name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
instIsPrimeValIdealMemSetAssociatedPrimes | Mathlib.RingTheory.Ideal.AssociatedPrime.Basic | [
"Submodule",
"CommSemiring.toSemiring",
"Membership.mem",
"Set.Elem",
"Bot.bot",
"Ideal",
"AddCommMonoid",
"CommSemiring",
"Submodule.instBot",
"associatedPrimes",
"Ideal.IsPrime",
"Module",
"Subtype.val",
"Set.instMembership",
"Subtype.property",
"Submodule.IsAssociatedPrime.toIsPrime... | true |
NonUnitalStarSubalgebra.prod_toNonUnitalSubalgebra | Mathlib.Algebra.Star.NonUnitalSubalgebra | [
"NonUnitalSubalgebra",
"CommSemiring.toSemiring",
"Prod.instNonUnitalNonAssocSemiring",
"NonUnitalStarSubalgebra.prod",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"StarAddMonoid.toInvolutiveStar",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"StarRing.toStarAddMonoid",
"NonUn... | true |
Lean.Server.RequestCancellationToken.wasCancelledByEdit | Lean.Server.RequestCancellation | [
"IO.CancelToken.isSet",
"Lean.Server.RequestCancellationToken.cancelledByEdit",
"Lean.Server.RequestCancellationToken",
"Bool",
"BaseIO"
] | true |
Topology.CWComplex.iUnion_openCell_eq_skeleton | Mathlib.Topology.CWComplex.Classical.Basic | [
"instAddMonoidWithOneENat",
"ENat.instNatCast",
"Topology.CWComplex.iUnion_openCell_eq_skeletonLT",
"Topology.CWComplex",
"Topology.RelCWComplex.openCell",
"Topology.CWComplex.instRelCWComplex",
"instAddENat",
"Nat.cast",
"AddMonoidWithOne.toOne",
"TopologicalSpace",
"instHAdd",
"SetLike.coe",... | true |
_private.Init.Grind.Ring.Envelope.0.Lean.Grind.Ring.OfSemiring.rel | Init.Grind.Ring.Envelope | [
"Lean.Grind.Ring.OfSemiring.r",
"Equivalence",
"Lean.Grind.Ring.OfSemiring.Q.liftOn₂",
"Lean.Grind.Semiring",
"_private.Init.Grind.Ring.Envelope.0.Lean.Grind.Ring.OfSemiring.rel._proof_1",
"Lean.Grind.Ring.OfSemiring.Q",
"Prod"
] | true |
_private.Mathlib.RingTheory.LittleWedderburn.0.LittleWedderburn.InductionHyp.center_eq_top._simp_1_3 | Mathlib.RingTheory.LittleWedderburn | [
"Finset",
"Membership.mem",
"Set.Elem",
"Set.toFinset",
"Fintype",
"Finset.instSetLike",
"propext",
"Set.mem_toFinset",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"Set"
] | false |
PFunctor.M.children._proof_3 | Mathlib.Data.PFunctor.Univariate.M | [
"PFunctor.Approx.agree_children",
"PFunctor",
"HEq.symm",
"PFunctor.A",
"PFunctor.M",
"PFunctor.B",
"HEq.trans",
"cast",
"cast_heq",
"PFunctor.MIntl.approx",
"PFunctor.MIntl.consistent",
"instOfNatNat",
"PFunctor.Approx.Agree",
"congr_arg",
"PFunctor.Approx.AllAgree",
"PFunctor.M.child... | false |
AddAction.prodEquiv | Mathlib.Algebra.Group.Action.Prod | [
"PSigma.snd",
"AddMonoidHom.inl",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"Equiv.mk",
"Equiv",
"AddAction.prodEquiv._proof_5",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddAction.compHom",
"AddAction.prodEquiv._proof_3",
"AddSemigroupAction.toVAdd",
"AddAction.prodEquiv... | true |
Filter.map_def | Mathlib.Order.Filter.Map | [
"Filter.map",
"Filter.instFunctor",
"Eq",
"Functor.map",
"Filter",
"rfl"
] | true |
_private.Mathlib.Analysis.Normed.Unbundled.RingSeminorm.0.map_pow_le_pow.match_1_1 | Mathlib.Analysis.Normed.Unbundled.RingSeminorm | [
"Ne",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Nat.zero",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
Std.DTreeMap.getKey_eq_getKey! | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.getKey!",
"Ord.mk",
"Membership.mem",
"Ordering",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Std.DTreeMap.instMembership",
"Std.DTreeMap.wf",
"Inhabited",
"Std.DTreeMap.Internal.Impl.getKey_eq_getKey!",
"Eq",
"Std.DTreeMap.getKey"
] | true |
Mathlib.Tactic.Abel.AbelMode.raw.sizeOf_spec | Mathlib.Tactic.Abel | [
"Mathlib.Tactic.Abel.AbelMode",
"instOfNatNat",
"Mathlib.Tactic.Abel.AbelMode.raw",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"Mathlib.Tactic.Abel.AbelMode._sizeOf_inst",
"OfNat.ofNat",
"Eq"
] | true |
Cardinal.mk_compl_finset_of_infinite | Mathlib.SetTheory.Cardinal.Arithmetic | [
