name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr.0.Lean.Meta.Grind.Arith.Cutsat.internalizeNatTerm | Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.Arith.Cutsat.toLinearExpr",
"Lean.MessageData",
"Unit.unit",
"Lean.Meta.Sym.ExprPtr.mk",
"Lean.Meta.Grind.Arith.Cutsat.State.conflict?",
"Lean.Meta.Grind.Arith.Cutsat.State.assignment",
"Lean.Meta.Grind.Arith.... | true |
CategoryTheory.Monoidal.CommMonFunctorCategoryEquivalence.inverse._proof_3 | Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory | [
"CategoryTheory.CommMon.instCategory",
"CategoryTheory.Monoidal.monFunctorCategoryEquivalence",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"id",
"CategoryTheo... | false |
Std.Sat.CNF.Clause.relabel_nil | Std.Sat.CNF.Relabel | [
"eq_self",
"Std.Sat.CNF.Clause",
"of_eq_true",
"Std.Sat.Literal",
"Eq",
"Std.Sat.CNF.Clause.relabel",
"List.nil"
] | true |
_private.Mathlib.Analysis.Asymptotics.Defs.0.Asymptotics.IsLittleO.comp_fst._simp_1_2 | Mathlib.Analysis.Asymptotics.Defs | [
"SProd.sprod",
"Filter.Eventually",
"Exists",
"Prod.mk",
"Filter.eventually_prod_iff",
"And",
"propext",
"Prod",
"Filter.instSProd",
"Eq",
"Filter"
] | false |
FirstOrder.Language.BoundedFormula.realize_relabelEquiv._simp_1 | Mathlib.ModelTheory.Semantics | [
"Equiv.instEquivLike",
"Function.comp",
"Equiv",
"FirstOrder.Language.BoundedFormula.Realize",
"FirstOrder.Language.BoundedFormula.realize_relabelEquiv",
"FirstOrder.Language.Structure",
"Nat",
"propext",
"FirstOrder.Language",
"FirstOrder.Language.BoundedFormula",
"Fin",
"FirstOrder.Language.... | false |
BoundedContinuousFunction.toContinuousMapStarₐ._proof_6 | Mathlib.Topology.ContinuousMap.Bounded.Star | [
"PseudoMetricSpace.toBornology",
"AddMonoid.toAddZeroClass",
"instBoundedAddOfLipschitzAdd",
"AddCommGroup.toAddGroup",
"NormedRing.toNonUnitalNormedRing",
"AddZeroClass.toAddZero",
"BoundedAdd",
"SeminormedAddCommGroup.to_lipschitzAdd",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"AddGroup.toSu... | false |
CompactlySupportedContinuousMap.finsetInf'_apply | Mathlib.Topology.ContinuousMap.CompactlySupported | [
"CompactlySupportedContinuousMap.semilatticeInf",
"Finset.inf'",
"CompactlySupportedContinuousMap",
"Finset",
"SemilatticeInf.toMin",
"TopologicalSpace",
"Finset.comp_inf'_eq_inf'_comp",
"SemilatticeInf",
"CompactlySupportedContinuousMap.instFunLike",
"Finset.Nonempty",
"ContinuousInf",
"Eq",
... | true |
instInhabitedCtopSet._proof_2 | Mathlib.Data.Analysis.Topology | [
"Membership.mem",
"id",
"HasSubset.Subset",
"Set.instInter",
"Inter.inter",
"Set.Subset.rfl",
"Set.instMembership",
"Set.instHasSubset",
"Set"
] | false |
CategoryTheory.Lax.StrongTrans.vComp._proof_1 | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax | [
"CategoryTheory.Lax.StrongTrans.toLax",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.whiskerLeftIso",
"CategoryTheory.Lax.LaxTrans.naturality",
"id",
"CategoryTheory.Lax.StrongTrans.app",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Lax.StrongTr... | false |
_private.Lean.Compiler.LCNF.Bind.0.Lean.Compiler.LCNF.CompilerM.codeBind.go._unsafe_rec | Lean.Compiler.LCNF.Bind | [
"Pure.pure",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Compiler.LCNF.Arg",
"Lean.Compiler.LCNF.Code.updateCont!",
"Lean.Compiler.LCNF.Code.inferType",
"Lean.Compiler.LCNF.Alt._auto_9",
"Lean.Compiler.LCNF.Code.unreach",
"instMonadReaderOfReaderTOfMonad",
"ReaderT",
"Str... | false |
_private.Std.Data.Internal.List.Associative.0.Std.Internal.List.isEmpty_filterMap_eq_true._simp_1_3 | Std.Data.Internal.List.Associative | [
"Option.none",
"Option.map",
"Option.map_eq_none_iff",
"propext",
"Eq",
"Option"
] | false |
AddGroupTopology.instInfSet.eq_1 | Mathlib.Topology.Algebra.Group.GroupTopology | [
"AddGroupTopology.instInfSet",
"InfSet.mk",
"CompleteLattice.toConditionallyCompleteLattice",
