name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
MeasureTheory.setToFun_mono_left' | Mathlib.MeasureTheory.Integral.SetToL1 | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"MeasureTheory.Measure",
"Preorder.toLT",
"CompleteSpace",
"NormedSpace.toIsBoundedSMul",
"MeasurableSet",
"NormedSpace",
"eq_false",
"MeasureTheory.setToFun_undef",
"Real.denselyNormedField",
"instRefl... | true |
PNat.instSuccAddOrder | Mathlib.Data.PNat.Order | [
"instLinearOrderPNat",
"PNat.instSuccOrder",
"SuccAddOrder",
"PartialOrder.toPreorder",
"SuccAddOrder.mk",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"PNat.instSuccAddOrder._proof_1",
"instOnePNat",
"instDistribLatticeOfLinearOrder",
"Lattice.toSemilatticeInf",
"instAddPNat",... | true |
_private.Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass.0.PeriodPair.weierstrassPExcept_eq_tsum._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass | [
"AddGroup.toSubtractionMonoid",
"sub_eq_zero",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq"
] | false |
contMDiff_zero_iff | Mathlib.Geometry.Manifold.ContMDiff.Defs | [
"Eq.mpr",
"Continuous",
"NormedSpace",
"congrArg",
"CommSemiring.toSemiring",
"ContMDiff",
"Set.univ",
"Iff.rfl",
"id",
"TopologicalSpace",
"ModelWithCorners",
"Iff",
"ENat",
"contMDiffOn_univ",
"propext",
"instCommSemiringENat",
"NontriviallyNormedField",
"Zero.toOfNat0",
"Conti... | true |
UniformSpaceCat.instFunLike | Mathlib.Topology.Category.UniformSpace | [
"UniformContinuous",
"DFunLike.mk",
"Subtype",
"UniformSpaceCat.carrier",
"UniformSpaceCat.str",
"UniformSpaceCat.instFunLike._proof_1",
"Subtype.val",
"UniformSpaceCat",
"FunLike"
] | true |
Nat.log_le_clog._simp_1 | Mathlib.Data.Nat.Log | [
"LE.le",
"instLENat",
"Nat",
"True",
"Nat.log_le_clog",
"eq_true",
"Nat.log",
"Nat.clog",
"Eq"
] | false |
dvd_differentIdeal_iff | Mathlib.RingTheory.DedekindDomain.Different | [
"IsDomain",
"FractionRing.field",
"IsDedekindDomain.toIsDomain",
"CommRing",
"Dvd.dvd",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"iff_not_comm",
"Semiring.toModule",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"OreLocalization.instAlgebra",
"CommSemiring.toSemiring",
"Subm... | true |
WType.toList.match_1 | Mathlib.Data.W.Constructions | [
"WType",
"WType.Listβ",
"WType.Listα",
"WType.Listα.cons",
"WType.mk",
"WType.casesOn",
"WType.Listα.casesOn",
"WType.Listα.nil"
] | false |
_private.Aesop.Util.Basic.0.Aesop.filterTrieM.go.match_3 | Aesop.Util.Basic | [
"Prod.mk",
"Lean.Meta.DiscrTree.Key",
"Lean.Meta.DiscrTree.Trie",
"Prod",
"Prod.casesOn"
] | false |
Lean.Server.Test.Runner.Client.InfoPopup.ctorIdx | Lean.Server.Test.Runner | [
"Nat",
"Lean.Server.Test.Runner.Client.InfoPopup"
] | false |
Aesop.ElabM.Context.casesOn | Aesop.ElabM | [
"Lean.MVarId",
"Aesop.ElabM.Context",
"Bool",
"Aesop.ElabM.Context.rec",
"Aesop.ElabM.Context.mk"
] | false |
Lean.MessageData.withContext | Lean.Message | [
"Lean.MessageData",
"Lean.MessageDataContext",
"Lean.MessageData.withContext"
] | true |
CategoryTheory.Mon.hom_one | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Mon.Hom.hom",
"CategoryTheory.Mon.monMonoidal",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.BraidedCategory",
"CategoryTheory.MonObj.one",
"Categ... | true |
_private.Mathlib.AlgebraicTopology.SimplexCategory.Basic.0.SimplexCategory.mkOfLe.match_1.splitter | Mathlib.AlgebraicTopology.SimplexCategory.Basic | [
"SimplexCategory.mkOfLe.match_1",
"Fin.instOfNat",
"instOfNatNat",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Fin"
] | true |
Convexity.StdSimplex.casesOn | Mathlib.Geometry.Convex.ConvexSpace.Defs | [
"Finsupp.instLE",
"One",
"AddMonoid.toAddZeroClass",
"Finsupp.sum",
"AddZeroClass.toAddZero",
"LE.le",
"Convexity.StdSimplex.rec",
"LE",
"AddCommMonoid",
"AddZero.toZero",
"Convexity.StdSimplex",
"Convexity.StdSimplex.mk",
"One.toOfNat1",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"... | false |
