInfo.noConfusion | Lean.Meta.Basic | [
"Lean.Meta.FunInfo.casesOn",
"Array",
"Lean.Meta.ParamInfo",
"Lean.Meta.FunInfo",
"Nat",
"Eq.ndrec",
"Eq.refl",
"Lean.Meta.FunInfo.noConfusionType",
"Eq"
] | false |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr.0.Lean.Meta.Grind.Arith.Cutsat.processNewNatEq | Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr | [
"Lean.Meta.Grind.Arith.Cutsat.EqCnstrProof.coreToInt",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.Arith.Cutsat.toLinearExpr",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.Sym.Context",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr.0.Lean.Meta.Grind.Arith.Cutsat.propag... | true |
Lean.Order.CompleteLattice | Init.Internal.Order.Basic | [
"Lean.Order.CompleteLattice.mk"
] | true |
CategoryTheory.instCompleteLatticePresieve._aux_19 | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve",
"iSup",
"Prop.instCompleteLattice",
"Membership.mem",
"Set.Elem",
"CompleteSemilatticeSup.toSupSet",
"CategoryTheory.Category.toCategoryStruct",
"CompleteLattice.toCompleteSemilatticeSup",
"Subtype.val",
"Set.in... | false |
SemiNormedGrp.ofHom_comp | Mathlib.Analysis.Normed.Group.SemiNormedGrp | [
"SemiNormedGrp.ofHom",
"NormedAddGroupHom",
"SeminormedAddCommGroup",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"NormedAddGroupHom.comp",
"SemiNormedGrp.of",
"CategoryTheory.CategoryStruct.comp",
"SemiNormedGrp.instLargeCategory",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
... | true |
Finsupp._sizeOf_1 | Mathlib.Data.Finsupp.Defs | [
"Finset",
"Membership.mem",
"Ne",
"instOfNatNat",
"instHAdd",
"Finsupp.rec",
"Iff",
"Finset.instSetLike",
"HAdd.hAdd",
"Finset._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Zero.toOfNat0",
"SizeOf",
"OfNat.ofNat",
"SetLike.instMembership",
"Finsupp",
"Zero"
] | false |
List.permutationsAux2.eq_def | Mathlib.Data.List.Permutation | [
"List.permutationsAux2.match_3",
"List.brecOn",
"Eq.mpr",
"List.brecOn.go",
"_private.Mathlib.Data.List.Permutation.0.List.permutationsAux2.match_3.splitter",
"List.brecOn.eq",
"congrArg",
"id",
"Prod.mk",
"List.rec",
"Prod.fst",
"List.cons",
"List",
"PProd",
"PUnit",
"Eq.ndrec",
"Li... | true |
AlgebraicGeometry.injective_germ_basicOpen | Mathlib.AlgebraicGeometry.SpreadingOut | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"CommRingCat.Hom.hom",
"Semiring.toModule",
"Opposite",
"HMul.hMul",
"CommRingCat.carrier",
"AlgebraicGeometry.Preshea... | true |
AddConstMapClass.map_add_ofNat' | Mathlib.Algebra.AddConstMap.Basic | [
"instHSMul",
"AddMonoid.toAddSemigroup",
"AddMonoid.toNSMul",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"AddMonoidWithOne.toOne",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Nat",
"AddMonoid",
"One.toOfNat1",
"AddConstMapClass.map_add_nat'",
"HSMul.hSMul",
"AddMonoidWithOne.toAdd... | true |
mul_le_of_le_div₀ | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic | [
"GroupWithZero.toMonoidWithZero",
"DivInvMonoid.toInv",
"instHDiv",
"MulPosReflectLT",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"MulZeroClass.toMul",
"Monoid.toMulOneClass",
"PartialOrder.toPreorder",
"GroupWithZero",
"Preorder.toLE",
"Eq.rec",
"PartialOrder",
"MulOne.toMul",
"HDiv.h... | true |
Array.count_range | Init.Data.Array.Range | [
"Eq.mpr",
"congrArg",
"List.count_range",
"List.count_toArray",
"id",
"instOfNatNat",
"List.range",
"List.toArray_range",
"instBEqOfDecidableEq",
"List.toArray",
"Array",
"List.count",
"Array.range",
"Nat",
"LT.lt",
"Nat.decLt",
"Eq.refl",
"instDecidableEqNat",
"instLTNat",
"Of... | true |
Real.zero_rpow | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"Real.instPow",
"False",
"Real",
"eq_false",
"Real.instZero",
"congrArg",
"Complex.instZero",
"Complex.instPow",
"Ne",
"Complex.ofReal_eq_zero._simp_1",
"Complex.ofReal",
"Complex.zero_cpow",
"Complex.re",
"HPow.hPow",
"True",
"eq_self",
"of_eq_true",
"Zero.toOfNat0",
"congrFun'"... | true |
Std.Http.instInhabitedRequest.default | Std.Internal.Http.Data.Request | [
"Inhabited.default",
"Std.Http.Extensions",
"Std.Http.Request.instInhabitedHead",
"Std.Http.Request.mk",
"Inhabited",
"Std.Http.Request.Head",
"Std.Http.instInhabitedExtensions",
"Std.Http.Request"
] | true |
Array.max_eq_max_toList | Init.Data.Array.MinMax | [
"Array.max",
"congrArg",
"Max",
"Ne",
"Array.toList",
"List.toArray",
"Array",
"Array.max_toList",
"Array.min_toList._proof_1",
"Array.min_eq_min_toList._proof_1",
"True",
"eq_self",
"of_eq_true",
"Eq",
"Eq.trans",
"List.nil",
"List.max"