"TopologicalSpace.instCompleteLattice",
"InfSet",
"AddGroupTopology.mk",
"AddGroupTopology.instInfSet._proof_1",
"TopologicalSpace",
"AddGroupTopology",
"AddGroup",
"AddGroupTopology.toTopologicalSpace"... | true |
Std.DTreeMap.getEntryGE._proof_1 | Std.Data.DTreeMap.AdditionalOperations | [
"Std.DTreeMap",
"Std.DTreeMap.Internal.Impl.Ordered",
"Ord.mk",
"Std.DTreeMap.Internal.Impl.WF.ordered",
"Ordering",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Std.DTreeMap.wf"
] | false |
Std.TreeMap.Raw.ordCompare_maxKey!_modify_eq | Std.Data.TreeMap.Raw.Lemmas | [
"Std.TreeMap.Raw.modify",
"Std.TreeMap.Raw.maxKey!",
"Ord",
"Std.TransOrd",
"Ordering",
"Ordering.eq",
"Std.TreeMap.Raw.WF",
"Ord.compare",
"Std.TreeMap.Raw.compare_maxKey!_modify_eq",
"Std.TreeMap.Raw",
"Inhabited",
"Eq"
] | true |
_private.Init.Data.Int.DivMod.Bootstrap.0.Int.ediv.match_1.eq_1 | Init.Data.Int.DivMod.Bootstrap | [
"Int.ediv.match_1",
"Int.ofNat",
"Int",
"instOfNat",
"Nat",
"Eq.refl",
"Int.negSucc",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
StarSubalgebra.commCStarAlgebra._proof_6 | Mathlib.Analysis.CStarAlgebra.Classes | [
"SetLike",
"NormedCommRing.toSeminormedCommRing",
"NormedCommRing.toCommRing",
"Semigroup.toMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedRing.toRing",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"SeminormedRing.toRing",... | false |
ModuleCat.isLimitKernelFork._proof_5 | Mathlib.Algebra.Category.ModuleCat.Kernels | [
"Function.Exact",
"Submodule",
"RingHomSurjective.ids",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.ker",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"LinearMap.range",
"SubtractionMonoid.t... | false |
MonoidHom.subgroupComap_surjective_of_surjective | Mathlib.Algebra.Group.Subgroup.Map | [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"Group",
"Membership.mem",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
"MonoidHom.subgroupComap",
"MonoidHom.submonoidComap_surjective_of_surjective",
"MulOneClass.toMulOne",
"Subgroup.toGroup",
"DFun... | true |
AddMonoidAlgebra.zero.eq_1 | Mathlib.Algebra.MonoidAlgebra.Defs | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"One",
"One.mk",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toOne",
"AddMonoidAlgebra.zero",
"Semiring",
"One.toOfNat1",
"Zero.toOfNat0",
"Eq.refl",
"AddMonoidAlgebra",
"OfNat.ofNat",
"AddMonoidAlgebra.single",
"Semiring.toNonAss... | true |
_private.Init.Data.BitVec.Lemmas.0.BitVec.toFin_signExtend._proof_1_2 | Init.Data.BitVec.Lemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
"Int.instNegInt",
"Int.sub_nonneg_of_le",
"instOfNatNat",
"Int",
"Nat.cast... | false |
Std.DHashMap.contains_of_isEmpty | Std.Data.DHashMap.Lemmas | [
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw₀.contains_of_isEmpty",
"Std.DHashMap.wf",
"instOfNatNat",
"LawfulHashable",
"Subtype.mk",
"Bool.true",
"Std.DHashMap.contains",
"EquivBEq",
"Std.DHashMap.inner",
"Nat",
"Std.DHashMap.Raw.buckets",
"LT.lt",
"Bool",
"Std.DHashMap.Internal.Asso... | true |
EuclideanGeometry.left_ne_of_oangle_eq_neg_pi_div_two | Mathlib.Geometry.Euclidean.Angle.Oriented.Affine | [
"EuclideanGeometry.oangle",
"InnerProductSpace.toNormedSpace",
"EuclideanGeometry.left_ne_of_oangle_ne_zero",
"Real.partialOrder",
"Real",
"instHDiv",
"Real.pi",
"Real.Angle",
"Real.Angle.coe",
"Module.Oriented",
"Real.instRCLike",
"AddCommGroup.toAddCommMonoid",
"Real.instDivInvMonoid",
"... | true |
Sublocale.carrier.instCompleteLattice._proof_8 | Mathlib.Order.Sublocale | [
"Lattice.toSemilatticeSup",
"completeLatticeOfInf",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Sublocale.instSetLike",
"CompleteLattice.toConditionallyCompleteLattice",
"Subtype",
"CompleteLattice.toSupSet",
"Sublocale.carrier.instInfSet",
"Orde... | false |
Coe.noConfusionType | Init.Coe | [
"HEq",
"Coe",
"Coe.casesOn"
] | false |
