name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CommGrpTypeEquivalenceCommGrp.inverse_obj_inv | Mathlib.CategoryTheory.Monoidal.Internal.Types.CommGrp_ | [
"CategoryTheory.CommGrp.comm",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"CategoryTheory.GrpObj.inv",
"CategoryTheory.typesCartesianMonoidalCategory",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.CommGrp.instCategory",
"CommGrpCat.instCategory",
"TypeCat.instF... | true |
UInt64.lt_of_le_of_ne | Init.Data.UInt.Lemmas | [
"Eq.mpr",
"congrArg",
"UInt64",
"instLTUInt64",
"id",
"Ne",
"LE.le",
"instLENat",
"UInt64.toNat",
"_private.Init.Data.UInt.Lemmas.0.UInt64.lt_of_le_of_ne._simp_1_2",
"_private.Init.Data.UInt.Lemmas.0.UInt64.lt_of_le_of_ne._simp_1_1",
"_private.Init.Data.UInt.Lemmas.0.UInt64.lt_of_le_of_ne._sim... | true |
Std.Internal.IO.Async.MonadAsync.mk._flat_ctor | Std.Internal.Async.Basic | [
"Std.Internal.IO.Async.MonadAsync",
"Task.Priority",
"Task.Priority.default",
"optParam",
"Std.Internal.IO.Async.MonadAsync.mk"
] | false |
CategoryTheory.NatTrans.unop_whiskerLeft_assoc._to_dual_1 | Mathlib.CategoryTheory.Opposites | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.NatTrans.unop_whiskerLeft._to_dual_1",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"Eq.mp",
"CategoryTheory.Functor.whiskerLeft",
"id",
"CategoryTheor... | false |
SimpleGraph.cliqueFree_two | Mathlib.Combinatorics.SimpleGraph.Clique | [
"Eq.mpr",
"False",
"Finset.coe_singleton",
"le_rfl",
"eq_false",
"SimpleGraph.Adj.ne",
"Sym2.mk",
"congrArg",
"Finset",
"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.cliqueFree_two._simp_1_4",
"SimpleGraph.Adj",
"instInhabitedTrue",
"Classical.propDecidable",
"SimpleGrap... | true |
_private.Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal.0.SSet.Truncated.StrictSegal.spineToSimplex_map._proof_1 | Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | [
"Lean.RArray.leaf",
"False",
"of_decide_eq_true",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"HSub.hSub",
"Nat.not_le_eq",
"Nat.ToInt.add_congr",
"Lean.RArray.branch",
"Nat.ToInt.natCast_ofNat",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"Int.instNegI... | false |
PartOrd.Iso.mk._proof_1 | Mathlib.Order.Category.PartOrd | [
"PartOrd.str",
"PartialOrder.toPreorder",
"Preorder.toLE",
"RelIso.instRelHomClass",
"LE.le",
"RelIso",
"RelIso.instFunLike",
"PartOrd",
"PartOrd.carrier",
"RelHomClass"
] | false |
isLinearSet_iff | Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs | [
"instVAddOfAdd",
"Iff.of_eq",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"Set.Finite",
"Exists",
"Set.vaddSet",
"Set.Finite.coe_toFinset",
"AddSubmonoid",
"IsLinearSet",
"AddCommMonoid",
"HVAdd.hVAdd",
"iff_self",
"funext",
"And",
"Iff",
"SetLike.coe",
"Finset.instSetLike"... | true |
Array.findSome?_eq_none_iff | Init.Data.Array.Find | [
"congrArg",
"Array.instMembership",
"Membership.mem",
"Array.casesOn",
"List.mem_toArray._simp_1",
"List.findSome?_toArray",
"List.toArray",
"Array",
"iff_self",
"Option.none",
"List",
"Iff",
"List.instMembership",
"Array.findSome?",
"List.findSome?",
"implies_congr",
"congr",
"Tru... | true |
_private.Init.Grind.Ring.CommSolver.0.Lean.Grind.CommRing.Expr.toPolyC.go.match_4.eq_8 | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Expr",
"Lean.Grind.CommRing.Expr.mul",
"Lean.Grind.CommRing.Expr.var",
"Lean.Grind.CommRing.Expr.sub",
"Lean.Grind.CommRing.Expr.natCast",
"Lean.Grind.CommRing.Expr.neg",
"Int",
"Lean.Grind.CommRing.Expr.add",
"Lean.Grind.CommRing.Var",
"Nat",
"Lean.Grind.CommRing.Expr.toPol... | true |
AlgebraicGeometry.instBraidedCategoryScheme | Mathlib.AlgebraicGeometry.Limits | [
"AlgebraicGeometry.Scheme",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.BraidedCategory.ofCartesianMonoidalCategory",
"CategoryTheory.BraidedCategory",
"AlgebraicGeometry.instCartesianMonoidalCategoryScheme",
"AlgebraicGeometry.Scheme.instCategory",
"CategoryTheory... | true |
hasFTaylorSeriesUpToOn_pi' | Mathlib.Analysis.Calculus.ContDiff.Operations | [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"SeminormedAddGroup.toAddGroup",
