name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Lean.Meta.Basic.0.Lean.Meta.isClassQuickConst? | Lean.Meta.Basic | [
"Pure.pure",
"Lean.Meta.State",
"Lean.LOption.undef",
"_private.Lean.Meta.Basic.0.Lean.Meta.isClassQuickConst?.match_1",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instDecidableEqBool",
"Lean.LOption.some",
"Applicative.toPure",
"Lean.LOption.none",
"Bool.true",
"Lean.Core.CoreM",
"Lean.Meta.instMo... | true |
CategoryTheory.GradedObject.BifunctorComp₂₃IndexData.hpq | Mathlib.CategoryTheory.GradedObject.Trifunctor | [
"CategoryTheory.GradedObject.BifunctorComp₂₃IndexData.p",
"Prod.mk",
"CategoryTheory.GradedObject.BifunctorComp₂₃IndexData",
"CategoryTheory.GradedObject.BifunctorComp₂₃IndexData.q",
"Prod.fst",
"Prod",
"CategoryTheory.GradedObject.BifunctorComp₂₃IndexData.I₂₃",
"Eq",
"Prod.snd"
] | true |
Std.ExtDHashMap.getKeyD_inter_of_mem_right | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Std.DHashMap.getKeyD_inter_of_mem_right",
"Std.ExtDHashMap.inductionOn₂",
"Membership.mem",
"Std.ExtDHashMap.mk",
"LawfulHashable",
"Inter.inter",
"Std.ExtDHashMap.instInterOfEquivBEqOfLawfulHashable",
"EquivBEq",
"Std.ExtDHashMap",
"H... | true |
_private.Mathlib.Analysis.Analytic.Constructions.0.AnalyticAt.neg.match_1_1 | Mathlib.Analysis.Analytic.Constructions | [
"NormedSpace",
"FormalMultilinearSeries",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"HasFPowerSeriesAt._proof_2",
"HasFPowerSeriesAt._proof_1",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"Exists.casesOn",
"Semin... | false |
_private.Mathlib.RingTheory.MvPowerSeries.Substitution.0.MvPowerSeries.rescale._simp_4 | Mathlib.RingTheory.MvPowerSeries.Substitution | [
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"mul_assoc",
"Eq.symm",
"Eq",
"instHMul"
] | false |
_private.Lean.Compiler.LCNF.Basic.0.Lean.Compiler.LCNF.eqImp._sparseCasesOn_11 | Lean.Compiler.LCNF.Basic | [
"Lean.Compiler.LCNF.Arg",
"Lean.Compiler.LCNF.Code.setTag",
"Nat.ne_of_beq_eq_false",
"Lean.Compiler.LCNF.Code.unreach",
"Lean.Compiler.LCNF.Code.fun",
"Lean.Compiler.LCNF.Code.rec",
"Lean.Compiler.LCNF.Code.cases",
"Lean.Compiler.LCNF.Code.oset",
"Lean.Compiler.LCNF.Code.let",
"Nat.shiftRight",
... | false |
_private.Std.Time.Format.Basic.0.Std.Time.GenericFormat.DateBuilder.build | Std.Time.Format.Basic | [
"Std.Time.PlainTime",
"Std.Time.TimeZone.ZoneRules.ofTimeZone",
"Std.Time.PlainTime.mk",
"Std.Time.TimeZone.Offset",
"Std.Time.Month.Ordinal.days",
"Std.Time.PlainDate",
"Std.Time.Day.instOfNatOrdinal",
"Option.instOrElse",
"Std.Time.Awareness.type",
"_private.Std.Time.Format.Basic.0.Std.Time.Gene... | true |
_private.Lean.Server.ProtocolOverview.0.Lean.Server.Overview.RpcRequestOverview.mk | Lean.Server.ProtocolOverview | [
"String",
"_private.Lean.Server.ProtocolOverview.0.Lean.Server.Overview.RpcRequestOverview",
"Lean.Name",
"_private.Lean.Server.ProtocolOverview.0.Lean.Server.Overview.RpcRequestOverview.mk"
] | true |
_private.Mathlib.AlgebraicGeometry.Geometrically.Integral.0.AlgebraicGeometry.GeometricallyIntegral.eq_geometricallyReduced_inf_geometricallyIrreducible._simp_1_2 | Mathlib.AlgebraicGeometry.Geometrically.Integral | [
"and_comm",
"And",
"propext",
"Eq"
] | false |
Lean.Meta.mkEqRefl | Lean.Meta.AppBuilder | [
"Pure.pure",
"Lean.Meta.State",
"Lean.mkApp2",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.Level",
"Lean.Meta.getLevel",
"Applicative.toPure",
"Lean.mkConst",
"List.cons",
"Lean.Core.CoreM",
"Lean.Meta.instMonadMetaM",
"StateRefT'",
"StateRefT'.instMonad",
"Lean.Name.mkStr2",... | true |
WithBot.subtypeOrderIso._proof_5 | Mathlib.Order.Hom.WithTopBot | [
"of_eq_false",
"WithBot.some",
"WithBot",
"eq_false",
"congrArg",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"PartialOrder",
"id",
"Subtype",
"Ne",
"Bot.bot",
"dite",
"Subtype.mk",
"DecidablePred",
"True",
"eq_self",
"of_eq_true",
"Eq.ndrec",
... | false |