InfHom.withTop_toFun | Mathlib.Order.Hom.WithTopBot | [
"WithTop.map",
"InfHom.withTop",
"InfTopHom.instFunLike",
"InfHom",
"SemilatticeInf.toMin",
"SemilatticeInf",
"WithTop.top",
"Eq.refl",
"WithTop.semilatticeInf",
"InfTopHom",
"InfHom.instFunLike",
"Eq",
"DFunLike.coe",
"WithTop"
] | true |
CategoryTheory.CoreSmallCategoryOfSet.arrowEquiv | Mathlib.CategoryTheory.SmallRepresentatives | [
"CategoryTheory.CoreSmallCategoryOfSet.functor",
"CategoryTheory.CoreSmallCategoryOfSet.arrowEquiv._proof_2",
"CategoryTheory.SmallCategoryOfSet.obj",
"Set.Elem",
"Equiv",
"CategoryTheory.CoreSmallCategoryOfSet.smallCategoryOfSet",
"CategoryTheory.instCategoryArrow",
"CategoryTheory.CoreSmallCategoryO... | true |
CategoryTheory.SmallObject.SuccStruct.Iteration.noConfusionType | Mathlib.CategoryTheory.SmallObject.Iteration.Basic | [
"CategoryTheory.Functor",
"Preorder.toLT",
"CategoryTheory.SmallObject.SuccStruct",
"LinearOrder",
"OrderBot.toBot",
"WellFoundedLT",
"PartialOrder.toPreorder",
"CategoryTheory.SmallObject.SuccStruct.toSuccArrow",
"Preorder.toLE",
"OrderBot",
"Membership.mem",
"CategoryTheory.SmallObject.SuccS... | false |
Algebra.intTraceAux._proof_5 | Mathlib.RingTheory.IntegralClosure.IntegralRestrict | [
"AlgHom.toLinearMap",
"IsIntegralClosure",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Algebra.isIntegral_trace",
"CommSemiring.toSemiring",
"IsScalarTower",
"IsScalarTower.toAlgHom",
"LinearMap.instFunLike",
"Algebra",
"... | false |
Set.mem_union._simp_1 | Mathlib.Data.Set.Basic | [
"Set.mem_union",
"Membership.mem",
"Set.instUnion",
"propext",
"Or",
"Union.union",
"Eq",
"Set.instMembership",
"Set"
] | false |
UInt8.neg_one_and | Init.Data.UInt.Bitwise | [
"Eq.mpr",
"BitVec.instAndOp",
"UInt8.instOfNat",
"UInt8.toBitVec_neg",
"congrArg",
"BitVec.neg_one_eq_allOnes",
"BitVec.allOnes",
"BitVec",
"id",
"instOfNatNat",
"BitVec.ofNat",
"BitVec.instNeg",
"UInt8.toBitVec",
"Nat",
"instNegUInt8",
"propext",
"UInt8.toBitVec_inj",
"UInt8.toBit... | true |
TopModuleCat.induced._proof_1 | Mathlib.Algebra.Category.ModuleCat.Topology.Basic | [
"iInf",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"CategoryTheory.ConcreteCategory.hom",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"AddCommGroup.toAddGroup",
"CompleteLattice.toConditionallyCompleteLattice",
"TopologicalSpace.instCompleteLattice",
"Linea... | false |
MeasureTheory.Measure.isComplete_iff | Mathlib.MeasureTheory.Measure.NullMeasurable | [
"MeasureTheory.Measure",
"MeasurableSet",
"MeasureTheory.Measure.IsComplete",
"MeasurableSpace",
"Iff",
"MeasureTheory.Measure.IsComplete.mk",
"Iff.intro",
"ENNReal",
"Zero.toOfNat0",
"MeasureTheory.Measure.IsComplete.out'",
"ENNReal.instZero",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"Measu... | true |
Turing.ToPartrec.Code.casesOn | Mathlib.Computability.TuringMachine.Config | [
"Turing.ToPartrec.Code.rec",
"Turing.ToPartrec.Code.succ",
"Turing.ToPartrec.Code.tail",
"Turing.ToPartrec.Code.comp",
"Turing.ToPartrec.Code.case",
"Turing.ToPartrec.Code.zero'",
"Turing.ToPartrec.Code.fix",
"Turing.ToPartrec.Code.cons",
"Turing.ToPartrec.Code"
] | false |
Quaternion.finrank_eq_four | Mathlib.Algebra.Quaternion | [
"NegZeroClass.toNeg",
"CommRing",
"Semiring.toModule",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"SubtractionMonoid.toSubNegZeroMonoid",
"instOfNatNat",
"SubNegZeroMonoid.toNegZeroClass",
"Subtract... | true |
_private.Mathlib.Analysis.Complex.Norm.0.Complex.isCauSeq_norm.match_1_1 | Mathlib.Analysis.Complex.Norm | [
"Norm.norm",
"Real",
"Preorder.toLT",
"AddGroupWithOne.toAddGroup",
"PartialOrder.toPreorder",
"HSub.hSub",
"Exists",
"SemilatticeInf.toPartialOrder",
"Complex.instNorm",
"GE.ge",
"DistribLattice.toLattice",
"instLENat",
"SubNegMonoid.toSub",
"instHSub",
"Exists.casesOn",
"AddGroup.toS... | false |