"Pi.addCommMonoid",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"AddMonoid.toAddSemigroup",
"Pi.topologicalSpace",
"FormalMultilinearSeries",
"DistribMulAction... | true |
Vector.instSub | Init.Data.Vector.Algebra | [
"Vector",
"Vector.sub",
"Sub.mk",
"Nat",
"Sub"
] | true |
dimH.eq_1 | Mathlib.Topology.MetricSpace.HausdorffDimension | [
"ENNReal.ofNNReal",
"MeasureTheory.Measure",
"iSup",
"dimH._proof_1",
"MeasureTheory.Measure.hausdorffMeasure",
"id",
"borel",
"EMetricSpace.toPseudoEMetricSpace",
"NNReal",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"EMetricSpace",
"CompleteLinearOrder.toConditionallyC... | true |
Std.Tactic.BVDecide.BVLogicalExpr.bitblast.go.eq_5 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Substructure | [
"Std.Tactic.BVDecide.BVLogicalExpr.bitblast.go.match_1",
"Std.Sat.AIG.Ref.cast",
"Std.Sat.AIG.Entrypoint.aig",
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.BinaryInput",
"Std.Sat.AIG.mkOrCached",
"Std.Tactic.BVDecide.BoolExpr",
"Std.Sat.AIG.BinaryInput.mk",
"Std.Sat.AIG.Entrypoint",
"Std.Tactic.BVDecide.BVLog... | true |
Polynomial.abs_div_tendsto_atTop_atTop_of_degree_gt | Mathlib.Analysis.Polynomial.Basic | [
"NormedCommRing.toNormedRing",
"WithBot.instPreorder",
"Polynomial.eval",
"NormedCommRing.toSeminormedCommRing",
"OrderTopology",
"WithBot",
"Preorder.toLT",
"instHDiv",
"NormedRing.toRing",
"AddGroupWithOne.toAddGroup",
"abs",
"LinearOrder",
"PartialOrder.toPreorder",
"PseudoMetricSpace.t... | true |
Profinite.NobelingProof.GoodProducts.SumEval.eq_1 | Mathlib.Topology.Category.Profinite.Nobeling.Successor | [
"Ordinal.instLinearOrder",
"Preorder.toLT",
"isWellOrder_lt",
"Pi.topologicalSpace",
"Ordinal.partialOrder",
"Profinite.NobelingProof.Products.eval",
"LinearOrder",
"WellFoundedLT",
"PartialOrder.toPreorder",
"instTopologicalSpaceBool",
"Profinite.NobelingProof.π",
"Membership.mem",
"Semilat... | true |
OneMemClass.coe_one | Mathlib.Algebra.Group.Submonoid.Defs | [
"SetLike",
"One",
"Membership.mem",
"OneMemClass.one",
"Subtype",
"One.toOfNat1",
"OfNat.ofNat",
"Subtype.val",
"Eq",
"OneMemClass",
"SetLike.instMembership",
"rfl"
] | true |
Std.DTreeMap.Internal.Impl.balanced_rotateR | Std.Data.DTreeMap.Internal.Balancing | [
"Eq.mpr",
"Std.DTreeMap.Internal.Impl.doubleR",
"HMul.hMul",
"and_true",
"Std.DTreeMap.Internal.Impl.singleR",
"congrArg",
"Std.DTreeMap.Internal.Impl.balanced_inner_iff._simp_1",
"Std.DTreeMap.Internal.Impl.rotateR",
"HEq.refl",
"Std.DTreeMap.Internal.Impl.Balanced",
"Eq.mp",
"Std.DTreeMap.In... | true |
Subarray.take | Init.Data.Array.Subarray.Split | [
"Subarray",
"_private.Init.Data.Array.Subarray.Split.0.Subarray.take._proof_3",
"_private.Init.Data.Array.Subarray.Split.0.Subarray.take._proof_4",
"Std.Slice.Internal.SubarrayData.mk",
"Subarray.stop",
"instHAdd",
"HAdd.hAdd",
"Std.Slice.mk",
"Std.Slice.Internal.SubarrayData",
"Nat",
"instAddNa... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_16 | Mathlib.Combinatorics.SimpleGraph.Circulant | [
"Fin.instSub",
"HSub.hSub",
"_private.Mathlib.Combinatorics.SimpleGraph.Circulant.0.SimpleGraph.cycleGraph.getVert_cycleCons._proof_1_15",
"Fin.instOfNat",
"instOfNatNat",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Or",
"OfNat.ofNat",
"Fin",
"Eq",
"SimpleGraph.cycleGraph.... | false |
CochainComplex.mappingCone.descShortComplex._proof_3 | Mathlib.Algebra.Homology.HomotopyCategory.ShortExact | [
"CategoryTheory.Abelian.toPreadditive",
"HomologicalComplex.instCategory",
"CategoryTheory.ShortComplex",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"CategoryTheory.ShortComplex.X₁",
"AddCancelMonoid.toAddRightCancelMonoid",
"CategoryTheory.Abelian",
"CochainComp... | false |
rank_fin_fun | Mathlib.LinearAlgebra.Dimension.Constructions | [
"Pi.Function.module",
"Fintype.card_fin",
"Semiring.toModule",
"Pi.addCommMonoid",
"HMul.hMul",
"Cardinal.instOne",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"Pi.module",
"Cardinal.commSemiring",
"Cardinal.lift",
"Cardinal.mk",
"Cardinal.instMul",
"Fintype.card",
"Finite.of_fi... | true |