Std.DHashMap.Internal.Raw₀.getKey?_eq_some_iff | Std.Data.DHashMap.Internal.RawLemmas | [
"Iff.mpr",
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.DHashMap.Internal.Raw₀.contains",
"Iff.of_eq",
"Std.DHashMap.Internal.Raw.WF.out",
"congrArg",
"Std.DHashMap.Internal.Raw₀.getKey?",
"Std.DHashMap.Internal.Raw₀.getKey",
"Std.DHashMap.Raw",
"Option.some",
"Std.DHashMap.Internal.Raw₀.contains_eq_... | true |
HomologicalComplex.mapBifunctor.hom_ext_iff | Mathlib.Algebra.Homology.Bifunctor | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Functor.category",
"HomologicalComplex",
"Eq.casesOn",
"HomologicalComplex.ιMapBifunctor",
"Prod.mk",
"ComplexShape",
"CategoryTheory.Preaddit... | true |
LieRinehartRing.lie_smul_eq_mul' | Mathlib.Algebra.LieRinehartAlgebra.Defs | [
"CommRing",
"instHSMul",
"HMul.hMul",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"Bracket.bracket",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"Lie... | true |
StieltjesFunction.measurable_measure | Mathlib.Probability.Kernel.Disintegration.MeasurableStieltjes | [
"Eq.mpr",
"MeasureTheory.Measure.instMeasurableSpace",
"Real.partialOrder",
"ConditionallyCompleteLinearOrder.toCompactIccSpace",
"Real",
"MeasureTheory.Measure",
"Measurable.ennreal_ofReal",
"MulZeroClass.toMul",
"Real.instZero",
"ENNReal.ofReal",
"congrArg",
"sub_zero",
"Real.instSub",
"... | true |
OrderMonoidWithZeroHom.toMonoidWithZeroHom_mk | Mathlib.Algebra.Order.Hom.MonoidWithZero | [
"OrderMonoidWithZeroHom.instMonoidWithZeroHomClass",
"MonoidWithZeroHomClass.toMonoidWithZeroHom",
"OrderMonoidWithZeroHom",
"OrderMonoidWithZeroHom.mk",
"Monotone",
"MonoidWithZeroHom.funLike",
"MulZeroOneClass",
"MonoidWithZeroHom",
"Eq.refl",
"Eq",
"DFunLike.coe",
"Preorder",
"OrderMonoid... | true |
_private.Batteries.Tactic.Trans.0.Batteries.Tactic.initFn.match_7._@.Batteries.Tactic.Trans.2247956323._hygCtx._hyg.2 | Batteries.Tactic.Trans | [
"Lean.Expr",
"Prod.mk",
"Array",
"Prod",
"Lean.BinderInfo",
"Prod.casesOn"
] | false |
_private.Mathlib.MeasureTheory.Group.Integral.0.MeasureTheory.integral_eq_zero_of_mul_right_eq_neg._simp_1_2 | Mathlib.MeasureTheory.Group.Integral | [
"NegZeroClass.toNeg",
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"MeasureTheory.integral_neg",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"MeasurableSpace",
"MeasureTheory.integral",
"NormedAddCommGroup.toAddCommGr... | false |
mem_leftCoset_leftCoset | Mathlib.GroupTheory.Coset.Basic | [
"Monoid",
"Eq.mpr",
"instHSMul",
"instSMulOfMul",
"Monoid.toMulOneClass",
"congrArg",
"Membership.mem",
"id",
"MulOne.toMul",
"MulOneClass.toMulOne",
"SetLike.coe",
"mem_own_leftCoset",
"SetLike.mem_coe",
"propext",
"HSMul.hSMul",
"Submonoid.instSetLike",
"Eq.symm",
"Eq",
"Set.in... | true |
Real.geom_mean_le_arith_mean4_weighted | Mathlib.Analysis.MeanInequalities | [
"Real.instPow",
"Real.instLE",
"Real",
"HMul.hMul",
"Real.instZero",
"Distrib.toAdd",
"NNReal",
"LE.le",
"NNReal.geom_mean_le_arith_mean4_weighted",
"instDistribOfSemiring",
"Subtype.mk",
"Real.instAdd",
"Real.instOne",
"instHAdd",
"HPow.hPow",
"HAdd.hAdd",
"Real.instMul",
"Iff.mp"... | true |
addSubgroupOfIdempotent._proof_3 | Mathlib.GroupTheory.OrderOfElement | [
"Finite",
"AddMonoid.toAddZeroClass",
"AddSubsemigroup.carrier",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddSubmonoid.toAddSubsemigroup",
"AddCancelMonoid.toAddLeftCancelMonoid",
"AddZero.toZero",
"instHAdd",
"Set.add",
"AddGroup",
"Set.Nonempty",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd... | false |
groupCohomology.instEpiModuleCatH2π | Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | [
"Pi.Function.module",
"Submodule",
"Rep.V",
"CommRing",
"Pi.addCommMonoid",
"CategoryTheory.Epi",
"ModuleCat",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Group",
"Rep.hV1",
"Membership.mem",
"Subtype",
"DivInvMonoid.toMonoid",