CategoryTheory.MonoidalCategory.MonoidalRightAction.oppositeRightAction._proof_19 | Mathlib.CategoryTheory.Monoidal.Action.Opposites | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.MonoidalCategory.MonoidalRightActionStruct.actionHomRight",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"Quiver.Hom.op",
"CategoryTheory.MonoidalCategory.MonoidalRightActionStruct.actionUnitIso",
... | false |
Std.TreeMap.contains_inter | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.instInter",
"Std.DTreeMap.contains_inter",
"Std.TreeMap.inner",
"Ordering",
"Bool.and",
"Std.TransCmp",
"Inter.inter",
"Std.TreeMap.contains",
"Bool",
"Eq",
"Std.TreeMap"
] | true |
_private.Mathlib.Lean.Name.0.allNamesByModule.match_1 | Mathlib.Lean.Name | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Array",
"Option.none",
"Unit",
"Lean.Name",
"Option"
] | false |
Nat.Partition.le_of_mem_parts | Mathlib.Combinatorics.Enumerative.Partition.Basic | [
"Multiset.sum",
"Nat.instCanonicallyOrderedAdd",
"congrArg",
"Nat.Partition.parts",
"Preorder.toLE",
"Membership.mem",
"Multiset",
"Eq.mp",
"LE.le",
"instLENat",
"Multiset.instMembership",
"Nat.instPreorder",
"Nat.Partition",
"Nat",
"Nat.instAddCommMonoid",
"Nat.Partition.parts_sum",
... | true |
IsUltraUniformity.rec | Mathlib.Topology.UniformSpace.Ultra.Basic | [
"Filter.instMembership",
"UniformSpace",
"SetRel",
"uniformity",
"Membership.mem",
"id",
"And",
"Filter.HasBasis",
"SetRel.IsTrans",
"IsUltraUniformity",
"IsUltraUniformity.mk",
"SetRel.IsSymm",
"Prod",
"Filter"
] | false |
CategoryTheory.OverPresheafAux.counitBackward | Mathlib.CategoryTheory.Comma.Presheaf.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.OverPresheafAux.YonedaCollection.fst",
"Opposite",
"CategoryTheory.CategoryStruct.opposite",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.OverPresheafAux.yonedaCollectionPresheafToA",
"CategoryTheory.OverPresheafAux.OverArrows.val",
"CategoryTheory.e... | true |
_private.Mathlib.Topology.UniformSpace.Cauchy.0.Filter.totallyBounded_principal_iff._simp_1_2 | Mathlib.Topology.UniformSpace.Cauchy | [
"Filter.instMembership",
"Membership.mem",
"HasSubset.Subset",
"Filter.mem_principal",
"propext",
"Filter.principal",
"Eq",
"Filter",
"Set.instHasSubset",
"Set"
] | false |
ReaderT.instAlternativeOfMonad | Init.Control.Reader | [
"Alternative.mk",
"ReaderT",
"ReaderT.orElse",
"Alternative",
"Monad",
"ReaderT.instApplicativeOfMonad",
"ReaderT.failure"
] | true |
TrivialLieModule | Mathlib.Algebra.Lie.Abelian | [] | true |
_private.Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy.0.HomotopicalAlgebra.BifibrantObject.instIsLocalizationCompFibrantObjectιFibrantObjectWeakEquivalences._proof_1 | Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy | [
"HomotopicalAlgebra.BifibrantObject",
"CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteColimits",
"CategoryTheory.Functor",
"HomotopicalAlgebra.ModelCategory.cm1a",
"HomotopicalAlgebra.ModelCategory.cm1b",
"CategoryTheory.Limits.hasColimitsOfShape_discrete",
"CategoryTheory.Limits.hasFiniteProduct... | false |
Real.rpow_lt_self_of_lt_one | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"Real.instPow",
"Real",
"Real.instZero",
"congrArg",
"Real.instLT",
"Eq.mp",
"Real.rpow_one",
"Real.instOne",
"HPow.hPow",
"LT.lt",
"One.toOfNat1",
"Zero.toOfNat0",
"instHPow",
"OfNat.ofNat",
"Real.rpow_lt_rpow_of_exponent_gt"
] | true |
Mathlib.Tactic.Ring.RatCoeff.mk | Mathlib.Tactic.Ring.Common | [
"Mathlib.Tactic.Ring.RatCoeff",
"Rat",
"Lean.Expr",
"Lean.Expr.sort",
"Lean.Level",
"Qq.Quoted",
"Mathlib.Tactic.Ring.RatCoeff.mk",
"Lean.Level.succ",
"Option"
] | true |
Ordinal.enumIsoToType | Mathlib.SetTheory.Ordinal.Basic | [
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Set.Elem",
"DistribLattice.toLattice",
"linearOrder_toType",
"OrderIso",
"Ordinal.ToType.mk",
"Ordinal.ToType",
"Set.Iio",
"Set.instMembership",