instSMulCommClass_sphere_closedBall_ball | Mathlib.Analysis.Normed.Module.Ball.Action | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"SeminormedAddCommGroup",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"instSMulElemClosedBallOfNatRealBall",
"AddCommGroup.toAddGroup",
"Membersh... | true |
ExistsContDiffBumpBase.u_neg | Mathlib.Analysis.Calculus.BumpFunction.FiniteDimension | [
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"Real",
"NormedSpace",
"Real.denselyNormedField",
"Real.instZero",
"instTopENat",
"Real.instRCLike",
"NormedSpace.toModule",
"Membership.mem",
"ExistsContDiffBumpBase.u_exists",
"Metric.ball",
"ContDiff",
"Real.normedAddCommGroup",
... | true |
ContDiffWithinAt.isSymmSndFDerivWithinAt_of_omega | Mathlib.Analysis.Calculus.FDeriv.Symmetric | [
"Eq.mpr",
"IsSymmSndFDerivWithinAt",
"NormedSpace",
"UniqueDiffOn",
"congrArg",
"ContinuousMultilinearMap.domDomCongr",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"ContinuousMultilinearMap",
"Membership.mem",
"NormedField.toField",
"id",
"Co... | true |
CategoryTheory.InjectiveResolution.cochainComplex_d | Mathlib.CategoryTheory.Abelian.Injective.Extend | [
"CategoryTheory.InjectiveResolution.cochainComplex",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Nat.instAddCancelCommMonoid",
"Int",
"Nat.cast",
... | true |
CategoryTheory.Iso.inv_comp_eq_id | Mathlib.CategoryTheory.Iso | [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Iff.rfl",
"CategoryTheory.CategoryStruct.id",
"id",
"CategoryTheory.Iso",
"CategoryTheory.Category.comp_id",
"CategoryTheory.Iso.eq_comp_inv._to_dual_1",
"Iff",
"propext",
"CategoryTheory.CategoryStruct.comp",
"... | true |
ProperVAdd.casesOn | Mathlib.Topology.Algebra.ProperAction.Basic | [
"AddMonoid.toAddSemigroup",
"instTopologicalSpaceProd",
"Prod.mk",
"Prod.fst",
"HVAdd.hVAdd",
"ProperVAdd",
"TopologicalSpace",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddGroup",
"AddSemigroupAction.toVAdd",
"AddGroup.toSubNegMonoid",
"instHVAdd",
"SubNegMonoid.toAddMonoid",
"Pro... | false |
Complex.cosh_ofReal_re | Mathlib.Analysis.Complex.Trigonometric | [
"Real",
"Complex.ofReal",
"Complex.re",
"Real.cosh",
"Eq",
"rfl",
"Complex.cosh"
] | true |
MeasureTheory.L1.dist_eq_integral_dist | Mathlib.MeasureTheory.Integral.Bochner.Basic | [
"MeasureTheory.ae",
"Norm.norm",
"Eq.mpr",
"Real",
"MeasureTheory.Measure",
"dist_eq_norm",
"congrArg",
"MeasureTheory.integral_congr_ae",
"MeasureTheory.AEEqFun.cast",
"HSub.hSub",
"PseudoMetricSpace.toUniformSpace",
"MeasureTheory.Lp.instDist",
"AddCommGroup.toAddGroup",
"Membership.mem"... | true |
Lean.Lsp.InlayHintLabelPart | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.InlayHintLabelPart.mk"
] | true |
CategoryTheory.IsReflexivePair | Mathlib.CategoryTheory.Limits.Shapes.Reflexive | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsReflexivePair.mk",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
TypeCat.Fun.ext_iff | Mathlib.CategoryTheory.Types.Basic | [
"HEq.refl",
"Eq.casesOn",
"TypeCat.Fun.toFun",
"TypeCat.Fun.ext",
"Iff",
"TypeCat.Fun",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq"
] | true |
Std.DTreeMap.Raw.getKey?_minKeyD | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.minKeyD",
"Ord.mk",
"Option.some",
"Ordering",
"Std.DTreeMap.Raw.isEmpty",
"Std.DTreeMap.Raw.getKey?",
"Std.TransCmp",
"Std.DTreeMap.Internal.Impl.getKey?_minKeyD",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Bool",
"Bool.false",
"Eq",
"Std.DTreeMap.Raw.WF",
"... | true |
_private.Lean.Meta.Sym.ReplaceS.0.Lean.Meta.Sym.visit.match_1.splitter | Lean.Meta.Sym.ReplaceS | [
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.Expr.forallE",
"List",
"_private.Lean.Meta.Sym.ReplaceS.0.Lean.Meta.Sym.visit.mat... | true |
CategoryTheory.Limits.ReflexiveCofork.mk_π | Mathlib.CategoryTheory.Limits.Shapes.Reflexive | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.WalkingReflexivePair.zero",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingReflexivePair.one",