"Cardinal",
"Compl.compl",
"Finset",
"PartialOrder.toPreorder",
"Cardinal.mk",
"Set.Elem",
"Cardinal.aleph0",
"Set.instCompl",
"Cardinal.partialOrder",
"SetLike.coe",
"Finset.instSetLike",
"LT.lt.trans_le",
"Infinite",
"Eq",
"Cardinal.mk_compl_of_infinite",
"Cardinal.finset_card_lt_ale... | true |
Cardinal.ofENat_lt_aleph0._simp_1 | Mathlib.SetTheory.Cardinal.ENat | [
"Preorder.toLT",
"Cardinal",
"instTopENat",
"Cardinal.ofENat_lt_aleph0",
"PartialOrder.toPreorder",
"Cardinal.aleph0",
"Cardinal.partialOrder",
"Cardinal.ofENat",
"ENat",
"LT.lt",
"propext",
"instLTENat",
"Top.top",
"Eq"
] | false |
Std.Rci.toArray_eq_toArray_roi | Init.Data.Range.Polymorphic.Lemmas | [
"Array.instAppend",
"Eq.mpr",
"Std.Rci",
"Std.PRange.UpwardEnumerable",
"congrArg",
"Std.Rxc.Iterator.toList_eq_match.match_1",
"Std.Rxi.Iterator.mk",
"Std.Rxi.instIteratorIteratorIdOfUpwardEnumerable",
"Std.Iter.internalState",
"id",
"Std.Roi.mk",
"Std.Iter.toArray",
"Std.PRange.UpwardEnume... | true |
ContinuousWithinAt.logb | Mathlib.Analysis.SpecialFunctions.Log.Base | [
"Filter.Tendsto.logb",
"Real",
"ContinuousWithinAt",
"Real.instZero",
"nhdsWithin",
"PseudoMetricSpace.toUniformSpace",
"Ne",
"Real.logb",
"TopologicalSpace",
"Zero.toOfNat0",
"Real.pseudoMetricSpace",
"OfNat.ofNat",
"UniformSpace.toTopologicalSpace",
"Set"
] | true |
FormalMultilinearSeries.unshift._proof_9 | Mathlib.Analysis.Calculus.FormalMultilinearSeries | [
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"IsBoundedSMul.toUniformContinuousConstSMul"... | false |
_private.Mathlib.Algebra.Polynomial.Degree.Defs.0.Polynomial.degree_lt_iff_coeff_zero._simp_1_3 | Mathlib.Algebra.Polynomial.Degree.Defs | [
"WithBot.some",
"WithBot",
"WithBot.instLT",
"WithBot.coe_lt_coe",
"LT.lt",
"propext",
"Eq",
"LT"
] | false |
CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.isInitialIso'_hom_left | Mathlib.CategoryTheory.Monoidal.PushoutProduct | [
"CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.isInitialIso'._proof_4",
"CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.isInitialIso'",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.IsPushout.isoPushout",
"CategoryTheory.CategoryStruct.toQuiver... | true |
Localization.partialOrder._proof_2 | Mathlib.GroupTheory.MonoidLocalization.Order | [
"Localization.mk",
"Monoid.toMulOneClass",
"Localization.partialOrder._proof_5",
"PartialOrder.toPreorder",
"Membership.mem",
"PartialOrder",
"Localization.induction_on₃",
"Subtype",
"Localization",
"LE.le",
"Prod.fst",
"CommMonoid.toMonoid",
"Localization.le",
"Submonoid.instSetLike",
"... | false |
Array.mapFinIdx_eq_append_iff | Init.Data.Array.MapIdx | [
"Iff.mpr",
"Array.instAppend",
"Eq.mpr",
"Iff.of_eq",
"congrArg",
"and_self",
"exists_const._simp_1",
"instInhabitedTrue",
"Exists",
"_private.Init.Data.Array.MapIdx.0.Array.mapFinIdx_eq_append_iff._simp_1_3",
"Eq.rec",
"Eq.mp",
"Array.casesOn",
"id",
"List.mapFinIdx",
"List.mapFinIdx_... | true |
CategoryTheory.MorphismProperty.IsStableUnderCoproducts.isStableUnderCoproductsOfShape._autoParam | Mathlib.CategoryTheory.MorphismProperty.Limits | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Plausible.GenError.genError | Plausible.Gen | [
"Plausible.GenError.genError",
"String",
"Plausible.GenError"
] | true |
RatFunc.induction_on | Mathlib.FieldTheory.RatFunc.Basic | [
"Eq.mpr",
"IsDomain",
"CommRing",
"instHDiv",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"RatFunc.instDiv",
"RingHom",
"RatFunc.induction_on'",
"Algebra.id",
"RatFunc.mk_eq_div",
"id",
"HDiv.hDiv",
"Ne",
"Field.toSemifield",
"Polynomial",
"CommRing.toCommSemiring"... | true |
CategoryTheory.Abelian.AbelianStruct.fac | Mathlib.CategoryTheory.Abelian.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.AbelianStruct.imageι",
"CategoryTheory.Preadditive",
"CategoryTheory.Abelian.AbelianStruct",
"CategoryTheory.Abelian.AbelianStruct.image",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