"instDistribLatticeOfLine... | true |
essSup_comp_le_essSup_map_measure._auto_1 | Mathlib.MeasureTheory.Function.EssSup | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
OpenPartialHomeomorph.coe_ofContinuousOpen_symm | Mathlib.Topology.OpenPartialHomeomorph.Basic | [
"PartialEquiv",
"PartialEquiv.symm",
"IsOpenMap",
"OpenPartialHomeomorph.toFun'",
"OpenPartialHomeomorph.ofContinuousOpen",
"TopologicalSpace",
"PartialEquiv.source",
"ContinuousOn",
"IsOpen",
"PartialEquiv.toFun",
"Eq",
"rfl",
"OpenPartialHomeomorph.symm"
] | true |
_private.Lean.Compiler.LCNF.Simp.SimpValue.0.Lean.Compiler.LCNF.Simp.applyImplementedBy?.match_1 | Lean.Compiler.LCNF.Simp.SimpValue | [
"_private.Lean.Compiler.LCNF.Simp.SimpValue.0.Lean.Compiler.LCNF.Simp.simpProj?._sparseCasesOn_3",
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Lean.Name",
"Option"
] | false |
_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Array.0._regBuiltin.Array.reduceGetElem.declare_6._@.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Array.561566828._hygCtx._hyg.22 | Lean.Meta.Tactic.Simp.BuiltinSimprocs.Array | [
"IO",
"Lean.Meta.DiscrTree.Key.star",
"Array.reduceGetElem",
"Lean.Meta.DiscrTree.Key",
"instOfNatNat",
"List.toArray",
"List.cons",
"Unit",
"Nat",
"Lean.Meta.Simp.registerBuiltinDSimproc",
"Lean.Name.mkStr2",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.Meta.DiscrTree.Key.const",
"List.nil"... | false |
Submodule.smul_mono | Mathlib.Algebra.Algebra.Operations | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"instHSMul",
"Submodule.toAddSubmonoid",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddSubmonoid.smu... | true |
Manifold.IsImmersionAtOfComplement.instNormedAddCommGroupSmallComplement._aux_19 | Mathlib.Geometry.Manifold.Immersion | [
"instHSMul",
"NormedSpace",
"Manifold.IsImmersionAtOfComplement",
"AddCommGroup.toAddGroup",
"Manifold.IsImmersionAtOfComplement.smallComplement",
"Int",
"TopologicalSpace",
"ModelWithCorners",
"AddGroup.toSubNegMonoid",
"ENat",
"NontriviallyNormedField",
"NormedAddCommGroup.toAddCommGroup",
... | false |
Lean.Grind.CutsatConfig.ext._inherited_default | Init.Grind.Config | [
"id",
"Bool",
"Bool.false"
] | false |
ContinuousMultilinearMap.alternatization.eq_1 | Mathlib.Topology.Algebra.Module.Alternating.Basic | [
"ContinuousAlternatingMap.instAddCommGroup._proof_7",
"instHSMul",
"MonoidHom.instFunLike",
"ContinuousMultilinearMap.alternatization._proof_2",
"Finset.univ",
"MonoidHom",
"ContinuousMultilinearMap.instAddMonoid",
"Monoid.toMulOneClass",
"ContinuousMultilinearMap.domDomCongr",
"DistribMulAction.t... | true |
Rat.ofInt._proof_1 | Init.Data.Rat.Basic | [
"Nat.Coprime",
"instOfNatNat",
"Int",
"Nat.coprime_one_right",
"Nat",
"Int.natAbs",
"OfNat.ofNat"
] | false |
Std.Http.URI.EncodedFragment | Std.Internal.Http.Data.URI.Encoding | [
"Std.Http.Internal.Char.isFragmentChar",
"Std.Http.URI.EncodedString"
] | true |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.neg_bmod._proof_1_5 | Init.Data.Int.DivMod.Lemmas | [
"instDecidableNot",
"Int.instDiv",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Lean.Omega.Int.le_of_not_lt",
"instHDiv",
"HMul.hMul",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
... | false |
List.filterTR.loop._unsafe_rec | Init.Data.List.Basic | [
"List.reverseAux.match_1",
"List.filter.match_1",
"List.cons",
"List",
"Unit",
"List.filterTR.loop._unsafe_rec",
"List.reverse",
"Bool"
] | false |
bihimp_hnot_self | Mathlib.Order.SymmDiff | [
"Lattice.toSemilatticeSup",
"Compl.compl",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"GeneralizedHeytingAlgebra.toHImp",
"Bot.bot",
"SemilatticeInf.toMin",
"bihimp",
"GeneralizedHeytingAlgebra.toLattice",
"HeytingAlgebra.toGeneralizedHeytingAlgebra",
"symmDiff_hnot_self",
... | true |
Mathlib.Tactic.CategoryTheory.ToApp.toNatTransExpr | Mathlib.Tactic.CategoryTheory.ToApp | [
"Lean.Name.mkStr5",