CategoryTheory.Pretriangulated.Opposite.instHasShiftOppositeInt._proof_7 | Mathlib.CategoryTheory.Triangulated.Opposite.Basic | [
"CategoryTheory.Functor.LaxMonoidal.μ_natural_left._autoParam",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.instCategoryOppositeShift",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"Int.instNegInt",
"CategoryTheory... | false |
HomotopicalAlgebra.trivialFibrations_eq_unop | Mathlib.AlgebraicTopology.ModelCategory.CategoryWithCofibrations | [
"CategoryTheory.MorphismProperty",
"Opposite",
"CategoryTheory.MorphismProperty.unop",
"HomotopicalAlgebra.instCategoryWithCofibrationsOpposite",
"HomotopicalAlgebra.instCategoryWithWeakEquivalencesOpposite",
"HomotopicalAlgebra.CategoryWithWeakEquivalences",
"CategoryTheory.Category.opposite",
"Categ... | true |
CochainComplex.HomComplex.Cochain.comp_assoc._proof_2 | Mathlib.Algebra.Homology.HomotopyCategory.HomComplex | [
"Int.instAddSemigroup",
"Eq.mpr",
"congrArg",
"add_assoc",
"id",
"Int",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Int.instAdd",
"Eq.refl",
"Eq.symm",
"Eq"
] | false |
Polynomial.toFinsuppIsoLinear_apply | Mathlib.Algebra.Polynomial.Basic | [
"Semiring.toModule",
"Polynomial.toFinsupp",
"AddMonoidAlgebra.addAddCommMonoid",
"Polynomial",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Polynomial.semiring",
"Nat",
"RingHomInvPair.ids",
"LinearEquiv",
"Semiring",
"LinearEquiv.instEquivLike... | true |
neg_one_lt_zero | Mathlib.Algebra.Order.Ring.Unbundled.Basic | [
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"Preorder.toLT",
"AddGroupWithOne.toAddGroup",
"LinearOrder",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Distrib.toAdd",
"Zero... | true |
CategoryTheory.MonObj.instIsMonHomHomRightUnitor | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.IsMonHom",
"CategoryTheory.IsMonHom.mk",
"CategoryTheory.BraidedCategory",
"CategoryTheory.MonObj.instTensorUnit",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.MonObj.tensorObj... | true |
CategoryTheory.Abelian.instAdditiveOppositeFunctorAddCommGrpCatExtFunctor | Mathlib.Algebra.Homology.DerivedCategory.Ext.Basic | [
"CategoryTheory.Abelian.Ext.add_comp",
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.Abelian.extFunctorObj",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"congrArg",... | true |
_private.Mathlib.Algebra.Module.Presentation.Basic.0.Module.Relations.Solution.ext.match_1 | Mathlib.Algebra.Module.Presentation.Basic | [
"Semiring.toModule",
"Finsupp.module",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"AddCommGroup",
"Module.Relations.Solution",
"Module.Relations.relation",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Linea... | false |
CategoryTheory.ShortComplex.RightHomologyData.ofAbelian_H | Mathlib.Algebra.Homology.ShortComplex.Abelian | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Abelian.image",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.Limits.cokernel",
"CategoryTheory.Abelian",
"CategoryTheory.Limits.kernel",
"CategoryTheory.ShortComplex.RightHomologyData.H",
"CategoryTheory.Shor... | true |
Sum.elim_single_zero | Mathlib.Algebra.Group.Pi.Basic | [
"Function.update",
"Sum.elim_zero_zero",
"congrArg",
"instDecidableEqSum",
"Sum",
"Pi.instZero",
"Sum.inl",
"Pi.single",
"True",
"eq_self",
"Sum.elim_update_left",
"of_eq_true",
"Zero.toOfNat0",
"congrFun'",
"OfNat.ofNat",
"Eq",
"Eq.trans",
"Sum.elim",
"DecidableEq",
"Zero"
] | true |
Valuation.valuationSubring_eq_top_iff._simp_1 | Mathlib.RingTheory.Valuation.ValuationSubring | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Field.toDivisionRing",
"DivisionRing.toRing",
"LinearOrderedCommGroupWithZero",
"Valuation.IsNontrivial",
"propext",
"Valuation.valuationSubring",
"ValuationSubring.instTop",
"Valuation.valuationSubring_eq_top_iff",
"Top.top",
... | false |
instMulFloat | Init.Data.Float | [
"Float.mul",
"Mul.mk",
"Mul",
"Float"
] | true |
Lean.IR.Expr.lit.sizeOf_spec | Lean.Compiler.IR.Basic | [
"Lean.IR.Expr",
"Lean.IR.Expr._sizeOf_inst",
"instOfNatNat",
"Lean.IR.LitVal._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"Lean.IR.Expr.lit",