... | true |
AlgebraicGeometry.Scheme.SpecMap_stalkMap_fromSpecStalk_assoc | Mathlib.AlgebraicGeometry.Stalk | [
"CategoryTheory.Category.assoc",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"TopCat.instCategory",
"ContinuousMap",
... | true |
IsAddCyclic.exists_addMonoid_generator | Mathlib.GroupTheory.SpecificGroups.Cyclic.Basic | [
"Eq.mpr",
"congrArg",
"IsAddCyclic.exists_generator",
"Finite",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Exists",
"id",
"AddSubmonoid",
"mem_multiples_iff_mem_zmultiples",
"AddSubgroup",
"funext",
"AddGroup",
"AddGroup.toSubNegMonoid",
"AddSubgroup.instSetLike",
"AddSubgroup.zmul... | true |
_private.Mathlib.CategoryTheory.Abelian.Injective.Dimension.0.CategoryTheory.instHasInjectiveDimensionLTSucc._proof_1 | Mathlib.CategoryTheory.Abelian.Injective.Dimension | [
"CategoryTheory.HasInjectiveDimensionLT",
"CategoryTheory.Abelian",
"instOfNatNat",
"Nat",
"CategoryTheory.instHasInjectiveDimensionLTHAddNat",
"OfNat.ofNat",
"Nat.succ",
"CategoryTheory.Category"
] | false |
Std.DHashMap.Raw.Equiv.inter_congr | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.DHashMap.Internal.Raw₀.inter",
"Std.DHashMap.Internal.Raw.inter_eq",
"congrArg",
"Std.DHashMap.Raw",
"Std.DHashMap.Raw.instInterOfBEqOfHashable",
"id",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"Std.DHashMap.Internal.Raw₀.Equiv.inter_congr",
... | true |
extProc._@.Mathlib.Tactic.Attr.Register.1568842782._hygCtx._hyg.3 | Mathlib.Tactic.Attr.Register | [
"Inhabited.default",
"Lean.Meta.Simp.SimprocEntry",
"Lean.Meta.Simp.SimprocOLeanEntry",
"Lean.instInhabitedScopedEnvExtension",
"Lean.Meta.Simp.Simprocs",
"Lean.Meta.Simp.instInhabitedSimprocOLeanEntry",
"Lean.Meta.Simp.SimprocExtension"
] | false |
String.Slice.Pos.get?_eq_some_get | Init.Data.String.Lemmas.Slice | [
"of_eq_false",
"eq_false",
"congrArg",
"Option.some",
"String.Slice",
"Ne",
"String.instDecidableIsAtEnd_1",
"Option.none",
"String.Slice.endPos",
"String.Slice.Pos.get?",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"String.Slice.Pos.get",
"String.Slice.Pos",
"Char",
"dite_cond_e... | true |
String.Model.map_get_positionsFrom_of_splits | Init.Data.String.Lemmas.Iterate | [
"String.Pos.Splits",
"String.toSlice",
"Iff.mpr",
"String.instLEPos_1",
"String.Slice.Model.positionsFrom",
"congrArg",
"String.Slice.Model.map_get_positionsFrom_of_splits",
"String",
"List.map",
"String.Model.positionsFrom",
"String.Pos.toSlice",
"Function.comp",
"Membership.mem",
"Subtyp... | true |
_private.Init.Data.Array.Subarray.0.Array.toSubarray._proof_1 | Init.Data.Array.Subarray | [
"Nat.le_refl",
"LE.le",
"instLENat",
"Array",
"Nat",
"Array.size"
] | false |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric.0._aux_Mathlib_Analysis_CStarAlgebra_ContinuousFunctionalCalculus_Isometric___unexpand_quasispectrum_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Isometric | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk... | false |
CategoryTheory.Precoverage.ZeroHypercover.mk.injEq | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.Precoverage",
"Eq.propIntro",
"CategoryTheory.Presieve",
"CategoryTheory.PreZeroHypercover.presieve₀",
"Membership.mem",
"CategoryTheory.Precoverage.ZeroHypercover.mk.inj",
"CategoryTheory.Precoverage.ZeroHypercover",
"CategoryTheory.PreZeroHypercover",
"CategoryTheory.Precoverage.Ze... | true |
Set.subset_empty_iff._simp_1 | Mathlib.Data.Set.Basic | [
"HasSubset.Subset",
"propext",
"Set.instEmptyCollection",
"Set.subset_empty_iff",
"EmptyCollection.emptyCollection",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
List.all_eq_false._simp_1 | Init.Data.List.Lemmas | [
"List.all_eq_false",
"List.all",
"Membership.mem",
"Exists",
"Bool.true",
"List",
"And",
"List.instMembership",
"propext",
"Bool",
"Bool.false",
"Eq",
"Not"
] | false |
_private.Mathlib.Topology.Compactification.OnePoint.Basic.0.OnePoint.infinite._proof_1 | Mathlib.Topology.Compactification.OnePoint.Basic | [