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Meta.mkAppM",
"List.toArray",
"List.cons",
"Lean.Meta.mapForallTelescope",
"List.nil"
] | true |
_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.coeffSubmodule.eq_1 | Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | [
"Submodule",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.InductionObj.coeffSubmodule",
"Algebra",... | true |
CategoryTheory.subterminalsEquivMonoOverTerminal._proof_11 | Mathlib.CategoryTheory.Subterminal | [
"CategoryTheory.subterminalsEquivMonoOverTerminal._proof_10",
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.instCategorySubterminals",
"CategoryTheory.subterminalsEquivMonoOverTerminal._proof_4",
"CategoryTheory.subterminalsEquivMono... | false |
IsMin.pred_eq | Mathlib.Order.SuccPred.Basic | [
"Iff.mpr",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"Order.pred_eq_iff_isMin",
"Order.pred",
"PredOrder",
"Eq",
"IsMin"
] | true |
MonoidHom.subgroupComap | Mathlib.Algebra.Group.Subgroup.Map | [
"MonoidHom",
"Monoid.toMulOneClass",
"Group",
"Membership.mem",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"MonoidHom.submonoidComap",
"Subgroup.toGroup",
"Subgroup.comap",
"SetLike.instMembership",
"Subgroup.instSetLike",
"Subgroup.to... | true |
CategoryTheory.SimplicialThickening.Path.mk.sizeOf_spec | Mathlib.AlgebraicTopology.SimplicialNerve | [
"CategoryTheory.SimplicialThickening.Path.left._autoParam",
"CategoryTheory.SimplicialThickening.Path.mk",
"LinearOrder",
"PartialOrder.toPreorder",
"instSizeOfDefault",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"instOfNatNat",
"LE.le",
"au... | true |
Polynomial.evalEval | Mathlib.Algebra.Polynomial.Bivariate | [
"Polynomial.C",
"Polynomial.eval",
"RingHom",
"Polynomial",
"RingHom.instFunLike",
"Polynomial.semiring",
"Semiring",
"Semiring.toNonAssocSemiring",
"DFunLike.coe"
] | true |
CategoryTheory.ShortComplex.comp_τ₃ | Mathlib.Algebra.Homology.ShortComplex.Basic | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.ShortComplex.X₃",
"rf... | true |
Lean.Lsp.SignatureHelpContext.mk._flat_ctor | Lean.Data.Lsp.LanguageFeatures | [
"String",
"Lean.Lsp.SignatureHelpContext",
"Lean.Lsp.SignatureHelp",
"Lean.Lsp.SignatureHelpTriggerKind",
"Bool",
"Lean.Lsp.SignatureHelpContext.mk",
"Option"
] | false |
HasStrictDerivAt.of_notMem_tsupport | Mathlib.Analysis.Calculus.Deriv.Support | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"Membership.mem",
... | true |
Std.HashMap.getKey_eq_get_getKey? | Std.Data.HashMap.Lemmas | [
"Std.HashMap.getKey",
"Std.DHashMap.getKey_eq_get_getKey?",
"Membership.mem",
"Std.HashMap",
"LawfulHashable",
"Bool.true",
"Std.HashMap.mem_iff_isSome_getKey?",
"EquivBEq",
"Option.get",
"Iff.mp",
"Bool",
"Std.HashMap.getKey?",
"Hashable",
"Option.isSome",
"Std.HashMap.inner",
"BEq",
... | true |
instNormalizedGCDMonoidNat._proof_1 | Mathlib.Algebra.GCDMonoid.Nat | [
"Nat.unique_units",
"Units",
"CommMonoidWithZero.toMonoidWithZero",
"Unique.instSubsingleton",
"Nat",
"Nat.instCommMonoidWithZero",
"Subsingleton",
"MonoidWithZero.toMonoid"
] | false |
CategoryTheory.Functor.EssSurj.rec | Mathlib.CategoryTheory.EssentialImage | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.EssSurj.mk",
"CategoryTheory.Functor.essImage",
"CategoryTheory.Functor.EssSurj",
"CategoryTheory.Category"
] | false |
TopCat.GlueData.fromOpenSubsetsGlue_isOpenEmbedding | Mathlib.Topology.Gluing | [
"CategoryTheory.GlueData.diagram",
"CategoryTheory.Limits.MultispanShape.prod",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Limits.WalkingMultispan",
"CategoryTheory.Limits.MultispanShape.L",
"TopCat.GlueData.fromOpenSubsetsGlue",
"CategoryTheory.ConcreteCategory.hom",
"Top... | true |
Monoid.CoprodI.Word.Pair._sizeOf_inst | Mathlib.GroupTheory.CoprodI | [
"Monoid",
"Monoid.CoprodI.Word.Pair._sizeOf_1",
"SizeOf.mk",
"Monoid.CoprodI.Word.Pair",
"SizeOf"
] | false |