"OfNat.ofNat",
"Eq",
"Lean.IR.LitVal"
] | true |
Lean.Lsp.WorkspaceClientCapabilities | Lean.Data.Lsp.Capabilities | [
"Lean.Lsp.WorkspaceClientCapabilities.mk"
] | true |
Lean.Syntax.setHeadInfoAux._unsafe_rec | Init.Meta.Defs | [
"Lean.Syntax.node",
"Lean.Syntax.ident",
"String",
"Lean.SourceInfo",
"_private.Init.Meta.Defs.0.Lean.Syntax.setTailInfoAux.match_3",
"Lean.Syntax.atom",
"Option.some",
"Lean.Syntax",
"_private.Init.Meta.Defs.0.Lean.Syntax.setHeadInfoAux.match_1",
"instOfNatNat",
"Substring.Raw",
"Array",
"O... | false |
neg_eq_of_add_eq_zero_right | Mathlib.Algebra.Group.Defs | [
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegMonoid",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"SubtractionMonoid",
"SubNegMonoid.toNeg",
"AddZero.toAdd",
"Zero.toOfNat0",
"SubNegMonoid.toAddMonoid",
"OfNat.ofNat",
"Eq",
"Neg.neg",
"SubtractionMonoid... | true |
MeasureTheory.memLp_stoppedProcess_of_mem_finset | Mathlib.Probability.Process.Stopping | [
"Eq.mpr",
"MeasureTheory.IsStoppingTime",
"OrderTopology",
"MeasureTheory.Measure",
"Preorder.toLT",
"Pi.addCommMonoid",
"WithTop.instPreorder",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Set.indicator",
"HEq.refl",
"Finset",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toP... | true |
NumberField.AdeleRing.algebraMap_injective | Mathlib.NumberTheory.NumberField.AdeleRing | [
"CommRing",
"IsDedekindDomain.FiniteAdeleRing",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"IsFractionRing",
"NumberField.InfiniteAdeleRing",
"Algebra",
"RingHom",
"Field.toDivisionRing",
"Prod.ext_iff",
"NumberField.instCommRingAdeleRing",
"CommRing.toNonAssocCommRing",
"Field.toSemif... | true |
Lean.Compiler.LCNF.Cases.getCtorNames | Lean.Compiler.LCNF.Basic | [
"Lean.NameSet",
"Lean.Compiler.LCNF.CtorInfo.name",
"instOfNatNat",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Purity.pure",
"autoParam",
"Array.foldl",
"Array",
"Lean.Compiler.LCNF.Code",
"_private.Lean.Compiler.LCNF.Basic.0.Lean.Compiler.LCNF.Cases.getCtorNames.match_1",
"Lean.NameSet.in... | true |
_private.Lean.Server.Watchdog.0.Lean.Server.Watchdog.handleCallHierarchyIncomingCalls.match_3 | Lean.Server.Watchdog | [
"Lean.Lsp.Location",
"Lean.Server.References.DocumentRefInfo.casesOn",
"Lean.Server.References.DocumentRefInfo.mk",
"Lean.Server.References.ParentDecl",
"Lean.Name",
"Option",
"Lean.Server.References.DocumentRefInfo"
] | false |
Lean.PrettyPrinter.Delaborator.delabRange._regBuiltin.Lean.PrettyPrinter.Delaborator.delabRange_1 | Lean.PrettyPrinter.Delaborator.Builtins | [
"Lean.PrettyPrinter.Delaborator.delabRange",
"Lean.Name.mkStr5",
"IO",
"Lean.PrettyPrinter.Delaborator.Delab",
"Unit",
"Lean.Name.mkStr4",
"Lean.PrettyPrinter.Delaborator.delabAttribute",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
Submonoid.LocalizationMap.ofMulEquivOfDom_id | Mathlib.GroupTheory.MonoidLocalization.Maps | [
"MonoidHom.instMonoidHomClass",
"MulEquiv.refl",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"Membership.mem",
"Eq.rec",
"MulOne.toMul",
"Submonoid.LocalizationMap.ofMulEquivOfDom_id.match_1",
"Submonoid.LocalizationMap.ofMulEquivOfDom",
"Submonoid.ext",
"Submonoid.map",
"M... | true |
Subgroup.coe_toAddSubgroup_symm_apply | Mathlib.Algebra.Group.Subgroup.Lattice | [
"Equiv.instEquivLike",
"Subgroup.toAddSubgroup",
"Additive",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Group",
"Preorder.toLE",
"Equiv",
"Subgroup",
"RelIso.symm",
"LE.le",
"AddSubgroup",
"Multiplicative",
"RelIso",
"SetLike.coe",
"Set.preimage",
"AddSubgroup.instSe... | true |
Std.Http.Internal.ChunkedBuffer.rec | Std.Internal.Http.Internal.ChunkedBuffer | [
"Std.Http.Internal.ChunkedBuffer.mk",
"Array",
"Nat",
"ByteArray",
"Std.Http.Internal.ChunkedBuffer"
] | false |
PMF.ofMultiset_apply_of_notMem | Mathlib.Probability.Distributions.Uniform | [
"Eq.mpr",
"False",
"instHDiv",
"congrArg",
"PMF.ofMultiset",
"PMF",
"ENNReal.instCharZero",
"AddMonoid.toAddZeroClass",
"PMF.instFunLike",
"Classical.propDecidable",
"_private.Mathlib.Probability.Distributions.Uniform.0.PMF.ofMultiset_apply_of_notMem._simp_1_2",