"CategoryTheory.Functor.map",
"CategoryTheory.Limits.WalkingReflexivePair.category",
"CategoryTheory.CategoryStruct.com... | true |
Ordinal.boundedLimitRec_zero | Mathlib.SetTheory.Ordinal.Arithmetic | [
"Eq.mpr",
"Preorder.toLT",
"Order.succ",
"Ordinal.partialOrder",
"congrArg",
"Ordinal.limitRecOn_zero",
"Ordinal.instOrderBot",
"PartialOrder.toPreorder",
"Subtype.casesOn",
"Membership.mem",
"Set.Elem",
"Order.IsSuccLimit",
"id",
"Ordinal.instSuccOrder",
"Order.IsSuccLimit.succ_lt",
"... | true |
Monotone.expGrowthInf_comp_mul | Mathlib.Analysis.Asymptotics.ExpGrowth | [
"instAddCommMonoidWithOneEReal",
"ExpGrowth.expGrowthInf",
"HMul.hMul",
"PartialOrder.toPreorder",
"Monotone",
"EReal",
"Function.comp",
"ENNReal.log",
"Monotone.comp",
"ENNReal.log_monotone",
"AddMonoidWithOne.toNatCast",
"Ne",
"instMulNat",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMo... | true |
Filter.isOpen_iff | Mathlib.Topology.Filter | [
"congrArg",
"PartialOrder.toPreorder",
"Set.sUnion",
"Function.comp",
"Membership.mem",
"Exists",
"TopologicalSpace.IsTopologicalBasis.open_iff_eq_sUnion",
"HasSubset.Subset",
"iff_self",
"funext",
"And",
"Iff",
"Set.sUnion_image",
"_private.Mathlib.Topology.Filter.0.Filter.isOpen_iff._sim... | true |
Int.Linear.Poly.add.elim | Init.Data.Int.Linear | [
"PULift.up",
"Int.Linear.Poly.ctorElim",
"Int",
"Int.Linear.Var",
"Int.Linear.Poly.add",
"Int.Linear.Poly.ctorIdx",
"Nat",
"Eq.symm",
"Eq",
"Int.Linear.Poly"
] | false |
AlgebraicTopology.DoldKan.MorphComponents.noConfusionType | Mathlib.AlgebraicTopology.DoldKan.Decomposition | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"AlgebraicTopology.DoldKan.MorphComponents",
"Quiver.Hom",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"SimplexCategory.mk",
"Opposite.op",
"Nat",
"AlgebraicTopology.DoldKan.MorphComponents.casesOn",
"SimplexCategory",
"instAddNat",
"Categ... | false |
CategoryTheory.Limits.ImageFactorisation.copy_isImage | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.Limits.MonoFactorisation.I",
"CategoryTheory.Limits.IsImage.copy._proof_8",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.ImageFactorisation.copy",
"CategoryTheory.Limits.IsImage.copy",
"autoParam",
"CategoryTheory.Limits.ImageFactorisation.copy._proof_... | true |
MvPolynomial.C | Mathlib.Algebra.MvPolynomial.Basic | [
"Finsupp.instAddZeroClass",
"MulOne.toOne",
"Nat.instMulZeroClass",
"RingHom.mk",
"Semiring.toModule",
"AddMonoidAlgebra.addAddCommMonoid",
"CommSemiring.toSemiring",
"MvPolynomial.C._proof_2",
"OneHom.mk",
"AddMonoid.toAddZeroClass",
"MvPolynomial.monomial",
"LinearMap.instFunLike",
"Nat.in... | true |
List.foldl_flip_eq_foldr | Mathlib.Data.List.Fold | [
"congrArg",
"LeftCommutative",
"flip",
"List.rec",
"List.foldl",
"List.cons",
"List.foldr_cons_eq_foldr_apply",
"List",
"congr",
"True",
"eq_self",
"of_eq_true",
"List.foldr",
"Eq",
"Eq.trans"
] | true |
AffineMap.hasStrictDerivAt | Mathlib.Analysis.Calculus.Deriv.AffineMap | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"AffineMap.hasDerivAtFilter",
"Semiring.toModule",
"AffineMap.instFunLike",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"AddGroupWithOne.toAddGroup",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAdd... | true |
FractionalIdeal.coeIdeal_injective' | Mathlib.RingTheory.FractionalIdeal.Basic | [
"CommRing",
"Eq.ge",
"Semiring.toModule",
"IsLocalization",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"nonZeroDivisors",
"LE.le.antisymm",
"FractionalIdeal.coeIdeal_le_coeIdeal'",
"Eq.le",
"Submodule.instPartialOrder",
"LE.le",
"Ideal",
"MulZeroO... | true |
Lean.Parser.Tactic.dsimpArg | Init.Tactics | [
"Lean.Parser.Tactic.simpLemma",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.Parser.Tactic.simpErase",
"Lean.Name.mkStr1"