DiffeologicalSpace.CorePlotsOn.noConfusionType | Mathlib.Geometry.Diffeology.Basic | [
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"PiLp.normedSpace",
"fact_one_le_two_ennreal",
"Real.denselyNormedField",
"instTopENat",
"Real.instRCLike",
"TopologicalSpace.IsOpen",
"Set.univ",
"PseudoMetricSpace.toUniformSpace",
"ContDiffOn",
"Diffeologica... | false |
_private.Mathlib.Analysis.SpecialFunctions.Log.Base.0.Real.logb_eq_zero._simp_1_2 | Mathlib.Analysis.SpecialFunctions.Log.Base | [
"GroupWithZero.toMonoidWithZero",
"instHDiv",
"GroupWithZero.toDivInvMonoid",
"GroupWithZero",
"HDiv.hDiv",
"MonoidWithZero.toMulZeroOneClass",
"propext",
"DivInvMonoid.toDiv",
"Zero.toOfNat0",
"Or",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq",
"div_eq_zero_iff",
"MulZeroClass.... | false |
FirstOrder.Language.infiniteTheory | Mathlib.ModelTheory.Syntax | [
"FirstOrder.Language.Theory",
"Nat",
"FirstOrder.Language.Sentence.cardGe",
"FirstOrder.Language",
"FirstOrder.Language.Sentence",
"Set.range"
] | true |
_private.Lean.Elab.Tactic.Grind.Trace.0.Lean.Elab.Tactic.Grind.evalFinishTrace | Lean.Elab.Tactic.Grind.Trace | [
"Pure.pure",
"Lean.Syntax.TSepArray.mk",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.Params",
"Lean.TSyntax",
"Lean.MessageData",
"Lean.MonadError.mk",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Tactic.TryThis.SuggestionText.tsyntax",
"Lean.Core.inst... | true |
ComplexShape.Embedding.AreComplementary.Boundary.equiv._proof_10 | Mathlib.Algebra.Homology.Embedding.AreComplementary | [
"ComplexShape.Embedding.BoundaryGE",
"ComplexShape.Embedding.AreComplementary.Boundary.indexOfBoundaryLE",
"ComplexShape.Embedding.AreComplementary.Boundary.snd",
"ComplexShape.Embedding.AreComplementary.Boundary.fst",
"Subtype",
"ComplexShape.Embedding.AreComplementary.Boundary.indexOfBoundaryGE",
"Com... | false |
Mathlib.Meta.SetNotationForOrder.ssupsetStx' | Mathlib.Tactic.SetNotationForOrder | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.TrailingParserDescr"
] | true |
LieDerivation.lie_der_ad_eq_ad_der | Mathlib.Algebra.Lie.AdjointAction.Derivation | [
"LieHom",
"LieAlgebra.toModule",
"LieDerivation.ad_apply_lieDerivation",
"LieDerivation.instNeg",
"Eq.mpr",
"NegZeroClass.toNeg",
"CommRing",
"LieDerivation.instLieRingModule",
"LieDerivation",
"LieRing.toAddCommGroup",
"congrArg",
"Bracket.bracket",
"lieAlgebraSelfModule",
"LieDerivation.... | true |
HasFDerivAt.fst | Mathlib.Analysis.Calculus.FDeriv.Prod | [
"ContinuousLinearMap.comp",
"Pure.pure",
"HasFDerivAt",
"NormedSpace",
"SProd.sprod",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"instTopologicalSpaceProd",
"NormedField.toField",
"nhds",
"Field.toSemifield",
"Prod.fst",
"ContinuousLinearMap... | true |
CategoryTheory.MonoidalCategoryStruct.mk | Mathlib.CategoryTheory.Monoidal.Category | [
"CategoryTheory.MonoidalCategoryStruct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso",
"CategoryTheory.MonoidalCategoryStruct.mk",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
MvPolynomial.finsum_weightedHomogeneousComponent | Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous | [
"Eq.mpr",
"Nat.instMulZeroClass",
"Semiring.toModule",
"AddMonoidAlgebra.addAddCommMonoid",
"congrArg",
"CommSemiring.toSemiring",
"finsum",
"LinearMap.instFunLike",
"id",
"MvPolynomial.sum_weightedHomogeneousComponent",
"MvPolynomial.weightedHomogeneousComponent",
"LinearMap",
"AddCommMonoi... | true |
Finmap.notMem_erase_self | Mathlib.Data.Finmap | [
"Finmap.erase",
"Eq.mpr",
"Finmap.mem_erase",
"Classical.not_not",
"congrArg",
"Finmap.instMembership",
"Membership.mem",
"id",
"Ne",
"And",
"not_and_or",
"propext",
"Eq.refl",
"Or.inl",
"Or",
"Eq",
"Not",
"Finmap",
"DecidableEq"
] | true |
Mathlib.Tactic.Sat.LRATStep.add.injEq | Mathlib.Tactic.Sat.FromLRAT | [
"Eq.propIntro",
"Mathlib.Tactic.Sat.LRATStep.add",
"Lean.injEq_helper",
"Int",
"Array",
"Mathlib.Tactic.Sat.LRATStep.add.inj",