"Membership.mem",
"AddZeroCla... | true |
_private.Mathlib.Topology.Semicontinuity.Basic.0.LowerSemicontinuousWithinAt.add'._simp_1_1 | Mathlib.Topology.Semicontinuity.Basic | [
"Exists",
"not_exists",
"propext",
"Eq",
"Not"
] | false |
polynomialFunctions.starClosure_eq_adjoin_X | Mathlib.Topology.ContinuousMap.Polynomial | [
"polynomialFunctions.eq_adjoin_X",
"Eq.mpr",
"congrArg",
"ContinuousMap.instStarModule",
"CommSemiring.toSemiring",
"polynomialFunctions",
"IsTopologicalSemiring",
"AlgHom",
"ContinuousStar",
"ContinuousMap",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"StarMul.toStarModule",
"Algebra... | true |
affineHomeomorph_image_Ioc | Mathlib.Topology.Algebra.Field | [
"Set.Ioc",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Set.image_affine_Ioc",
"MulZeroClass.toMul",
"AddGroupWithOne.toAddGroup",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
... | true |
Set.initialSegIic._proof_5 | Mathlib.Order.Interval.Set.InitialSeg | [
"Eq.mpr",
"RelEmbedding.mk",
"Preorder.toLT",
"congrArg",
"setOf",
"Preorder.toLE",
"Set.mem_Iic._simp_2",
"Membership.mem",
"Set.initialSegIic._proof_4",
"Function.Embedding.mk",
"Set.Elem",
"id",
"Subtype",
"LT.lt.le",
"Subtype.range_coe_subtype",
"LE.le",
"funext",
"RelEmbedding... | false |
Std.DTreeMap.Internal.Impl.getKeyD_minKey? | Std.Data.DTreeMap.Internal.Lemmas | [
"Std.DTreeMap.Internal.Impl.getKeyD",
"Eq.mpr",
"Std.DTreeMap.Internal.Impl.getKeyD_eq_getKeyD",
"Std.Internal.List.getKeyD_minKey?",
"Ord",
"Std.instLawfulBEqOrd",
"congrArg",
"Std.Internal.List.getKeyD",
"beqOfOrd",
"Std.DTreeMap.Internal.Impl.Ordered.distinctKeys",
"Std.TransOrd",
"Std.Inte... | true |
Int.emod_eq_add_self_emod | Init.Data.Int.DivMod.Lemmas | [
"Int.add_emod_right",
"instHMod",
"Int",
"instHAdd",
"HMod.hMod",
"HAdd.hAdd",
"Int.instAdd",
"Int.instMod",
"Eq.symm",
"Eq"
] | true |
Lean.Elab.WF.GuessLex.MutualMeasure.args.inj | Lean.Elab.PreDefinition.WF.GuessLex | [
"Lean.Elab.WF.GuessLex.MutualMeasure.args",
"Lean.Elab.WF.GuessLex.MutualMeasure.args.noConfusion",
"Array",
"Nat",
"Lean.Elab.WF.GuessLex.MutualMeasure",
"Eq"
] | true |
EMetricSpace.ofRiemannianMetric | Mathlib.Geometry.Manifold.Riemannian.Basic | [
"Real",
"instAddMonoidWithOneENat",
"PseudoEMetricSpace.ofRiemannianMetric._proof_3",
"TangentSpace.fiberBundle",
"NormedSpace",
"Real.denselyNormedField",
"instAddCommGroupTangentSpace",
"instIsTopologicalAddGroupTangentSpace",
"IsContinuousRiemannianBundle",
"EMetricSpace.ofT0PseudoEMetricSpace"... | true |
ModuleCat.instPreservesProjectiveObjectsUliftFunctorOfSmall | Mathlib.Algebra.Category.ModuleCat.Ulift | [
"ULift.addCommGroup",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Functor.PreservesProjectiveObjects",
"ULift",
"inferInstance",
"id",
"Module.instProjectiveULift",
"ModuleCat.of",
"ModuleCat.projective_of_categoryTheory_projective",
"ModuleCat.isAddCommGroup",
"ULift.module'"... | true |
ExteriorAlgebra.toTrivSqZeroExt | Mathlib.LinearAlgebra.ExteriorAlgebra.Basic | [
"ExteriorAlgebra.toTrivSqZeroExt._proof_2",
"ExteriorAlgebra.toTrivSqZeroExt._proof_1",
"CommRing",
"TrivSqZeroExt",
"Semiring.toModule",
"Equiv.instEquivLike",
"HMul.hMul",
"QuadraticMap.instZero",
"ExteriorAlgebra",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.t... | true |
Finset.Colex.toColex_image_le_toColex_image | Mathlib.Combinatorics.Colex | [
"not_exists._simp_1",
"Equiv.instEquivLike",
"StrictMono",
"Colex",
"LinearOrder.toDecidableEq",
"Finset.Colex.instLE",
"congrArg",
"Finset",
"LinearOrder",
"exists_exists_and_eq_and._simp_1",
"PartialOrder.toPreorder",
"Finset.mem_image._simp_1",
"Function.Injective.eq_iff",
"Preorder.toL... | true |
Submodule.comap_dualAnnihilator | Mathlib.LinearAlgebra.Dual.Defs | [
"Submodule",
"Semiring.toModule",
"Submodule.dualCoannihilator",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Submodule.dualAnnihilator",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.module",
"IsScalarTower.left",
"AddCommMono... | true |
PointDerivation | Mathlib.Geometry.Manifold.DerivationBundle | [
"Derivation",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"NormedSpace",