"Submodule.module",
"Group.to... | true |
CategoryTheory.StrictlyUnitaryPseudofunctorCore.map₂_whisker_right._autoParam | Mathlib.CategoryTheory.Bicategory.Functor.StrictlyUnitary | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Lean.Meta.Grind.AC.EqCnstrProof.superpose_head_idempotent.noConfusion | Lean.Meta.Tactic.Grind.AC.Types | [
"Lean.Meta.Grind.AC.EqCnstr",
"Lean.Meta.Grind.AC.EqCnstrProof.noConfusion",
"id",
"Lean.Meta.Grind.AC.EqCnstrProof.superpose_head_idempotent",
"Lean.Meta.Grind.AC.EqCnstrProof",
"Lean.Grind.AC.Var",
"Eq"
] | false |
CategoryTheory.Limits.CoproductDisjoint.isPullback_of_isInitial | Mathlib.CategoryTheory.Limits.Shapes.DisjointCoproduct | [
"CategoryTheory.Limits.pullback",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.Cofan",
"CategoryTheory.Limits.IsInitial.uniqueUpToIso",
"CategoryTheory.CommSq",
"congrArg",
"CategoryTheory.Limits.CoproductDisjoint",
"CategoryTheory.Limits.pullback.snd",
"CategoryT... | true |
AlgEquiv.ofInjectiveField._proof_1 | Mathlib.Algebra.Algebra.Subalgebra.Basic | [
"Nontrivial",
"Ring.toNonAssocRing",
"AlgHom",
"Algebra",
"RingHom",
"DivisionRing.toDivisionSemiring",
"DivisionRing.toRing",
"RingHom.injective",
"CommSemiring",
"RingHom.instFunLike",
"DivisionRing.isSimpleRing",
"AlgHom.toRingHom",
"DivisionSemiring.toSemiring",
"Semiring",
"Division... | false |
Lean.Meta.Sym.AlphaShareCommon.State.noConfusionType | Lean.Meta.Sym.AlphaShareCommon | [
"Lean.Meta.Sym.instBEqAlphaKey",
"Lean.PHashSet",
"Lean.Meta.Sym.AlphaKey",
"Lean.Meta.Sym.AlphaShareCommon.State.casesOn",
"Lean.Meta.Sym.instHashableAlphaKey",
"Eq",
"Lean.Meta.Sym.AlphaShareCommon.State"
] | false |
Sum.map_bijective | Mathlib.Data.Sum.Basic | [
"Sum.map",
"Sum.map_injective",
"Sum",
"And",
"Iff",
"and_and_and_comm",
"Iff.and",
"Iff.trans",
"Function.Bijective",
"Function.Injective",
"Function.Surjective",
"Sum.map_surjective"
] | true |
SubAddAction.ofStabilizer.conjMap._proof_5 | Mathlib.GroupTheory.GroupAction.SubMulAction.OfStabilizer | [
"SubAddAction.vadd'",
"AddMonoid.toAddSemigroup",
"instVAddOfAdd",
"SubAddAction.ofStabilizer.conjMap._proof_1",
"AddSubgroup.toAddGroup",
"Membership.mem",
"VAddAssocClass.left",
"SubAddAction.ofStabilizer.conjMap._proof_3",
"Set.instSingletonSet",
"Subtype",
"SubAddAction.ofStabilizer.conjMap.... | false |
Set.chainHeight_eq_top_iff | Mathlib.Order.Height | [
"Mathlib.Tactic.Push.not_forall_eq",
"Mathlib.Tactic.Push.not_exists._simp_1",
"Set.chainHeight",
"Eq.mpr",
"ENat.some_eq_coe",
"Mathlib.Tactic.Push.not_and_eq",
"Set.encard",
"Preorder.toLT",
"instCompleteLinearOrderENat",
"Nat.instIsOrderedAddMonoid",
"instCharZeroENat",
"instAddMonoidWithOn... | true |
_private.Init.Data.UInt.Bitwise.0.UInt8.xor_eq_zero_iff._simp_1_1 | Init.Data.UInt.Bitwise | [
"BitVec",
"instOfNatNat",
"UInt8.toBitVec",
"Nat",
"propext",
"UInt8.toBitVec_inj",
"OfNat.ofNat",
"Eq.symm",
"UInt8",
"Eq"
] | false |
Lean.Elab.CompletionInfo.option.inj | Lean.Elab.InfoTree.Types | [
"Lean.Elab.CompletionInfo.option.noConfusion",
"Lean.Elab.CompletionInfo.option",
"Lean.Elab.CompletionInfo",
"Lean.Syntax",
"Eq"
] | true |
CategoryTheory.ShortComplex.LeftHomologyData.copy._proof_1 | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ShortComplex",
"CategoryTheory.Limits.comp_zero",
"id",
"CategoryTheory.Iso",
... | false |
Lean.Expr.name? | Lean.Util.Recognizers | [
"Lean.Expr.brecOn",
"Lean.Expr",
"Lean.Name",
"Lean.Expr.name?._f",
"Option"
] | true |
_private.Mathlib.RingTheory.WittVector.StructurePolynomial.0.wittStructureRat_vars._proof_1_5 | Mathlib.RingTheory.WittVector.StructurePolynomial | [
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"False",
"of_decide_eq_true",
"Lean.Grind.iff_eq",
"Lean.Grind.CommRing.Expr.var",
"congrArg",
"Finset",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"HSub.hSub",
"Nat.not_le_eq",
"Nat.ToInt... | false |