"And",
"Nat",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Mathlib.Tactic.Sat.LRATStep"
] | true |
LinearMap.mem_fixedSubmodule_iff._simp_1 | Mathlib.LinearAlgebra.FixedSubmodule | [
"Submodule",
"LinearMap.instFunLike",
"Membership.mem",
"LinearMap",
"AddCommMonoid",
"LinearMap.fixedSubmodule",
"Submodule.setLike",
"propext",
"Semiring",
"LinearMap.mem_fixedSubmodule_iff",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe",
"SetLike.instMe... | false |
CategoryTheory.Equivalence.instMonoidalFunctorTrans._proof_22 | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Equivalence.instMonoidalFunctorTrans._proof_6",
"CategoryTheory.Equivalence.instMonoidalFunctorTrans._proof_17",
"CategoryTheory.Equivalence",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.... | false |
AlgebraicGeometry.Scheme.Modules.pseudofunctor_mapComp_inv_τr | Mathlib.AlgebraicGeometry.Modules.Sheaf | [
"AlgebraicGeometry.Scheme.Modules.pullback",
"CategoryTheory.Functor",
"AlgebraicGeometry.Scheme.Modules.pushforward",
"AlgebraicGeometry.Scheme",
"Opposite",
"AlgebraicGeometry.Scheme.Modules.instCategory",
"CategoryTheory.Bicategory.Adj.Hom₂.τr",
"CategoryTheory.CategoryStruct.toQuiver",
"Algebrai... | true |
NumberField.InfinitePlace.IsRamified | Mathlib.NumberTheory.NumberField.InfinitePlace.Ramification | [
"Algebra",
"Field.toSemifield",
"NumberField.InfinitePlace.IsUnramified",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"NumberField.InfinitePlace",
"Semifield.toCommSemiring",
"Field",
"Not"
] | true |
_private.Std.Data.DHashMap.Internal.RawLemmas.0.Std.DHashMap.Internal.Raw₀.Const.equiv_iff_toList_perm_toList.match_1_2 | Std.Data.DHashMap.Internal.RawLemmas | [
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
HasCompactMulSupport.is_one_at_infty | Mathlib.Topology.Algebra.Support | [
"Filter.instMembership",
"Eq.mpr",
"One",
"congrArg",
"Filter.map",
"Compl.compl",
"HasCompactMulSupport.isCompact",
"HasCompactMulSupport",
"Membership.mem",
"Exists",
"nhds",
"id",
"Set.compl_subset_comm",
"HasSubset.Subset",
"mem_of_mem_nhds",
"Set.instCompl",
"Filter.cocompact",
... | true |
_private.Mathlib.Data.Finset.Sups.0.Finset.disjSups_comm._simp_1_1 | Mathlib.Data.Finset.Sups | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"OrderBot",
"PartialOrder",
"disjoint_comm",
"propext",
"Eq"
] | false |
Associates.instCommMonoid._proof_1 | Mathlib.Algebra.GroupWithZero.Associated | [
"Mul.mk",
"Quotient.inductionOn₃",
"One.mk",
"HMul.hMul",
"Semigroup.mk",
"npowRecAuto",
"instOfNatNat",
"Quotient.mk",
"One.one",
"Associated.setoid",
"Associates",
"CommMonoid.toMonoid",
"Mul.mul",
"Nat",
"One.toOfNat1",
"Associates.instMul",
"OfNat.ofNat",
"Eq",
"CommMonoid",
... | false |
PrimeSpectrum.rankAtStalk_pos_iff_comap_surjective | Mathlib.RingTheory.Flat.Rank | [
"Eq.mpr",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Module.rankAtStalk",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"Set.univ",
"Algebra",
"_private.Mathlib.RingTheory.Flat.Rank.0.PrimeSpectrum.rankAtStalk_pos_iff_comap_surjec... | true |
Std.Tactic.BVDecide.BVExpr.bitblast.blastUdiv.ShiftConcatInput.ctorIdx | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Udiv | [
"Std.Sat.AIG",
"Nat",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastUdiv.ShiftConcatInput",
"Hashable",
"DecidableEq"
] | false |
Matrix.toLin'_apply | Mathlib.LinearAlgebra.Matrix.ToLin | [
"Pi.Function.module",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Pi.addCommMonoid",
"Matrix.module",
"CommSemiring.toSemiring",
"Matrix",
"Function.smulCommClass",
"LinearMap.instFunLike",
"Matrix.toLin'",
"Algebra.id",
"Matrix.addCommMonoid",
"LinearMap.module",
"LinearMap",
"Com... | true |
Ideal.comap | Mathlib.RingTheory.Ideal.Maps | [
"Semiring.toModule",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Ideal",
"AddSubmonoid.mk",
"AddSubsemigroup.mk",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"SetLike.coe",