"instTopENat",
"CommSemiring.toSemiring",
"PointedContMDiffMap.evalAlgebra",
"NormedField.toField",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NormedCommRing.toNonUni... | true |
Algebra.PreSubmersivePresentation.ofBijectiveAlgebraMap | Mathlib.RingTheory.Extension.Presentation.Submersive | [
"CommRing",
"Algebra.PreSubmersivePresentation.ofBijectiveAlgebraMap._proof_1",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"PEmpty",
"Algebra.PreSubmersivePresentation.mk",
"PEmpty.elim",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"Algebra.PreSubmersivePresen... | true |
MeasureTheory.ComplexMeasure.re._proof_3 | Mathlib.MeasureTheory.Measure.Complex | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"Real.instZero",
"DistribMulAction.toDistribSMul",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"IsBoundedSMul.... | false |
SimpleGraph.UnitDistEmbedding.subsingleton_p_apply | Mathlib.Combinatorics.SimpleGraph.UnitDistance.Basic | [
"SimpleGraph.UnitDistEmbedding.subsingleton",
"Function.Embedding",
"SimpleGraph",
"MetricSpace",
"SimpleGraph.UnitDistEmbedding.p",
"Subsingleton",
"Eq.refl",
"Function.instFunLikeEmbedding",
"Eq",
"DFunLike.coe"
] | true |
Lean.defaultMaxRecDepth | Init.Prelude | [
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | true |
_private.Mathlib.MeasureTheory.Constructions.Cylinders.0.MeasureTheory.generateFrom_measurableCylinders._simp_1_1 | Mathlib.MeasureTheory.Constructions.Cylinders | [
"Set.mem_image",
"Membership.mem",
"Exists",
"And",
"propext",
"Set.image",
"Eq",
"Set.instMembership",
"Set"
] | false |
RingPreordering.copy._proof_8 | Mathlib.Algebra.Order.Ring.Ordering.Defs | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"SetLike.mem_coe._simp_1",
"CommRing",
"CommSemiring.toSemiring",
"SubsemiringClass.toAddSubmonoidClass",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"RingPreordering",
"ZeroMemClass... | false |
CategoryTheory.MonoidalCategory.ofTensorHom._proof_5 | Mathlib.CategoryTheory.Monoidal.Category | [
"CategoryTheory.MonoidalCategoryStruct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"of_eq_true",
"CategoryTheory.Category.toCategoryStruct",
"congrFun'",
"Categ... | false |
CategoryTheory.Adjunction.isLocalization_leftAdjoint | Mathlib.CategoryTheory.Localization.CalculusOfFractions.OfAdjunction | [
"CategoryTheory.Localization.liftingLift",
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Localization.liftNatIso",
"CategoryTheory.Functor",
"CategoryTheory.IsIso",
"congrArg",
"CategoryTheory.MorphismProperty.Q",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"... | true |
_private.Mathlib.Algebra.Group.Commute.Defs.0.Commute.mul_pow.match_1_1 | Mathlib.Algebra.Group.Commute.Defs | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
smul_set_closure_subset | Mathlib.Topology.Algebra.MulAction | [
"Iff.mpr",
"instHSMul",
"ContinuousSMul",
"map_mem_closure₂",
"Set.smul_mem_smul",
"SMul",
"Set.smul",
"Set.smul_subset_iff",
"Membership.mem",
"HasSubset.Subset",
"TopologicalSpace",
"closure",
"HSMul.hSMul",
"ContinuousSMul.continuous_smul",
"Set.instMembership",
"Set.instHasSubset",... | true |
PolynomialLaw.zero_smul | Mathlib.RingTheory.PolynomialLaw.Basic | [
"PolynomialLaw.instSMul",
"instHSMul",
"congrArg",
"CommSemiring.toSemiring",
"SMulWithZero.toSMulZeroClass",
"TensorProduct.addCommMonoid",
"Module.toMulActionWithZero",
"Algebra",
"Algebra.toModule",
"Pi.smulWithZero",
"Pi.instZero",
"PolynomialLaw",
"AddCommMonoid",
"CommSemiring",
"N... | true |
_private.Mathlib.Topology.Instances.EReal.Lemmas.0.EReal.continuousAt_mul_coe_coe | Mathlib.Topology.Instances.EReal.Lemmas | [
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"congrArg",
"ContinuousAt",
"Filter.map",
"IsTopologicalSemiring.toContinuousMul",
"EReal.instTopologicalSpace",
"PseudoMetricSpace.toUniformSpace",
... | true |
Module.Grassmannian.map_id | Mathlib.RingTheory.Grassmannian | [
"Module.Grassmannian",
"TensorProduct.AlgebraTensorModule.cancelBaseChange",
"Submodule",
"LinearMap.baseChange",
"CommAlgCat.instConcreteCategoryAlgHomCarrier",