"instInfiniteOption",
"Infinite",
"OnePoint"
] | false |
Std.Time.PlainDateTime.withMilliseconds | Std.Time.DateTime.PlainDateTime | [
"Std.Time.Millisecond.Ordinal",
"Std.Time.PlainDateTime.date",
"Std.Time.PlainDateTime",
"Std.Time.PlainDateTime.mk",
"Std.Time.PlainTime.withMilliseconds",
"Std.Time.PlainDateTime.time"
] | true |
Int.Linear.Expr.toPoly'.go.eq_3 | Init.Data.Int.Linear | [
"Function.comp",
"Int.Linear.Expr.add",
"Int",
"Int.Linear.Expr",
"Int.Linear.Expr.toPoly'.go",
"Eq.refl",
"Eq",
"Int.Linear.Poly"
] | true |
_private.Mathlib.NumberTheory.JacobiSum.Basic.0.jacobiSum_mul_nontrivial._simp_1_3 | Mathlib.NumberTheory.JacobiSum.Basic | [
"Finset.mem_singleton",
"Finset",
"Membership.mem",
"Finset.instSetLike",
"propext",
"Finset.instSingleton",
"Singleton.singleton",
"Eq",
"SetLike.instMembership"
] | false |
CategoryTheory.Limits.limitIsoSwapCompLim_inv_app | Mathlib.CategoryTheory.Limits.FunctorCategory.Basic | [
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.lim",
"CategoryTheory.Functor.uncurry",
"CategoryTheor... | true |
AlgebraicGeometry.Scheme.IdealSheafData.ideal_sSup | Mathlib.AlgebraicGeometry.IdealSheaf.Basic | [
"AlgebraicGeometry.Scheme",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Opposite",
"CommRingCat.carrier",
"CommRing.toNonUnitalCommRing",
"AlgebraicGeometry.PresheafedSpace.carrier",
"TopologicalSpace.Opens.instPartialOrder",
"CommSemiring.toSemiring",
"CommRingCat",
"... | true |
Turing.PartrecToTM2.Λ'.instDecidableEq._proof_62 | Mathlib.Computability.TuringMachine.ToPartrec | [
"Turing.PartrecToTM2.Cont'",
"False",
"Turing.PartrecToTM2.Γ'",
"Turing.PartrecToTM2.Λ'.push",
"HEq.refl",
"False.elim",
"noConfusion_of_Nat",
"Turing.PartrecToTM2.Λ'",
"Eq.casesOn",
"Turing.PartrecToTM2.Λ'.ret",
"Eq.refl",
"HEq",
"Turing.PartrecToTM2.Λ'.ctorIdx",
"Turing.PartrecToTM2.K'",... | false |
Std.Internal.List.getValueD | Std.Data.Internal.List.Associative | [
"Option.getD",
"List",
"Std.Internal.List.getValue?",
"BEq",
"Sigma"
] | true |
Finset.toDual_sup' | Mathlib.Data.Finset.Lattice.Fold | [
"OrderDual.toDual",
"Equiv.instEquivLike",
"Finset.inf'",
"Finset",
"Function.comp",
"Equiv",
"Finset.Nonempty",
"OrderDual",
"Finset.sup'",
"Eq",
"SemilatticeSup",
"DFunLike.coe",
"rfl",
"OrderDual.instSemilatticeInf",
"EquivLike.toFunLike"
] | true |
_private.Mathlib.Algebra.QuadraticDiscriminant.0.quadratic_eq_zero_iff._simp_1_2 | Mathlib.Algebra.QuadraticDiscriminant | [
"False",
"eq_false",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"three_ne_zero",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
StandardEtalePresentation.toPresentation._proof_1 | Mathlib.RingTheory.Etale.StandardEtale | [
"Algebra.Generators.ker",
"Matrix.range_cons",
"Finsupp.instAddZeroClass",
"AlgHom.comp_toRingHom",
"Eq.mpr",
"Polynomial.C",
"AlgEquiv.instEquivLike",
"RingHom.instRingHomClass",
"Polynomial.instOne",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"MonoidHom.instFunLike",
... | false |
eventuallyEq_nhdsWithin_of_eqOn | Mathlib.Topology.NhdsWithin | [
"nhdsWithin",
"setOf",
"nhds",
"Filter.EventuallyEq",
"Set.EqOn",
"Filter.mem_inf_of_right",
"TopologicalSpace",
"Filter.principal",
"Eq",
"Set"
] | true |
TopCat.sigmaCofanIsColimit._proof_3 | Mathlib.Topology.Category.TopCat.Limits.Products | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"TopCat.sigmaCofan",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.instCategory",
"ContinuousMap.mk",
"ContinuousMap",
"CategoryTheory.Functor.category",
"CategoryTheory.Discrete.fu... | false |
Equiv.Perm.OnCycleFactors.toPermHom | Mathlib.GroupTheory.Perm.Centralizer | [
"MonoidHom",
"Monoid.toMulOneClass",
"Finset",
"Subgroup.centralizer",
"Equiv.Perm.cycleFactorsFinset",
"MulAction.toPermHom",
"Membership.mem",
"Set.instSingletonSet",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"Group.toDivInvMonoid",
"Equiv.Perm.permGroup",
"MulOneClass.toMulOne",
... | true |