] | true |
Batteries.RBSet.upperBoundP? | Batteries.Data.RBMap.Basic | [
"Batteries.RBNode.WF",
"Batteries.RBNode",
"Batteries.RBSet",
"Ordering",
"Batteries.RBNode.upperBound?",
"Option.none",
"Subtype.val",
"Option"
] | true |
NFA.instInhabited | Mathlib.Computability.NFA | [
"NFA",
"NFA.mk",
"Set.instEmptyCollection",
"Inhabited",
"EmptyCollection.emptyCollection",
"Inhabited.mk",
"Set"
] | true |
TopologicalSpace.Opens.frameHom | Mathlib.Topology.Sets.Opens | [
"FrameHom",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"TopologicalSpace.Opens.instCompleteLattice",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"SemilatticeInf.toMin",
"TopologicalSpace.Opens.instSetLike",
"TopologicalSpa... | true |
UniformOnFun.toFun_one | Mathlib.Topology.Algebra.UniformConvergence | [
"One",
"Equiv.instEquivLike",
"instOneUniformOnFun",
"Equiv",
"UniformOnFun.toFun",
"Pi.instOne",
"One.toOfNat1",
"UniformOnFun",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike",
"Set"
] | true |
_private.Mathlib.Topology.Algebra.Group.ClosedSubgroup.0.ClosedSubgroup.ext.match_1 | Mathlib.Topology.Algebra.Group.ClosedSubgroup | [
"ClosedSubgroup.mk",
"Subsemigroup.casesOn",
"MulOne.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Subsemigroup.mk",
"Submonoid.toSubsemigroup",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Subgroup.mk",
"MulOne.... | false |
_private.Mathlib.Analysis.SpecialFunctions.Log.RpowTendsto.0.Real.tendstoLocallyUniformlyOn_rpow_sub_one_log._proof_1_11 | Mathlib.Analysis.SpecialFunctions.Log.RpowTendsto | [
"instLawfulOrderLT_mathlib",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"GroupWithZero.toMonoidWithZero",
"NormedCommRing.toSeminormedCommRing",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.RArray.leaf",
"Lean.Grind.Field.toCommRing",
"False",
"Real.partialOrder",
"Real.instLE",
"Real",
"Preorde... | false |
Lean.Lsp.PlainGoalParams.mk.injEq | Lean.Data.Lsp.Extra | [
"Eq.propIntro",
"Lean.Lsp.PlainGoalParams",
"Lean.Lsp.PlainGoalParams.mk",
"Lean.Lsp.PlainGoalParams.mk.inj",
"Lean.Lsp.TextDocumentPositionParams",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
Lean.Lsp.LeanDidOpenTextDocumentParams._sizeOf_inst | Lean.Data.Lsp.Extra | [
"Lean.Lsp.LeanDidOpenTextDocumentParams",
"Lean.Lsp.LeanDidOpenTextDocumentParams._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
Ordinal.instAddLeftMono | Mathlib.SetTheory.Ordinal.Basic | [
"CovariantClass.mk",
"_private.Mathlib.SetTheory.Ordinal.Basic.0.Ordinal.instAddLeftMono.match_1",
"False",
"Sum.lex_inr_inr._simp_1",
"Ordinal.partialOrder",
"instAsymmOfIsWellFounded",
"congrArg",
"Sum.instTrichotomousLex_mathlib",
"and_self",
"InitialSeg.map_rel_iff",
"Sum.lex_inl_inl._simp_1... | true |
algebraMap.coe_sum | Mathlib.Algebra.Algebra.Basic | [
"Algebra.cast",
"RingHom.instRingHomClass",
"RingHomClass.toAddMonoidHomClass",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Finset",
"Algebra",
"RingHom",
"map_sum",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"RingHom.instFunLike",
"NonAssocSemiring.toNonUnitalNonAsso... | true |
intervalIntegral.FTCFilter.nhdsUIcc | Mathlib.MeasureTheory.Integral.IntervalIntegral.FundThmCalculus | [
"Real",
"Lattice.toSemilatticeSup",
"Real.lattice",
"nhdsWithin",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"Fact",
"SemilatticeSup.toMax",
"intervalIntegral.FTCFilter.nhdsIcc",
"SemilatticeInf.toMin",
"intervalIntegral.FTCFilter",
"Max.max",
"Real.pseudoMetricSpace",
"UniformS... | true |
Lean.SubExpr.instToJsonGoalsLocation | Lean.SubExpr | [
"Lean.SubExpr.instToJsonGoalsLocation.toJson",
"Lean.SubExpr.GoalsLocation",
"Lean.ToJson.mk",
"Lean.ToJson"
] | true |
NumberField.mixedEmbedding.fundamentalCone.intNorm_coe | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone | [
"NormedCommRing.toNormedRing",
"NumberField.mixedEmbedding.fundamentalCone.preimageOfMemIntegerSet",
"Int.cast",
"Eq.mpr",
"Int.cast_abs",
"Rat.cast_intCast",
"Real",
"MonoidHom.instFunLike",
"NumberField.mixedEmbedding.norm_eq_norm",
"NormedRing.toRing",
"DivisionRing.toRatCast",
"MonoidHom",... | true |
OrderHom.isLeast_lfp | Mathlib.Order.FixedPoints | [
"ChainCompletePartialOrder.instOfCompleteLattice",
"lowerBounds",
"PartialOrder.toPreorder",
"Function.fixedPoints",
"Preorder.toLE",
"Membership.mem",
"OrderHom.instPreorder",
"ChainCompletePartialOrder.toPartialOrder",
"OrderHom.isFixedPt_lfp",
"IsLeast",
"OrderHom.instFunLike",
"And.intro",... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.