"LinearEquiv.symm",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Com... | true |
Differentiable.finCons | Mathlib.Analysis.Calculus.FDeriv.Prod | [
"Differentiable",
"Iff.mpr",
"NormedSpace",
"Pi.topologicalSpace",
"differentiable_finCons'",
"Fin.succ",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Pi.module",
"PseudoMetricSpace.toUniformSpace",
"Fin.cons",
"NormedField.toField",
"Fin.instOfNat",
"instOfNatNat",
"Field.to... | true |
RestrictedProduct.instCommMonoidCoeOfSubmonoidClass._proof_5 | Mathlib.Topology.Algebra.RestrictedProduct.Basic | [
"SetLike",
"Monoid.toMulOneClass",
"RestrictedProduct.instPow",
"RestrictedProduct.instDFunLike",
"RestrictedProduct",
"SetLike.coe",
"HPow.hPow",
"CommMonoid.toMonoid",
"Nat",
"instHPow",
"SubmonoidClass",
"Eq",
"CommMonoid",
"DFunLike.coe",
"Filter",
"rfl"
] | false |
CategoryTheory.Presheaf.IsSheaf' | Mathlib.CategoryTheory.Sites.Sheaf | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Fork.ofι",
"Opposite",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Presieve",
"CategoryTheory.Limits.HasProducts",
"CategoryTheory.Presheaf.firstObj",
"CategoryTheory.Presheaf.forkMap",
"Membership.mem",
"CategoryTheory.Limits.walki... | true |
Function.Injective.addCancelCommMonoid | Mathlib.Algebra.Group.InjSurj | [
"AddCancelCommMonoid.mk",
"instHSMul",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"AddLeftCancelSemigroup",
"AddCancelCommMonoid",
"SMul",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"AddZeroClass.toAddZero",
"AddCommMonoid",
"Function.Injective.addLeftCancelSemigroup",
"AddLeftCancelMon... | true |
HomologicalComplex.congr_hom | Mathlib.Algebra.Homology.HomologicalComplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex",
"ComplexShape",
"congr_arg",
"HomologicalComplex.Hom",
"CategoryTheory.Category.toCategoryStruct",
"HomologicalCo... | true |
Lean.PrettyPrinter.Delaborator.whenPPOption | Lean.PrettyPrinter.Delaborator.Basic | [
"Lean.PrettyPrinter.Delaborator.getPPOption",
"Lean.PrettyPrinter.Delaborator.Context",
"Lean.PrettyPrinter.Delaborator.Delab",
"ReaderT.instMonad",
"Lean.PrettyPrinter.Delaborator.DelabM",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instDecidableEqBool",
"Lean.Syntax.Term",
"Bool.true",
"Lean.Meta.inst... | true |
DividedPowers.dpow_span_isSubideal | Mathlib.RingTheory.DividedPowers.SubDPIdeal | [
"DividedPowers.dpow_mem",
"Ideal.span_le",
"Eq.mpr",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Eq.rec",
"id",
"HasSubset.Subset",
"Ne",
"Submodule.instPartialOrder",
"instOfNatNat",
... | true |
PrimrecRel.comp₂ | Mathlib.Computability.Primrec.Basic | [
"PrimrecRel",
"PrimrecRel.comp",
"Prod.fst",
"Primcodable.prod",
"Primcodable",
"Prod",
"Prod.snd",
"Primrec₂"
] | true |
Polynomial.iterate_derivative_X_pow_eq_natCast_mul | Mathlib.Algebra.Polynomial.Derivative | [
"Polynomial.derivative",
"Function.iterate_succ_apply'",
"Eq.mpr",
"Polynomial.C",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Nat.instOrderedSub",
"Semigroup.toMul",
"Nat.recAux",
"Semiring.toModule",
"HMul.hMul",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSe... | true |
Polynomial.leadingCoeff_cons_eraseLead | Mathlib.Algebra.Polynomial.CoeffList | [
"Eq.mpr",
"congrArg",
"Polynomial.natDegree_eraseLead_add_one",
"List.map",
"WithBot.succ",
"Membership.mem",
"mt",
"Polynomial.natDegree_pos_of_nextCoeff_ne_zero",
"id",
"List.mem_range._simp_1",
"Polynomial.leadingCoeff",
"Ne",
"instOfNatNat",
"List.range",
"Polynomial.degree",
"Poly... | true |
Lean.instInhabitedLeanOptionValue | Lean.Util.LeanOptions | [
"Lean.instInhabitedLeanOptionValue.default",
"Inhabited",
"Lean.LeanOptionValue",
"Inhabited.mk"
] | true |
ModuleCat.ofHom₂._proof_3 | Mathlib.Algebra.Category.ModuleCat.Basic | [
"CommRing",
"RingHomInvPair",
"RingHomInvPair.ids",
"CommRing.toRing",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring"
] | false |
CategoryTheory.ObjectProperty.triangEnvelopeIter_add._auto_1 | Mathlib.CategoryTheory.Triangulated.Generators | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