Measurable.coe_real_ereal | Mathlib.MeasureTheory.Constructions.BorelSpace.Real | [
"Real",
"Measurable.comp",
"Measurable",
"EReal",
"MeasurableSpace",
"Real.measurableSpace",
"measurable_coe_real_ereal",
"EReal.measurableSpace",
"Real.toEReal"
] | true |
NFA.evalFrom_append | Mathlib.Computability.NFA | [
"congrArg",
"NFA.evalFrom",
"NFA",
"List.foldl",
"instHAppendOfAppend",
"List",
"NFA.stepSet",
"List.foldl_append",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"List.instAppend",
"Eq",
"HAppend.hAppend",
"Eq.trans",
"Set"
] | true |
Std.Tactic.BVDecide.BVExpr.bitblast.blastExtractAndExtendTarget.mk.congr_simp | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Operations.Cpop | [
"HMul.hMul",
"Eq.rec",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastExtractAndExtendTarget.mk",
"instMulNat",
"Std.Sat.AIG",
"Nat",
"Eq.refl",
"Hashable",
"Std.Sat.AIG.RefVec",
"Std.Tactic.BVDecide.BVExpr.bitblast.blastExtractAndExtendTarget",
"Eq",
"instHMul",
"DecidableEq"
] | true |
Monoid.Coprod.fst | Mathlib.GroupTheory.Coprod.Basic | [
"Monoid",
"Monoid.Coprod.lift",
"MonoidHom",
"Monoid.toMulOneClass",
"MulOneClass.toMulOne",
"MonoidHom.id",
"Monoid.Coprod.instMulOneClass",
"One.toOfNat1",
"Monoid.Coprod",
"OfNat.ofNat",
"instOneMonoidHom"
] | true |
_private.Mathlib.Analysis.Calculus.ContDiff.Defs.0.ContDiffWithinAt.congr_of_eventuallyEq.match_1_1 | Mathlib.Analysis.Calculus.ContDiff.Defs | [
"NormedSpace",
"Option.casesOn",
"Option.some",
"WithTop.some",
"Option.none",
"WithTop.top",
"ENat",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"ContDiffWithinAt",
"Top.top",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"NormedAddCommGroup",
"WithTop",
"Set"
] | false |
ProfiniteGrp.coe_comp | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ProfiniteGrp.group",
"Function.comp",
"ProfiniteGrp",
"DivInvMonoid.toMonoid",
"TotallyDisconnectedSpace",
"Group.toDivInvMonoid",
"TopCat.str",
"TopCat.carrier",
"ContinuousMonoidHom.instFunLike",
"ProfiniteGrp.toProfinite",
"Category... | true |
Option.toArray_pmap | Init.Data.Option.Attach | [
"congrArg",
"List.map_toArray",
"Option.toArray",
"Option.casesOn",
"Option.some",
"Array.map",
"Subtype",
"Option.attach",
"List.toArray",
"List.cons",
"Subtype.mk",
"Array",
"Option.none",
"True",
"eq_self",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"Eq.symm",
"Subtype.val",
"Eq... | true |
IntermediateField.extendScalars_self | Mathlib.FieldTheory.IntermediateField.Adjoin.Defs | [
"IntermediateField.restrictScalars",
"IntermediateField.instPartialOrder",
"IntermediateField.isScalarTower_mid'",
"le_refl",
"Lattice.toSemilatticeSup",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"CompleteLattice.toLattice",
"congrArg",
"In... | true |
noConfusionTypeEnum | Init.Core | [
"Decidable.casesOn",
"Decidable",
"Eq",
"Not",
"DecidableEq"
] | true |
Lean.Elab.Tactic.Grind.SimpCacheKey.mk.injEq | Lean.Elab.Tactic.Grind.Basic | [
"Lean.Elab.Tactic.Grind.ExtraTheorem",
"Eq.propIntro",
"Lean.Elab.Tactic.Grind.SimpCacheKey",
"Lean.Elab.Tactic.Grind.SimpCacheKey.mk",
"Lean.injEq_helper",
"Array",
"And",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Eq",
"Lean.Elab.Tactic.Grind.SimpCacheKey.mk.inj"
] | true |
Subfield.extendScalars.orderIso._proof_5 | Mathlib.FieldTheory.IntermediateField.Basic | [
"IntermediateField.algebraMap_mem",
"Subfield.toAlgebra",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"IntermediateField",
"RingHom",
"Membership.mem",
"Field.toDivisionRing",
"Subtype",
"Subfield.instSetLike",
"Field.toSemifield",
"Subtype.mk",
"Subfield.toField",
"RingHom.instFunLik... | false |
Lean.Lsp.SemanticTokenType.leanSorryLike | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SemanticTokenType.leanSorryLike",
"Lean.Lsp.SemanticTokenType"
] | true |
Std.DTreeMap.Raw.Const.mem_iff_isSome_get? | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.instMembership",