"Set.preimage",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Submodule.setLike",
"Sem... | true |
String.Pos.Raw.instLawfulOrderBEq | Init.Data.String.OrderInstances | [
"Eq.mpr",
"instLawfulBEq",
"Std.LawfulOrderBEq",
"congrArg",
"_private.Init.Data.String.OrderInstances.0.String.Pos.Raw.instToIntCiOfNatInt._simp_1",
"id",
"LE.le",
"instLENat",
"instBEqOfDecidableEq",
"String.Pos.Raw",
"Bool.true",
"And",
"BEq.beq",
"Iff",
"instDecidableEqRaw",
"Nat",... | true |
_private.Lean.Meta.Tactic.Grind.CheckResult.0.Lean.Meta.Grind.CheckResult.lt.match_1 | Lean.Meta.Tactic.Grind.CheckResult | [
"Lean.Meta.Grind.CheckResult.none",
"Unit.unit",
"Lean.Meta.Grind.CheckResult.progress",
"Nat.hasNotBit",
"Lean.Meta.Grind.CheckResult",
"Lean.Meta.Grind.CheckResult.casesOn",
"Lean.Meta.Grind.CheckResult.propagated",
"Unit",
"Lean.Meta.Grind.CheckResult.ctorIdx",
"Lean.Meta.Grind.CheckResult.clos... | false |
Polynomial.cauchyBound_X_sub_C | Mathlib.Analysis.Polynomial.CauchyBound | [
"Polynomial.C",
"Polynomial.natDegree_X",
"instHDiv",
"NormedRing.toRing",
"DivisionCommMonoid.toDivisionMonoid",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"congrArg",
"Finset.sup_singleton",
"Finset",
"SeminormedAddGroup.toNNNorm",
"nnnorm_one",
"NNNorm.nnnorm",
"AddGroupWithOn... | true |
_private.Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas.0.RootPairing.termα | Mathlib.LinearAlgebra.RootSystem.Finite.Lemmas | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
Orientation.oangle_rotation_oangle_left | Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | [
"LinearIsometryEquiv.instEquivLike",
"InnerProductSpace.toNormedSpace",
"Orientation",
"False",
"Real.partialOrder",
"Real",
"Orientation.oangle_zero_left",
"Orientation.oangle",
"Real.Angle",
"eq_false",
"sub_self",
"Real.instRCLike",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"LinearI... | true |
OrderIso.map_sup | Mathlib.Order.Hom.Basic | [
"Eq.mpr",
"OrderEmbedding.le_map_sup",
"LE.le.antisymm'",
"congrArg",
"OrderIso.toOrderEmbedding",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"Eq.mp",
"id",
"OrderIso",
"OrderIso.le_iff_le",
"LE.le",
"OrderIso.symm",
"sup_le_iff",
"And",
"instFunLikeOrderIso"... | true |
LinearMap.iterateRange_succ | Mathlib.Algebra.Module.Submodule.Range | [
"Submodule",
"_private.Mathlib.Algebra.Module.Submodule.Range.0.LinearMap.iterateRange_succ._simp_1_1",
"Module.End.iterate_succ'",
"RingHomSurjective.ids",
"Module.End.instMonoid",
"congrArg",
"PartialOrder.toPreorder",
"LinearMap.range",
"LinearMap.iterateRange",
"Submodule.instPartialOrder",
... | true |
_private.Lean.Meta.MethodSpecs.0.Lean.startsWithFollowedByNumber | Lean.Meta.MethodSpecs | [
"String",
"Bool.and",
"String.startsWith",
"String.length",
"Bool",
"String.Slice.Pattern.ForwardSliceSearcher.instForwardPattern_1",
"String.Slice.isNat",
"String.drop"
] | true |
HasFiniteFPowerSeriesOnBall.eq_const_of_bound_one | Mathlib.Analysis.Analytic.CPolynomialDef | [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Preorder.toLT",
"le_rfl",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"congrArg",
"FormalMultilinearSeries",
"NormedAddCommGroup.toMetricSpace",
"DistribMulAction.toDistribSMul",
"AddCommGr... | true |
CategoryTheory.Bicategory.Pith.whiskerLeft_iso_inv | Mathlib.CategoryTheory.Bicategory.LocallyGroupoid | [
"CategoryTheory.Core.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CoreHom.iso",
"CategoryTheory.Bicategory.Pith.as",
"inferInstance",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Core.of",
"CategoryTheory.Bicategory",
"CategoryTheory.Bicategory.Pith... | true |
MeasurableSpace.DynkinSystem.ofMeasurableSpace | Mathlib.MeasureTheory.PiSystem | [
"Function.onFun",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"MeasurableSpace.DynkinSystem.mk",
"Disjoint",
"CompleteLattice.toConditionallyCompleteLattice",