Matrix.kroneckerMapBilinear._proof_5 | Mathlib.LinearAlgebra.Matrix.Kronecker | [
"Matrix.smul",
"instHSMul",
"DistribMulAction.toDistribSMul",
"Matrix",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.module",
"LinearMap",
"AddCommMonoid",
"AddZero.toZero",
"LinearMap.map_smul",
"LinearMap.addComm... | false |
_private.Mathlib.Analysis.InnerProductSpace.OfNorm.0.inner_ | Mathlib.Analysis.InnerProductSpace.OfNorm | [
"NormedCommRing.toNormedRing",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real",
"instHSMul",
"NormedRing.toRing",
"RCLike.toNormedAlgebra",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"NormedSpace",
"Algebra.algebraMap",
"AddGroupWithOne.to... | true |
Subgroup.quotientEquivProdOfLE' | Mathlib.GroupTheory.Coset.Basic | [
"Subgroup.subgroupOf",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"QuotientGroup.mk",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Group.toDivisionMonoid",
"Quotient.mk''",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"QuotientGroup.leftRel",
"E... | true |
_private.Lean.Compiler.LCNF.EmitUtil.0.Lean.Compiler.LCNF.CollectUsedDeclsState.mk | Lean.Compiler.LCNF.EmitUtil | [
"_private.Lean.Compiler.LCNF.EmitUtil.0.Lean.Compiler.LCNF.CollectUsedDeclsState",
"Lean.NameSet",
"Lean.Compiler.LCNF.Signature",
"Lean.Compiler.LCNF.Decl",
"Array",
"Lean.Compiler.LCNF.Purity.impure",
"_private.Lean.Compiler.LCNF.EmitUtil.0.Lean.Compiler.LCNF.CollectUsedDeclsState.mk"
] | true |
_private.Init.Data.List.MinMax.0.List.max?_attach | Init.Data.List.MinMax | [
"Iff.mpr",
"Eq.mpr",
"False",
"List.foldl_hom",
"Iff.of_eq",
"Option.ctorIdx",
"congrArg",
"List.map",
"List.attach_cons.match_1",
"False.elim",
"List.mem_cons_of_mem",
"noConfusion_of_Nat",
"Option.some.injEq",
"Option.some",
"Membership.mem",
"Max",
"id",
"Subtype",
"Option.pma... | true |
IsAddUnit.add_val_neg | Mathlib.Algebra.Group.Units.Defs | [
"Eq.mpr",
"AddUnits.val",
"congrArg",
"AddMonoid.toAddZeroClass",
"Eq.rec",
"AddZeroClass.toAddZero",
"id",
"IsAddUnit",
"AddZero.toZero",
"instHAdd",
"AddUnits.add_neg",
"HAdd",
"HAdd.hAdd",
"AddMonoid",
"IsAddUnit.addUnit",
"AddZero.toAdd",
"Zero.toOfNat0",
"Eq.refl",
"AddUnits... | true |
Vector.reverse_attach | Init.Data.Vector.Attach | [
"Vector.instMembership",
"Vector.attach",
"Array.pmap_reverse._proof_1",
"Array.pmap",
"Vector.reverse_pmap._proof_1",
"Vector",
"Array.reverse",
"congrArg",
"Array.attach_push.match_1",
"Array.instMembership",
"Vector.casesOn",
"Membership.mem",
"Array.map",
"Vector.map_mk._proof_1",
"i... | true |
Std.Format.FlattenAllowability | Init.Data.Format.Basic | [
"Std.Format.FlattenAllowability.disallow",
"Std.Format.FlattenAllowability.allow"
] | true |
_private.Mathlib.Topology.Spectral.Prespectral.0.instTotallySeparatedSpaceOfT2SpaceOfPrespectralSpace.match_1 | Mathlib.Topology.Spectral.Prespectral | [
"Compl.compl",
"setOf",
"Membership.mem",
"Exists",
"Set.instSingletonSet",
"HasSubset.Subset",
"Set.instCompl",
"And.casesOn",
"TopologicalSpace",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"IsOpen",
"Singleton.singleton",
"Set.instMembership",
"IsCompact",
"Set.instHas... | false |
Finset.piecewise_mem_Icc_of_mem_of_mem | Mathlib.Data.Finset.Piecewise | [
"Pi.preorder",
"Finset",
"Decidable",
"Preorder.toLE",
"Membership.mem",
"Finset.piecewise",
"LE.le",
"Finset.piecewise_le_of_le_of_le",
"Set.Icc",
"And.right",
"Finset.instSetLike",
"And.left",
"Finset.le_piecewise_of_le_of_le",
"And.intro",
"Set.instMembership",
"SetLike.instMembersh... | true |
MeasureTheory.addFundamentalFrontier.eq_1 | Mathlib.MeasureTheory.Group.FundamentalDomain | [
"AddGroup.toSubtractionMonoid",
"AddMonoid.toAddSemigroup",
"Set.vaddSet",
"Ne",
"SubtractionMonoid.toSubNegZeroMonoid",
"Set.instInter",
"SubNegZeroMonoid.toNegZeroClass",
"HVAdd.hVAdd",
"Inter.inter",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddGroup",
"AddSemigroupAction.toVAdd",
... | true |
Lean.hasAssignedLevelMVar._unsafe_rec | Lean.MetavarContext | [
"Pure.pure",