] | true |
ContinuousLinearMap.norm_compContinuousAlternatingMap_le | Mathlib.Analysis.Normed.Module.Alternating.Basic | [
"Norm.norm",
"Real.instLE",
"Real",
"ContinuousLinearMap.norm_compContinuousMultilinearMap_le",
"SeminormedAddCommGroup",
"HMul.hMul",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"LE.le",
"ContinuousAlterna... | true |
List.isPrefixOf?_eq_some_iff_append_eq | Batteries.Data.List.Lemmas | [
"False",
"_private.Batteries.Data.List.Lemmas.0.List.isPrefixOf?_eq_some_iff_append_eq._simp_1_5",
"Option.ctorIdx",
"congrArg",
"False.elim",
"noConfusion_of_Nat",
"Option.some.injEq",
"Option.some",
"LawfulBEq",
"instDecidableEqBool",
"List.rec",
"List.cons",
"List.cons.injEq",
"iff_self... | true |
ModuleCat.restrictCoextendScalarsAdj._proof_4 | Mathlib.Algebra.Category.ModuleCat.ChangeOfRings | [
"ModuleCat.RestrictionCoextensionAdj.counit'._proof_1",
"Semiring.toModule",
"Equiv.instEquivLike",
"LinearMap.comp.congr_simp",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat.coextendScalars",
"ModuleCat",
"LinearMap.ext",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
... | false |
AddSubmonoid.mk | Mathlib.Algebra.Group.Submonoid.Defs | [
"AddSubsemigroup.carrier",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddSubmonoid",
"AddSubmonoid.mk",
"AddZero.toZero",
"AddZeroClass",
"AddSubsemigroup",
"AddZero.toAdd",
"Zero.toOfNat0",
"OfNat.ofNat",
"Set.instMembership",
"Set"
] | true |
CategoryTheory.Quiv.equivOfIso | Mathlib.CategoryTheory.Category.Quiv | [
"CategoryTheory.Quiv.equivOfIso._proof_1",
"CategoryTheory.Quiv.str'",
"Equiv.mk",
"Equiv",
"CategoryTheory.Iso",
"CategoryTheory.Quiv.category",
"CategoryTheory.Bundled.α",
"CategoryTheory.Quiv.equivOfIso._proof_2",
"CategoryTheory.Quiv",
"Quiver",
"CategoryTheory.Iso.hom",
"CategoryTheory.Is... | true |
Subgroup.closure_singleton_inv | Mathlib.Algebra.Group.Subgroup.Pointwise | [
"Eq.mpr",
"Subgroup.closure",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"InvolutiveInv.toInv",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"Set.instSingletonSet",
"id",
"Subgroup",
"DivisionMonoid.toInvolutiveInv",
"Inv.inv",
"Set.inv",
"Subgroup.closure_inv... | true |
_private.Mathlib.FieldTheory.RatFunc.Basic.0.RatFunc.wrapped._proof_1._@.Mathlib.FieldTheory.RatFunc.Basic.1687740377._hygCtx._hyg.2 | Mathlib.FieldTheory.RatFunc.Basic | [
"CommRing",
"RatFunc.definition._@.Mathlib.FieldTheory.RatFunc.Basic.1687740377._hygCtx._hyg.2",
"RatFunc",
"Eq",
"rfl"
] | false |
Pi.coe_evalLatticeHom | Mathlib.Order.Hom.Lattice | [
"Lattice",
"LatticeHom",
"Function.eval",
"Pi.instLattice",
"Pi.evalLatticeHom",
"LatticeHom.instFunLike",
"Eq",
"DFunLike.coe",
"rfl"
] | true |
CategoryTheory.Comma.coconeOfPreserves_pt_hom | Mathlib.CategoryTheory.Limits.Comma | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Functor.mapCocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Comma.fst",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.IsColimit",
"CategoryTheory.Comma.hom",
"CategoryTheory.Comma",
... | true |
IsMaxOn.isLUB | Mathlib.Order.Filter.Extr | [
"IsMinOn.isGLB",
"IsMaxOn",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Exists",
"And",
"IsLUB",
"OrderDual",
"OrderDual.instPreorder",
"Eq",
"Set.instMembership",
"Preorder",
"Set"
] | true |
Aesop.Frontend.Parser.transparency | Aesop.Frontend.RuleExpr | [
"Lean.ParserDescr.nonReservedSymbol",
"Lean.ParserDescr.nodeWithAntiquot",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.Name.mkStr2",
"Bool.false",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | true |
CochainComplex.HomComplex.Cocycle.diff._proof_2 | Mathlib.Algebra.Homology.HomotopyCategory.HomComplex | [
"Int",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"Int.instAdd",
"OfNat.ofNat",
"Eq",
"rfl"
] | false |
Finset.single_lt_sum | Mathlib.Algebra.Order.BigOperators.Group.Finset | [