"Ord.mk",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"Std.DTreeMap.Internal.Impl.Const.mem_iff_isSome_get?",
"Bool.true",
"Iff",
"Std.DTreeMap.Raw.Const.get?",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Bool",
"Option.isSome",
"Eq",
"Std.D... | true |
instRingWithIdealFilter._proof_36 | Mathlib.RingTheory.IdealFilter.Topology | [
"instRingWithIdealFilter._proof_3",
"instRingWithIdealFilter._aux_28",
"AddMonoid.toAddSemigroup",
"instRingWithIdealFilter._proof_19",
"instRingWithIdealFilter._aux_4",
"HSub.hSub",
"instRingWithIdealFilter._aux_16",
"AddMonoid.mk",
"Semigroup.mk",
"instRingWithIdealFilter._proof_18",
"Ring.sub... | false |
ZetaAsymptotics.zeta_limit_aux1 | Mathlib.NumberTheory.Harmonic.ZetaAsymp | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Real.instIsOrderedRing",
"Mathlib.Tactic.FieldSimp.zpow'_one",
"Not.intro",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg... | true |
Std.Internal.Async.IO.AsyncWrite.mk.noConfusion | Std.Internal.Async.IO | [
"Std.Internal.Async.IO.AsyncWrite",
"Std.Internal.Async.IO.AsyncWrite.noConfusion",
"id",
"Array",
"Std.Internal.Async.IO.AsyncWrite.mk",
"heq_of_eq",
"Unit",
"Eq.refl",
"HEq",
"Std.Internal.IO.Async.Async",
"Eq"
] | false |
Subfield.copy._proof_6 | Mathlib.Algebra.Field.Subfield.Defs | [
"GroupWithZero.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"DivisionSemiring.toGroupWithZero",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Eq.rec",
"DivisionRing.toDivisionSemiring",
"Subfield.instSetLike",
"Inv.inv",
"SetLike.coe",
"DivisionRing",
"InvOneClass.toInv",
"Su... | false |
Lean.IR.EmitLLVM.emitDel | Lean.Compiler.IR.EmitLLVM | [
"Pure.pure",
"LLVM.functionType",
"Lean.IR.EmitLLVM.State",
"Lean.IR.EmitLLVM.M",
"Lean.IR.EmitLLVM.Context",
"Unit.unit",
"ReaderT",
"Monad.toApplicative",
"Lean.IR.EmitLLVM.getLLVMModule",
"LLVM.buildCall2",
"Lean.IR.EmitLLVM.getOrCreateFunctionPrototype",
"instMonadLiftT",
"IO",
"LLVM.L... | true |
List.max?_eq_some_iff' | Init.Data.List.Nat.Basic | [
"Option.some",
"Membership.mem",
"Nat.instLawfulOrderMax",
"LE.le",
"instLENat",
"List.max?",
"List",
"And",
"Iff",
"List.instMembership",
"Nat",
"Nat.instMax",
"Eq",
"Nat.instIsLinearOrder",
"List.max?_eq_some_iff",
"Option"
] | true |
PiTensorProduct.reindex_trans | Mathlib.LinearAlgebra.PiTensorProduct | [
"PiTensorProduct.instModule",
"Eq.mpr",
"LinearEquiv.symm",
"Equiv.instEquivLike",
"congrArg",
"CommSemiring.toSemiring",
"Equiv.trans",
"MultilinearMap.addCommMonoid",
"PiTensorProduct.reindex_comp_tprod",
"PiTensorProduct.instSMulCommClass",
"PiTensorProduct.reindex_tprod",
"id",
"Equiv",
... | true |
Ordinal.mul_two | Mathlib.SetTheory.Ordinal.Arithmetic | [
"Eq.mpr",
"MulOne.toOne",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"MulZeroClass.toMul",
"congrArg",
"Nat.instAtLeastTwoHAddOfNat",
"id",
"MulOne.toMul",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"one_add_one_eq_two",
"MulZeroOneClass.toMulOneClass",
"Ordinal.addMonoidWithOne",
"AddM... | true |
Polynomial.Gal.instUniqueOfFactSplits | Mathlib.FieldTheory.PolynomialGaloisGroup | [
"Polynomial.Gal.instUniqueOfFactSplits._proof_1",
"Polynomial.Gal",
"Unique",
"Fact",
"Field.toSemifield",
"Polynomial",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"Polynomial.Splits",
"Field",
"Polynomial.Gal.uniqueGalOfSplits"
] | true |
Matroid.loopyOn_isBasis_iff | Mathlib.Combinatorics.Matroid.Constructions | [
"Eq.mpr",
"Matroid.isBasis_iff",
"Matroid.loopyOn",
"Matroid.IsBasis.subset_ground",
"congrArg",
"and_self",
"Matroid.loopyOn_indep_iff",
"instInhabitedTrue",
"Matroid.Indep",
"id",
"HasSubset.Subset",
"imp_self._simp_1",
"And.casesOn",
"And",
"Iff",
"Set.empty_subset._simp_1",
"fora... | true |
_private.Mathlib.Order.Antichain.0.IsMaxAntichain.nonempty_iff._simp_1_1 | Mathlib.Order.Antichain | [
"Set.not_nonempty_iff_eq_empty",
"Set.Nonempty",