"Monad.toApplicative",
"Lean.isLevelMVarAssigned",
"Lean.Level",
"Applicative.toPure",
"_private.Lean.MetavarContext.0.Lean.hasAssignedLevelMVar.match_1",
"Lean.Level.hasMVar",
"andM",
"Lean.hasAssignedLevelMVar._unsafe_rec",
"instToBoolBool",
"Unit",
"Bool",
"Lean.Name",
"Mon... | false |
Nat.prod_modEq_ite | Mathlib.Algebra.BigOperators.ModEq | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"ZMod.commRing",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"AddGroupWithOne.toAddMonoidWithOne",
"Decidable",
"Membership.mem",
"apply_ite",
"Eq.mp",
"NatCast",
"id",
"AddMonoidWithOne.toNatCast",
"Finset.prod_eq_ite",
"Ne",
... | true |
DirichletCharacter.absicssaOfAbsConv_eq_one | Mathlib.NumberTheory.LSeries.Dirichlet | [
"Eq.mpr",
"instInfSetEReal",
"Real",
"Set.Ioi",
"ZMod.commRing",
"congrArg",
"PartialOrder.toPreorder",
"setOf",
"AddGroupWithOne.toAddMonoidWithOne",
"EReal",
"Real.instLT",
"instTopEReal",
"id",
"MulChar.instFunLike",
"AddMonoidWithOne.toNatCast",
"Ne",
"instOfNatNat",
"Condition... | true |
Batteries.RBNode.insert_toList_zoom_node | Batteries.Data.RBMap.Lemmas | [
"Batteries.RBNode",
"Batteries.RBNode.Path",
"Batteries.RBNode.toList",
"Batteries.RBNode.Path.withList",
"Ordering",
"Batteries.RBNode.zoom",
"Prod.mk",
"Batteries.RBNode.insert_toList_zoom",
"Batteries.RBNode.Path.root",
"Batteries.RBNode.insert",
"List",
"Batteries.RBColor",
"Nat",
"Pro... | true |
SummationFilter.casesOn | Mathlib.Topology.Algebra.InfiniteSum.SummationFilter | [
"SummationFilter.mk",
"SummationFilter.rec",
"Finset",
"SummationFilter",
"Filter"
] | false |
Lean.Lsp.WorkDoneProgressReport.mk.noConfusion | Lean.Data.Lsp.Basic | [
"String",
"Lean.Lsp.WorkDoneProgressReport.mk",
"id",
"Lean.Lsp.WorkDoneProgressReport",
"Lean.Lsp.WorkDoneProgressReport.noConfusion",
"Nat",
"Bool",
"Eq",
"Option"
] | false |
AlgEquiv.coe_restrictScalars_symm | Mathlib.Algebra.Algebra.Tower | [
"AlgEquiv.symm",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra",
"Algebra.toSMul",
"Distrib.toAdd",
"AlgEquiv.restrictScalars",
"instDistribOfSemiring",
"CommSemiring",
"Distrib.toMul",
"AlgEquiv",
"AlgEquiv.toRingEquiv",
"Semiring",
"RingEquiv",
"Eq",
"rfl"
] | true |
_private.Lean.Widget.Diff.0.Lean.Widget.ExprDiffTag.noConfusionType | Lean.Widget.Diff | [
"noConfusionTypeEnum",
"_private.Lean.Widget.Diff.0.Lean.Widget.ExprDiffTag",
"Nat",
"instDecidableEqNat",
"_private.Lean.Widget.Diff.0.Lean.Widget.ExprDiffTag.ctorIdx"
] | true |
Std.IterM.any_map | Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | [
"Pure.pure",
"Eq.mpr",
"Std.Shrink.deflate",
"bind_congr",
"Std.IterStep",
"Std.Iterators.Types.FilterMap.PlausibleStep.skip",
"congrArg",
"Std.Shrink",
"LawfulMonad.bind_assoc",
"Std.IterM.length_eq_match_step.match_1",
"Monad.toApplicative",
"Std.Iterators.Types.Map.instIterator",
"MonadLi... | true |
_private.Lean.Meta.Tactic.Grind.Arith.Linear.Model.0.Lean.Meta.Grind.Arith.Linear.assignTerms.match_1 | Lean.Meta.Tactic.Grind.Arith.Linear.Model | [
"Lean.Expr",
"Prod.mk",
"Nat",
"Prod",
"Prod.casesOn"
] | false |
Int32.sub | Init.Data.SInt.Basic | [
"Int32.toBitVec",
"Int32.ofUInt32",
"HSub.hSub",
"BitVec",
"instOfNatNat",
"BitVec.instSub",
"UInt32.ofBitVec",
"instHSub",
"Nat",
"OfNat.ofNat",
"Int32"
] | true |
_private.Mathlib.GroupTheory.Perm.Support.0.Equiv.Perm.support_noncommProd._simp_1_1 | Mathlib.GroupTheory.Perm.Support | [
"Insert.insert",
"HasSubset.Subset",
"Set.instInsert",
"True",
"eq_true",
"Eq",
"Set.subset_insert",
"Set.instHasSubset",
"Set"
] | false |
Lean.Elab.Term.MatchExpr.ElseAlt.mk._flat_ctor | Lean.Elab.MatchExpr | [
"Lean.Syntax",
"Lean.Elab.Term.MatchExpr.ElseAlt",
"Lean.Elab.Term.MatchExpr.ElseAlt.mk"
] | false |
_private.Mathlib.Analysis.Complex.UpperHalfPlane.Metric.0.UpperHalfPlane.dist_log_im_le._simp_1_1 | Mathlib.Analysis.Complex.UpperHalfPlane.Metric | [
"Norm.norm",
"Real",
"SeminormedAddCommGroup",
"dist_eq_norm",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"SubNegMonoid.toSub",