"Iff.mpr",
"Eq.mpr",
"Finset.mem_singleton",
"Trans.trans",
"Preorder.toLT",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"Preorder.toLE",
"Membership.mem",
"mt",
"AddZeroClass.toAddZero",
"Finset.singleton_subset_iff",
"id",
"HasSubset.Subset",
"Ne",
"LE.le",
"AddCommMonoid",... | true |
instFintypeSymbol._proof_7 | Mathlib.Computability.Language | [
"Symbol",
"Function.LeftInverse",
"instFintypeSymbol.match_3",
"Sum.casesOn",
"Sum",
"instFintypeSymbol.match_5",
"Sum.inl",
"Sum.inr",
"Eq.ndrec",
"Eq.refl",
"Eq.symm",
"Eq",
"Symbol.terminal",
"Symbol.nonterminal"
] | false |
Lean.instHashableLocalDeclKind.hash | Lean.LocalContext | [
"UInt64.instOfNat",
"UInt64",
"Lean.LocalDeclKind",
"Unit",
"_private.Lean.LocalContext.0.Lean.instReprLocalDeclKind.repr.match_1",
"OfNat.ofNat"
] | true |
Lean.Meta.AC.PreExpr.noConfusionType | Lean.Meta.Tactic.AC.Main | [
"Lean.Meta.AC.PreExpr",
"Lean.Expr",
"Lean.Meta.AC.PreExpr.casesOn",
"Eq"
] | false |
Std.HashMap.Raw.mem_map._simp_1 | Std.Data.HashMap.RawLemmas | [
"Membership.mem",
"Std.HashMap.Raw.WF",
"LawfulHashable",
"Std.HashMap.Raw",
"EquivBEq",
"Std.HashMap.Raw.map",
"propext",
"Std.HashMap.Raw.instMembershipOfBEqOfHashable",
"Hashable",
"Std.HashMap.Raw.mem_map",
"BEq",
"Eq"
] | false |
Lean.PrintImportsResult.mk.inj | Lean.Elab.ParseImportsFast | [
"Lean.PrintImportsResult.mk.noConfusion",
"Lean.PrintImportResult",
"Array",
"Lean.PrintImportsResult",
"Eq",
"Lean.PrintImportsResult.mk"
] | true |
TensorProduct.AlgebraTensorModule.lift._proof_5 | Mathlib.LinearAlgebra.TensorProduct.Tower | [
"TensorProduct.leftHasSMul",
"CommSemiring.toSemiring",
"TensorProduct.instSMul",
"IsScalarTower",
"Algebra.toSMul",
"Algebra.id",
"IsScalarTower.left",
"AddCommMonoid",
"CommSemiring",
"TensorProduct.instSMul._proof_1",
"Semiring.toMonoid",
"TensorProduct",
"Module.toDistribMulAction",
"A... | false |
MulAction.instChartedSpaceQuotient._proof_2 | Mathlib.Geometry.Manifold.Instances.Quotient | [
"Group",
"DivInvMonoid.toMonoid",
"MulAction.orbitRel",
"Quotient.mk",
"Group.toDivInvMonoid",
"Quotient",
"MulAction",
"Quotient.mk_surjective",
"Function.Surjective"
] | false |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.sign_ediv._proof_1_8 | Init.Data.Int.DivMod.Lemmas | [
"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",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Int.decLe",
"Lean.Omega.LinearCombo.eval",
... | false |
_private.Mathlib.Topology.Instances.ENat.0.ENat.tendsto_nhds_top_iff_natCast_lt._simp_1_2 | Mathlib.Topology.Instances.ENat | [
"iInf",
"Filter.instInfSet",
"Filter.Tendsto",
"propext",
"Filter.tendsto_iInf",
"Eq",
"Filter"
] | false |
_private.Mathlib.Tactic.IntervalCases.0.Mathlib.Tactic.IntervalCases.Methods.getBound.match_8 | Mathlib.Tactic.IntervalCases | [
"Mathlib.Tactic.IntervalCases.Bound",
"Lean.Expr",
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
_private.Init.Grind.Ordered.Ring.0.Lean.Grind.OrderedRing.mul_le_mul_of_nonneg_right._simp_1_1 | Init.Grind.Ordered.Ring | [
"Std.le_refl",
"Std.Refl",
"LE.le",
"LE",
"True",
"eq_true",
"Eq"
] | false |
_private.Mathlib.GroupTheory.QuotientGroup.Defs.0.Con.subgroup_quotientGroupCon._simp_1_1 | Mathlib.GroupTheory.QuotientGroup.Defs | [
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"QuotientGroup.leftRel",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Inv.... | false |
CategoryTheory.Limits.cokernel.desc_zero | Mathlib.CategoryTheory.Limits.Shapes.Kernels | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.cokernel.desc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.comp_zero",
"CategoryTheory.Limits.cokernel",
"CategoryTheory.Limits.coequalizer.hom_ext",
"CategoryTheory.Limits.HasCokernel",
... | true |
Lean.Expr.NumObjs.State | Lean.Util.NumObjs | [
"Lean.Expr.NumObjs.State.mk"
] | true |