"propext",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Not",
"Set"
] | false |
Topology.IsEmbedding.specialLinearGroup_map | Mathlib.Topology.Algebra.Group.Matrix | [
"CommRing",
"Matrix.SpecialLinearGroup",
"MonoidHom.instFunLike",
"MonoidHom",
"continuous_subtype_val",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"Matrix",
"Matrix.SpecialLinearGroup.instTopologicalSpace",
"AddGroupWithOne.toAddMonoidWithOne",
"RingHom",
"Subtype",
"Topology.IsEmbe... | true |
EsakiaHom.toPseudoEpimorphism | Mathlib.Topology.Order.Hom.Esakia | [
"EsakiaHom.toContinuousOrderHom",
"TopologicalSpace",
"EsakiaHom.exists_map_eq_of_map_le'",
"ContinuousOrderHom.toOrderHom",
"PseudoEpimorphism.mk",
"EsakiaHom",
"PseudoEpimorphism",
"Preorder"
] | true |
IndepMatroid.ofFinitaryCardAugment_E | Mathlib.Combinatorics.Matroid.IndepAxioms | [
"IndepMatroid.ofFinitaryCardAugment",
"Set.Finite",
"Membership.mem",
"Exists",
"Insert.insert",
"HasSubset.Subset",
"And",
"Set.instInsert",
"Nat",
"LT.lt",
"Set.instEmptyCollection",
"Eq.refl",
"instLTNat",
"EmptyCollection.emptyCollection",
"Set.ncard",
"Eq",
"Set.instMembership",... | true |
ZLattice.sum_piFinset_Icc_rpow_le | Mathlib.Algebra.Module.ZLattice.Summable | [
"Finsupp.instIntSMul",
"Int.instAddCommGroup",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"CharP.cast_eq_zero",
"Iff.mpr",
"zero_le",
"Finsupp.instFunLike",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Real.instIsOrderedRing",
"Norm.norm",
"Mathlib.Tactic.Ring.Common.neg_zero",
... | true |
_private.Mathlib.ModelTheory.Encoding.0.FirstOrder.Language.BoundedFormula.listEncode.match_1.eq_5 | Mathlib.ModelTheory.Encoding | [
"FirstOrder.Language.BoundedFormula.imp",
"FirstOrder.Language.BoundedFormula.listEncode.match_1",
"FirstOrder.Language.Term",
"Sum",
"instOfNatNat",
"FirstOrder.Language.BoundedFormula.equal",
"FirstOrder.Language.BoundedFormula.falsum",
"instHAdd",
"HAdd.hAdd",
"Nat",
"FirstOrder.Language.Rela... | true |
Lean.Elab.instInhabitedDefViewElabHeaderData.default | Lean.Elab.DefView | [
"Lean.Elab.DefViewElabHeaderData.mk",
"Inhabited.default",
"instInhabitedNat",
"Lean.Syntax",
"Lean.Expr",
"Array",
"Lean.instInhabitedExpr",
"List",
"Array.instInhabited",
"Nat",
"Lean.Elab.DefViewElabHeaderData",
"Lean.Name",
"Lean.instInhabitedName",
"instInhabitedList"
] | true |
CochainComplex.mappingCone.mapOfHomotopy | Mathlib.Algebra.Homology.HomotopyCategory.Pretriangulated | [
"HomologicalComplex.instCategory",
"Equiv.instEquivLike",
"CochainComplex.HomComplex.instAddCommGroupCochain",
"CategoryTheory.CategoryStruct.toQuiver",
"CochainComplex.mappingCone.inr",
"Quiver.Hom",
"CochainComplex.mappingCone.mapOfHomotopy._proof_2",
"CochainComplex.HomComplex.Cochain.comp",
"Add... | true |
DivisionRing.nnratCast_def | Mathlib.Algebra.Field.Defs | [
"Semiring.toNatCast",
"instHDiv",
"HDiv.hDiv",
"NNRat",
"DivisionRing.toRing",
"DivisionRing.toDiv",
"NNRat.num",
"Nat.cast",
"NNRat.den",
"DivisionRing",
"NNRat.cast",
"Ring.toSemiring",
"Eq",
"DivisionRing.toNNRatCast"
] | true |
IsLocalization.noZeroDivisors | Mathlib.RingTheory.Localization.Defs | [
"IsLocalization",
"CommSemiring.toSemiring",
"Algebra",
"CommSemiring.toCommMonoidWithZero",
"Submonoid.LocalizationMap.noZeroDivisors",
"MulZeroOneClass.toMulOneClass",
"instDistribOfSemiring",
"instMulZeroOneClassOfSemiring",
"CommSemiring",
"NoZeroDivisors",
"Distrib.toMul",
"IsLocalization... | true |
Std.OrientedCmp.not_isGE_of_gt | Init.Data.Order.Ord | [
"Ordering.gt",
"Eq.mpr",
"congrArg",
"Ordering",
"Std.OrientedCmp",
"id",
"imp_self._simp_1",
"Ordering.swap",
"Bool.true",
"implies_congr",
"Ordering.lt",
"Bool.not_eq_true",
"True",
"Bool",
"of_eq_true",
"Ordering.isGE_eq_false._simp_1",
"Ordering.isGE",
"Ordering.swap_eq_gt._sim... | true |
CategoryTheory.Localization.lift₂NatIso.eq_1 | Mathlib.CategoryTheory.Localization.Monoidal.Braided | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.Iso",