fourierLp._proof_5 | Mathlib.Analysis.Fourier.AddCircle | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"Complex.instNormedAddCommGroup",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"EMetricSpace.toPseudoEMetricSpace",
"AddCircle",
"EMetric.instIsCountablyGeneratedUniformity",
"Real.instAddCommGroup",
"Uni... | false |
CategoryTheory.Subobject.functor_map | Mathlib.CategoryTheory.Subobject.Lattice | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Subobject.functor",
"PartialOrder.toPreorder",
"Quiver.Hom.unop",
"TypeCat.ofHom",
"Preorder.smallCategory",
"CategoryTheory.instPartialOrderSubobject",
"CategoryTheory.Limits.HasPullbacks",
"CategoryTheory.Funct... | true |
_private.Mathlib.Geometry.Euclidean.Volume.Measure.0.MeasureTheory.Measure.euclideanHausdorffMeasure._proof_4 | Mathlib.Geometry.Euclidean.Volume.Measure | [
"Real",
"BorelSpace",
"PiLp",
"AddMonoidWithOne.toNatCast",
"Real.normedAddCommGroup",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"PiLp.borelSpace",
"PiLp.topologicalSpace",
"Real.measurableSpace",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"PseudoEMetricSpace.toUniformSpace",
"MeasurableSp... | false |
SimpleGraph.Walk.bypass | Mathlib.Combinatorics.SimpleGraph.Paths | [
"SimpleGraph.Walk.bypass._f",
"SimpleGraph.Walk",
"SimpleGraph",
"SimpleGraph.Walk.brecOn",
"DecidableEq"
] | true |
Module.Basis.reindex | Mathlib.LinearAlgebra.Basis.Defs | [
"Module.Basis.ofRepr",
"Semiring.toModule",
"Finsupp.module",
"Module.Basis.map._proof_1",
"Finsupp.domLCongr",
"Equiv",
"Module.Basis.repr",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Module.Basis",
"NonAssocSemiring.toNonUnitalNonAssocSemiring... | true |
CategoryTheory._aux_Mathlib_Combinatorics_Quiver_ReflQuiver___unexpand_CategoryTheory_ReflQuiver_id_1 | Mathlib.Combinatorics.Quiver.ReflQuiver | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
... | false |
RightOrdContinuous.map_inf | Mathlib.Order.OrdContinuous | [
"Set.image_pair",
"RightOrdContinuous",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"Set.instSingletonSet",
"isGLB_pair",
"Insert.insert",
"SemilatticeInf.toMin",
"SemilatticeInf",
"Set.instInsert",
"IsGLB",
"True",
"eq_true",
"of_eq_true",
... | true |
Std.Time.Month.Ordinal.june | Std.Time.Date.Unit.Month | [
"OfNat.ofNat",
"Std.Time.Month.Ordinal",
"Std.Time.Month.instOfNatOrdinal"
] | true |
Std.Http.Headers.mk.injEq | Std.Internal.Http.Data.Headers | [
"Std.Http.Headers.mk.inj",
"Eq.propIntro",
"Std.Http.Header.Name.instBEq",
"Std.Http.Header.Name",
"Std.Http.Header.Value",
"Std.Http.Header.Name.instHashable",
"Std.Http.Headers.mk",
"Eq.ndrec",
"Eq.refl",
"Std.Http.Headers",
"Std.Internal.IndexMultiMap",
"Eq"
] | true |
Std.HashMap.Raw.toList_keysArray | Std.Data.HashMap.RawLemmas | [
"Std.HashMap.Raw.WF.out",
"Std.HashMap.Raw.keysArray",
"Std.HashMap.Raw.WF",
"Std.DHashMap.Raw.toList_keysArray",
"Array.toList",
"Std.HashMap.Raw",
"List",
"Std.HashMap.Raw.keys",
"Std.HashMap.Raw.inner",
"Hashable",
"BEq",
"Eq"
] | true |
BumpCovering.mk.sizeOf_spec | Mathlib.Topology.PartitionOfUnity | [
"Real.partialOrder",
"Real",
"Real.instZero",
"ContinuousMap",
"Set.univ",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"ContinuousMap.instOne",
"Preorder.toLE",
"Membership.mem",
"Exists",
"nhds",
"Filter.EventuallyEq",
"Pi.instZero",
"BumpCovering._sizeOf_inst",
"in... | true |
SaturatedSubmonoid.mem_sInf | Mathlib.Algebra.Group.Submonoid.Saturation | [
"SaturatedSubmonoid",
"Set.mem_iInter₂",
"Membership.mem",
"Iff",
"SaturatedSubmonoid.instInfSet",
"SetLike.coe",
"MulOneClass",
"Set.instMembership",
"SetLike.instMembership",
"InfSet.sInf",
"SaturatedSubmonoid.instSetLike",
"Set"
] | true |
spectrum.zero_mem_iff | Mathlib.Algebra.Algebra.Spectrum.Basic | [
"Eq.mpr",
"RingHom.instRingHomClass",
"Algebra.algebraMap",
"spectrum",
"Ring.toNonAssocRing",
"Monoid.toMulOneClass",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"Iff.rfl",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"IsUnit",
"Algebra",
"RingHom",
"Membership.me... | true |
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