Lean.Compiler.LCNF.JoinPointContextExtender.ExtendContext.candidates._default | Lean.Compiler.LCNF.JoinPoints | [
"id",
"Lean.instEmptyCollectionFVarIdSet",
"Lean.FVarIdSet",
"EmptyCollection.emptyCollection"
] | false |
CategoryTheory.MorphismProperty.ContainsIdentities.id_mem | Mathlib.CategoryTheory.MorphismProperty.Composition | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.MorphismProperty.ContainsIdentities",
"CategoryTheory.Category"
] | true |
Lean.Server.DocumentMeta.mk | Lean.Server.Utils | [
"Lean.Server.DocumentMeta.mk",
"Lean.FileMap",
"Lean.Lsp.DocumentUri",
"Nat",
"Lean.Server.DocumentMeta",
"Lean.Name",
"Lean.Lsp.DependencyBuildMode"
] | true |
CategoryTheory.Functor.CoreMonoidal.mk'_μIso | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.CoreMonoidal.mk'._auto_5",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Functor.CoreMonoidal.μIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"CategoryTheory.Mon... | true |
_private.Lean.Meta.Tactic.Grind.AC.Seq.0.Lean.Grind.AC.StartsWithResult.casesOn | Lean.Meta.Tactic.Grind.AC.Seq | [
"_private.Lean.Meta.Tactic.Grind.AC.Seq.0.Lean.Grind.AC.StartsWithResult.rec",
"_private.Lean.Meta.Tactic.Grind.AC.Seq.0.Lean.Grind.AC.StartsWithResult.prefix",
"_private.Lean.Meta.Tactic.Grind.AC.Seq.0.Lean.Grind.AC.StartsWithResult.exact",
"_private.Lean.Meta.Tactic.Grind.AC.Seq.0.Lean.Grind.AC.StartsWithRe... | false |
MeasureTheory.Measure.MutuallySingular.haveLebesgueDecomposition | Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | [
"MeasureTheory.Measure.withDensity",
"MeasureTheory.Measure",
"MeasureTheory.withDensity_zero",
"congrArg",
"AddMonoid.toAddZeroClass",
"Measurable",
"ENNReal.measurableSpace",
"Pi.instZero",
"Prod.mk",
"MeasureTheory.Measure.HaveLebesgueDecomposition",
"MeasureTheory.Measure.instZero",
"Prod.... | true |
RingCat.forget_obj | Mathlib.Algebra.Category.Ring.Basic | [
"outParam",
"CategoryTheory.forget_obj",
"CategoryTheory.ConcreteCategory",
"CategoryTheory.types",
"CategoryTheory.forget",
"CategoryTheory.ToType",
"Eq",
"CategoryTheory.Functor.obj",
"FunLike",
"CategoryTheory.Category"
] | true |
LinearMap.BilinForm.tensorDistrib.eq_1 | Mathlib.LinearAlgebra.QuadraticForm.TensorProduct | [
"LinearMap.BilinMap.tensorDistrib",
"IsScalarTower.to_smulCommClass'",
"LinearMap.BilinMap.tensorDistrib._proof_9",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"IsScalarTower.right",
"LinearEquiv.congrRight₂",
"LinearMap.BilinMap.tensorDistrib._proof_10",
"LinearMap.BilinForm.tensorDistrib._pro... | true |
Set.VAddAntidiagonal.finite_of_isPWO | Mathlib.Data.Set.SMulAntidiagonal | [
"Set.IsPWO",
"False",
"Set.PartiallyWellOrderedOn",
"Set.PartiallyWellOrderedOn.exists_monotone_subseq",
"Classical.byContradiction",
"RelEmbedding.injective",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.Finite",
"Membership.mem",
"Exists",
"PartialOrder",
"Eq.mp",
"Set.Elem",
"Set.... | true |
Matrix.kroneckerTMul_mem_unitary | Mathlib.LinearAlgebra.UnitaryGroup | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Algebra.to_smulCommClass",
"HMul.hMul",
"_private.Mathlib.LinearAlgebra.UnitaryGroup.0.Matrix.kroneckerTMul_mem_unitary._simp_1_2",
"IsScalarTower.right",
"instDecidableEqProd",
"AddCommMonoidWithOne.toAddCommMonoid",
"Monoid.to... | true |
PSet.rank_le_iff | Mathlib.SetTheory.ZFC.Rank | [
"Eq.mpr",
"Preorder.toLT",
"Order.succ",
"PSet.instMembership",
"Ordinal.partialOrder",
"congrArg",
"Ordinal.iSup_le",
"PartialOrder.toPreorder",
"PSet.rank_lt_of_mem",
"Preorder.toLE",
"Membership.mem",
"id",
"PSet.Mem.mk",
"LE.le",
"PSet.mk",
"Ordinal.instSuccOrder",
"PSet",
"PSe... | true |
_private.Mathlib.Analysis.Hofer.0.termD | Mathlib.Analysis.Hofer | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
RatCast.rec | Batteries.Classes.RatCast | [
"Rat",
"RatCast",
"RatCast.mk"
] | false |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.