"CategoryTheory.Localization.lift₂NatTrans",
"CategoryTheory.Iso.mk",
"CategoryTheory.Localization.Lifting₂",
"CategoryTheory.Functor.IsLocalization",
"CategoryTheory.Localization.li... | true |
Continuous.cfcₙ_nnreal._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Continuity | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Std.Time.Modifier.Z | Std.Time.Format.Basic | [
"Std.Time.Modifier.Z",
"Std.Time.Modifier",
"Std.Time.OffsetZ"
] | true |
Lean.Lsp.instToJsonInlayHintKind.match_1 | Lean.Data.Lsp.LanguageFeatures | [
"Unit.unit",
"Lean.Lsp.InlayHintKind.type",
"Lean.Lsp.InlayHintKind",
"Unit",
"Lean.Lsp.InlayHintKind.parameter",
"Lean.Lsp.InlayHintKind.casesOn"
] | false |
differentiableAt_add_const_iff._simp_1 | Mathlib.Analysis.Calculus.FDeriv.Add | [
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"DifferentiableAt",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"instHAdd",
"differentiableAt_add_const_iff",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"HAdd.hAdd",
"propext",
"NontriviallyNormedField",
"NormedAddCommGroup.toAd... | false |
Lean.Meta.Occurrences.rec | Init.MetaTypes | [
"Lean.Meta.Occurrences.neg",
"List",
"Lean.Meta.Occurrences.pos",
"Lean.Meta.Occurrences",
"Nat",
"Lean.Meta.Occurrences.all"
] | false |
_private.Mathlib.MeasureTheory.Integral.Lebesgue.Basic.0.MeasureTheory.le_iInf_lintegral._simp_1_1 | Mathlib.MeasureTheory.Integral.Lebesgue.Basic | [
"iInf",
"iInf_apply",
"InfSet",
"Pi.infSet",
"Eq.symm",
"Eq"
] | false |
Real.Wallis.W._proof_1 | Mathlib.Analysis.Real.Pi.Wallis | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
CategoryTheory.GradedObject.mapBifunctorMapMapIso._proof_1 | Mathlib.CategoryTheory.GradedObject.Bifunctor | [
"CategoryTheory.GradedObject.ιMapBifunctorMapObj",
"CategoryTheory.GradedObject.ι_mapBifunctorMapMap",
"CategoryTheory.Functor",
"CategoryTheory.GradedObject.HasMap",
"CategoryTheory.GradedObject.mapBifunctorMapObj",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.GradedObject.... | false |
Set.one_subset | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Set.singleton_subset_iff",
"One",
"Set.one",
"Membership.mem",
"HasSubset.Subset",
"Iff",
"One.toOfNat1",
"OfNat.ofNat",
"Set.instMembership",
"Set.instHasSubset",
"Set"
] | true |
Std.ExtDTreeMap.Const.ordered_keys_toList | Std.Data.ExtDTreeMap.Lemmas | [
"Std.ExtDTreeMap.Const.toList",
"List.Pairwise",
"Std.DTreeMap",
"Ordering",
"Std.TransCmp",
"Prod.fst",
"Ordering.lt",
"Std.ExtDTreeMap.inductionOn",
"Std.ExtDTreeMap",
"Std.DTreeMap.Const.ordered_keys_toList",
"Prod",
"Eq"
] | true |
Batteries.Tactic.Instances._aux_Batteries_Tactic_Instances___elabRules_Batteries_Tactic_Instances_instancesCmd_1 | Batteries.Tactic.Instances | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Command.CommandElab",
"Lean.mkAppN",
"bne",
"Lean.Elab.Term.instAddErrorMessageContextTermElabM",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.MetavarKind.natural",... | false |
LowerSemicontinuousWithinAt.inv | Mathlib.Topology.Semicontinuity.Basic | [
"Iff.mpr",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"IsOrderedMonoid",
"PartialOrder.toPreorder",
"UpperSemicontinuousWithinAt",
"Pi.instInv",
"DivisionMonoid.toDivInvOneMonoid",
"PartialOrder",
"CommGroup",
"CommGroup.toDivisionCommMonoid",
"TopologicalSpace",
... | true |
Lean.Elab.Tactic.Omega.Justification.combine.sizeOf_spec | Lean.Elab.Tactic.Omega.Core | [
"Lean.Elab.Tactic.Omega.Justification._sizeOf_inst",
"Lean.Elab.Tactic.Omega.Justification.combine",
"Lean.Elab.Tactic.Omega.Justification",
"instOfNatNat",
"Int",
"instHAdd",
"HAdd.hAdd",
"Lean.Omega.Coeffs",
"Lean.Omega.Constraint._sizeOf_inst",
"Nat",
"List._sizeOf_inst",
"Int._sizeOf_inst"... | true |
Monoid.Coprod.swap_eq_one._simp_2 | Mathlib.GroupTheory.Coprod.Basic | [
"MulOne.toOne",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.Coprod.swap",