"MeasurableSpace.measurableSet_empty",
"MeasurableSpace.DynkinSystem",
"MeasurableSpace",
"MeasurableSpace.measurableSet_compl",
"Na... | true |
_private.Mathlib.Data.Nat.Multiplicity.0.Nat.emultiplicity_eq_card_pow_dvd._simp_1_1 | Mathlib.Data.Nat.Multiplicity | [
"Preorder.toLT",
"Finset",
"Preorder.toLE",
"Membership.mem",
"Finset.Ico",
"LE.le",
"And",
"Finset.instSetLike",
"LT.lt",
"propext",
"LocallyFiniteOrder",
"Eq",
"SetLike.instMembership",
"Preorder",
"Finset.mem_Ico"
] | false |
_private.Mathlib.Topology.UniformSpace.CompactConvergence.0.ContinuousMap.mem_compactConvergence_entourage_iff._simp_1_1 | Mathlib.Topology.UniformSpace.CompactConvergence | [
"And",
"and_assoc",
"propext",
"Eq"
] | false |
_private.Mathlib.Topology.Algebra.RestrictedProduct.Units.0.RestrictedProduct.eventually_isUnit_of_isUnit._simp_1_3 | Mathlib.Topology.Algebra.RestrictedProduct.Units | [
"And",
"propext",
"Eq.symm",
"Eq",
"forall_and"
] | false |
Bornology.IsVonNBounded.image | Mathlib.Analysis.LocallyConvex.Bounded | [
"image_smul_setₛₗ",
"Eq.mpr",
"RingHom.instRingHomClass",
"instHSMul",
"Filter.smallSets",
"SemilinearMapClass.toMulActionSemiHomClass",
"SemilinearMapClass.distribMulActionSemiHomClass",
"outParam",
"Bornology.IsVonNBounded",
"_private.Mathlib.Analysis.LocallyConvex.Bounded.0.Bornology.IsVonNBoun... | true |
CategoryTheory.IsCardinalAccessibleCategory | Mathlib.CategoryTheory.Presentable.LocallyPresentable | [
"Cardinal.IsRegular",
"Cardinal",
"Fact",
"CategoryTheory.IsCardinalAccessibleCategory.mk",
"CategoryTheory.Category"
] | true |
MvPowerSeries.le_order_mul | Mathlib.RingTheory.MvPowerSeries.Order | [
"HMul.hMul",
"MvPowerSeries.le_weightedOrder_mul",
"MvPowerSeries",
"MvPowerSeries.instMul",
"instAddENat",
"instOfNatNat",
"LE.le",
"instLEENat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"ENat",
"Semiring",
"OfNat.ofNat",
"MvPowerSeries.order",
"instHMul"
] | true |
UniformSpace.toTopologicalSpace.hcongr_2 | Mathlib.Analysis.Normed.Module.PiTensorProduct.InjectiveSeminorm | [
"UniformSpace",
"HEq.refl",
"TopologicalSpace",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"UniformSpace.toTopologicalSpace",
"Eq"
] | true |
Finsupp.update_eq_erase_add_single | Mathlib.Algebra.Group.Finsupp | [
"Finsupp.instFunLike",
"False",
"Finsupp.erase",
"Finsupp.erase_same",
"Function.update",
"Finsupp.single_eq_same",
"Finsupp.ext",
"eq_false",
"Finsupp.erase_ne",
"congrArg",
"Finsupp.single_eq_of_ne",
"Classical.propDecidable",
"Finsupp.update",
"AddZeroClass.toAddZero",
"Ne",
"Finsup... | true |
List.takeI_length | Mathlib.Data.List.TakeDrop | [
"List.takeI_length._f",
"Nat.brecOn",
"List.takeI",
"List",
"Nat",
"Inhabited",
"Eq",
"List.length"
] | true |
_private.Init.Data.List.Find.0.List.findIdx?_go_nil | Init.Data.List.Find | [
"Option.none",
"List.findIdx?.go",
"Nat",
"Bool",
"Eq",
"rfl",
"List.nil",
"Option"
] | true |
CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι_assoc | Mathlib.CategoryTheory.Abelian.Injective.Resolution | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Category.assoc",
"HomologicalComplex.instCategory",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CochainComplex.single₀",
"congrArg",
"CategoryTheory.InjectiveResolution.ι",
"AddRightCancelSemigroup.toAddSemigroup",... | true |
InitialSeg._sizeOf_1 | Mathlib.Order.InitialSeg | [
"InitialSeg.rec",
"Membership.mem",
"RelEmbedding._sizeOf_inst",
"instOfNatNat",
"instHAdd",
"RelEmbedding",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"InitialSeg",
"instAddNat",
"SizeOf",
"Set.range",
"OfNat.ofNat",
"Set.instMembership",
"DFunLike.coe",
"RelEmbedding.instFunLike",
"Set... | false |
_private.Std.Do.SPred.SVal.0.Std.Do.SVal.uncurry.match_3.eq_2 | Std.Do.SPred.SVal | [
"List.cons",
"List",
"Eq.refl",
"Std.Do.SVal",
"Eq",
"Std.Do.SVal.uncurry.match_3",
"List.nil"
] | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.