"SeminormedAddCommGroup.toNorm",
"instHSub",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"AddGroup.toSubNegMonoid",
"SeminormedAddCommGroup.toAddCommGroup",
"Dist.di... | false |
CategoryTheory.MorphismProperty.isSmall_iSup | Mathlib.CategoryTheory.MorphismProperty.IsSmall | [
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.MorphismProperty.IsSmall",
"congrArg",
"iSup",
"small_sigma",
"Set.mem_iUnion",
"Subtype.casesOn",
"_private.Mathlib.CategoryTheory.MorphismProperty.IsSmall.0.CategoryTheory.M... | true |
CondensedSet.toTopCatMap | Mathlib.Condensed.TopCatAdjunction | [
"CategoryTheory.Functor",
"CondensedSet.toTopCatMap._proof_5",
"Opposite",
"instTopologicalSpaceObjOppositeCompHausObjFunctorTypeIsSheafCoherentTopologyOpOfPUnit._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Condensed._proof_1",
"CategoryTheory.ConcreteCategory.hom",
"TopCat.in... | true |
Std.DHashMap.Raw.Equiv.getKeyD_eq | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"congrArg",
"Std.DHashMap.Raw",
"id",
"instOfNatNat",
"Std.DHashMap.Raw.WF.size_buckets_pos",
"LawfulHashable",
"Std.DHashMap.Raw.getKeyD",
"Std.DHashMap.Raw.Equiv",
"Subtype.mk",
"EquivBEq",
"Std.DHashMap.Internal.Raw₀.getKeyD",
"Nat",
"congr",
"Std.DH... | true |
AddOpposite.instAddCommGroup | Mathlib.Algebra.Group.Opposite | [
"AddOpposite.instAddCommGroup._proof_1",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"AddOpposite",
"AddCommGroup",
"AddOpposite.instAddCommSemigroup",
"AddGroup",
"AddOpposite.instAddGroup",
"AddCommGroup.mk",
"AddCommSemigroup",
"AddCommMonoid.toAddCommSemigroup"
] | true |
Path.Homotopy.map._proof_4 | Mathlib.Topology.Homotopy.Path | [
"ContinuousMap.continuous",
"Path.map",
"Real.instIsOrderedRing",
"Path.Homotopy",
"Real.partialOrder",
"Real",
"Continuous",
"Set.Icc.instZero",
"Path.Homotopy.target",
"congrArg",
"ContinuousMap.mk",
"ContinuousMap",
"Continuous.comp",
"PseudoMetricSpace.toUniformSpace",
"instTopologic... | false |
PresheafOfModules.Derivation'.app._proof_1 | Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf | [
"CategoryTheory.Functor",
"PresheafOfModules.Derivation.d",
"AddMonoidHom.instAddMonoidHomClass",
"Opposite",
"CommRingCat.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CommSemiring.toSemiring",
"CommRingCat",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZer... | false |
Affine.Simplex.ExcenterExists.excenter_mem_affineSpan_range | Mathlib.Geometry.Euclidean.Incenter | [
"InnerProductSpace.toNormedSpace",
"Affine.Simplex.ExcenterExists",
"Affine.Simplex.points",
"Nat.instMulZeroClass",
"Real",
"Affine.Simplex.excenter",
"Finset.univ",
"Real.instRCLike",
"Finset",
"NormedSpace.toModule",
"affineCombination_mem_affineSpan",
"Membership.mem",
"Affine.Simplex",
... | true |
_private.Lean.Level.0.Lean.Level.substParams.go._sparseCasesOn_3 | Lean.Level | [
"Lean.Level.ctorIdx",
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Lean.Level.mvar",
"Lean.Level.param",
"Nat.hasNotBit",
"Lean.Level.imax",
"instOfNatNat",
"Lean.Level",
"Nat.land",
"Lean.Level.zero",
"Nat",
"Bool",
"Lean.Level.rec",
"Lean.Name",
"Eq.refl",
"Lean.Level.succ",
"OfN... | false |
CategoryTheory.Triangulated.TStructure.le_isClosedUnderIsomorphisms | Mathlib.CategoryTheory.Triangulated.TStructure.Basic | [
"CategoryTheory.Functor.Additive",
"CategoryTheory.shiftFunctor",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Preadditive",
"CategoryTheory.Triangulated.TStructure",
"CategoryTheory.Limits.HasZeroObject",
"CategoryTheory.Pretriangulated",
"CategoryTheory.HasShift",
"CategoryTheory.Category",
"Ca... | true |
Lean.IR.VarId.ctorIdx | Lean.Compiler.IR.Basic | [
"Lean.IR.VarId",
"Nat"
] | false |
Nat.shiftRight_one | Mathlib.Data.Nat.BinaryRec | [
"instHDiv",
"HDiv.hDiv",
"instOfNatNat",
"instHShiftRightOfShiftRight",
"Nat.instShiftRight",
"HShiftRight.hShiftRight",
"Nat",
"Nat.instDiv",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