"MulOneClass.toMulOne",
"Monoid.Coprod.instMulOneClass",
"Monoid.Coprod.swap_eq_one",
"propext",
"One.toOfNat1",
"MulOneClass",
"Monoid.Coprod",
"OfNat.ofNat",
"Eq",
"DFunLike.coe"
] | false |
Fin.cast_rev | Mathlib.Data.Fin.Rev | [
"Eq.rec",
"Fin.cast",
"Fin.rev",
"Nat",
"eq_self",
"of_eq_true",
"Fin",
"Eq"
] | true |
_private.Mathlib.LinearAlgebra.FixedSubmodule.0.LinearMap.fixedSubmodule_eq_ker._simp_1_1 | Mathlib.LinearAlgebra.FixedSubmodule | [
"AddGroup.toSubtractionMonoid",
"sub_eq_zero",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq"
] | false |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr.0.Lean.Meta.Grind.Arith.Cutsat.instReprSupportedTermKind.repr.match_1 | Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr | [
"Unit.unit",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr.0.Lean.Meta.Grind.Arith.Cutsat.SupportedTermKind.toNat",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr.0.Lean.Meta.Grind.Arith.Cutsat.SupportedTermKind.finMk",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.EqCnstr.0.Lean.Meta.Grind.Ari... | false |
FP.RMode.NE.sizeOf_spec | Mathlib.Data.FP.Basic | [
"instOfNatNat",
"FP.RMode._sizeOf_inst",
"Nat",
"FP.RMode.NE",
"SizeOf.sizeOf",
"FP.RMode",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
Std.DTreeMap.Raw.Const.getD_inter_of_not_mem_left | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.instMembership",
"congrArg",
"Ord.mk",
"Membership.mem",
"Ordering",
"Eq.mp",
"id",
"Std.DTreeMap.Raw.contains_eq_false_iff_not_mem",
"Std.TransCmp",
"Inter.inter",
"Std.DTreeMap.Raw.instInter",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Std.DTreeMap.Raw.contai... | true |
CategoryTheory.Bicategory.instIsIsoHomLeftZigzagHom | Mathlib.CategoryTheory.Bicategory.Adjunction.Basic | [
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory.leftZigzag",
"CategoryTheory.Bicategory",
"_private.Mathlib.CategoryTheory.Bicategory.Adj... | true |
Lean.LocalContext.findDecl? | Lean.LocalContext | [
"Pure.pure",
"Monad.toApplicative",
"Id.run",
"Id",
"Applicative.toPure",
"Lean.LocalContext.findDeclM?",
"Id.instMonad",
"Lean.LocalDecl",
"Lean.LocalContext",
"Option"
] | true |
_private.Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.Opposite.0.CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.generator | Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.Opposite | [
"CategoryTheory.Functor",
"_private.Mathlib.CategoryTheory.Abelian.GrothendieckCategory.ModuleEmbedding.Opposite.0.CategoryTheory.Abelian.IsGrothendieckAbelian.OppositeModuleEmbedding.generator._proof_1",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryThe... | true |
Lists'.mem_of_subset' | Mathlib.SetTheory.Lists | [
"Lists'.toList",
"Lists'.mem_of_subset'._unary",
"Lists",
"Membership.mem",
"Lists'.instMembershipLists",
"HasSubset.Subset",
"Bool.true",
"List",
"Lists'.instHasSubsetTrue",
"List.instMembership",
"PSigma.mk",
"PSigma",
"Lists'"
] | true |
_private.Mathlib.Data.Finset.NatDivisors.0.Nat.divisors_mul._simp_1_2 | Mathlib.Data.Finset.NatDivisors | [
"Dvd.dvd",
"Finset",
"Nat.mem_divisors",
"Membership.mem",
"Ne",
"instOfNatNat",
"Nat.divisors",
"And",
"Nat.instDvd",
"Finset.instSetLike",
"Nat",
"propext",
"OfNat.ofNat",
"Eq",
"SetLike.instMembership"
] | false |
ModP.preVal_eq_zero | Mathlib.RingTheory.Perfection | [
"Iff.mpr",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Submodule.Quotient.instZeroQuotient",
"CommRing",
"Preorder.toLT",
"Semiring.toModule",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"congrArg",
"CommSemiring.toSemiring",
"ModP",
"PartialOrder.toPreorder",
... | true |
Finset.mem_coe | Mathlib.Data.Finset.Defs | [
"Finset",
"Iff.rfl",
"Membership.mem",
"Iff",
"SetLike.coe",
"Finset.instSetLike",
"Set.instMembership",
"SetLike.instMembership",
"Set"
] | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.