BialgHom.toAlgHom_convMul | Mathlib.RingTheory.Bialgebra.Convolution | [
"WithConv.toConv",
"Coalgebra.toCoalgebraStruct",
"HMul.hMul",
"Bialgebra.toCoalgebra",
"CommSemiring.toSemiring",
"AlgHom",
"WithConv.ofConv",
"Coalgebra.IsCocomm",
"Algebra.toModule",
"BialgHom.toAlgHom",
"CommSemiring",
"BialgHom",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Bialgebra... | true |
ULift.mulAction' | Mathlib.Algebra.Module.ULift | [
"Monoid",
"ULift",
"SemigroupAction.mk",
"ULift.smul",
"MulAction",
"Monoid.toSemigroup",
"ULift.mulAction'._proof_2",
"SemigroupAction.toSMul",
"MulAction.mk",
"MulAction.toSemigroupAction",
"ULift.mulAction'._proof_1"
] | true |
_private.Init.Data.Vector.Basic.0.Vector.flatMapM.go._proof_3 | Init.Data.Vector.Basic | [
"HMul.hMul",
"HMul",
"Eq.rec",
"instMulNat",
"LE.le",
"instLENat",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"Eq.refl",
"instDecidableEqNat",
"instLTNat",
"Eq",
"Not",
"_private.Init.Data.Vector.Basic.0.Vector.mapM._proof_2",
"instHMul"
] | false |
_private.Mathlib.NumberTheory.Divisors.0.Nat.reverse_divisorsAntidiagonalList._simp_1_1 | Mathlib.NumberTheory.Divisors | [
"List.Perm",
"List.reverse_perm'",
"List",
"propext",
"List.reverse",
"Eq"
] | false |
HomotopicalAlgebra.trivialFibrations | Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations | [
"CategoryTheory.MorphismProperty",
"HomotopicalAlgebra.fibrations",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CompleteLattice.toLattice",
"SemilatticeInf.toMin",
"HomotopicalAlgebra.CategoryWithWeakEquivalences",
"CompleteBooleanAlgebra.toCompleteLattice",
"CategoryTheory.Category... | true |
CategoryTheory.preadditiveYoneda_obj | Mathlib.CategoryTheory.Preadditive.Yoneda.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.preadditiveYoneda",
"Opposite",
"AddCommGrpCat.instCategory",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"LinearMap.instFunLike",
"CategoryTheory.Functor.comp",
"AddCommGroup.toAddGroup",
... | true |
AddConjClasses.mk.eq_1 | Mathlib.Algebra.Group.Conj | [
"AddConjClasses.mk",
"AddConjClasses",
"Quotient.mk",
"AddMonoid",
"Eq.refl",
"Eq",
"IsAddConj.setoid"
] | true |
FreeAbelianGroup.seqAddGroupHom._simp_1 | Mathlib.GroupTheory.FreeAbelianGroup | [
"Pi.add_def",
"instHAdd",
"Pi.instAdd",
"HAdd.hAdd",
"Eq.symm",
"Eq",
"Add"
] | false |
Batteries.LawfulOrd | Batteries.Classes.Deprecated | [
"Ord",
"Ord.compare",
"LE",
"Batteries.LawfulCmp",
"BEq",
"LT"
] | true |
uniformity_eq_comap_nhds_zero_swapped | Mathlib.Topology.Algebra.IsUniformGroup.Defs | [
"AddGroup.toSubtractionMonoid",
"UniformSpace",
"Eq.mpr",
"congrArg",
"uniformity",
"HSub.hSub",
"Function.comp",
"nhds",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"uniformity_eq_comap_nhds_zero",
"SubNegZeroMonoid.toNegZeroClass",
"Prod.fst",
"SubNegMonoid.toSub",
"Function.comp_def... | true |
LinearOrderedCommGroupWithZero.mul_inv_cancel | Mathlib.Algebra.Order.GroupWithZero.Canonical | [
"CommMonoidWithZero.toCommMonoid",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Semigroup.toMul",
"HMul.hMul",
"Ne",
"LinearOrderedCommGroupWithZero",
"LinearOrderedCommMonoidWithZero.toCommMonoidWithZero",
"Inv.inv",
"LinearOrderedCommGroupWithZero.toInv",
"CommMonoid.toMo... | true |
Mathlib.Tactic.BicategoryLike.MkEvalWhiskerRight.casesOn | Mathlib.Tactic.CategoryTheory.Coherence.Normalize | [
"Mathlib.Tactic.BicategoryLike.NormalExpr",
"Mathlib.Tactic.BicategoryLike.MkEvalWhiskerRight.mk",
"Mathlib.Tactic.BicategoryLike.MkEvalWhiskerRight.rec",
"Mathlib.Tactic.BicategoryLike.WhiskerRight",
"Lean.Expr",
"Mathlib.Tactic.BicategoryLike.Structural",
"Mathlib.Tactic.BicategoryLike.MkEvalWhiskerRi... | false |
Std.DHashMap.Raw.forM_eq_forM | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.forM",
"ForM.forM",
"Std.DHashMap.Raw",
"Std.DHashMap.Raw.instForMSigmaOfMonad",
"LawfulMonad",
"Sigma.fst",
"PUnit",
"Monad",
"Sigma.snd",
"Eq",
"Sigma",
"rfl"
] | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.