name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.NumberTheory.FLT.Three.0.FermatLastTheoremForThreeGen.Solution'.hcdvd | Mathlib.NumberTheory.FLT.Three | [
"Dvd.dvd",
"CommRing.toNonUnitalCommRing",
"NumberField.instCommRingRingOfIntegers",
"AddGroupWithOne.toAddGroup",
"semigroupDvd",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"_private.Mathlib.NumberTheory.FLT.Three.0.FermatLastTheoremForThreeGen.Solution'",
"SemigroupWithZero.toSemigroup",
... | true |
DivisibleHull.nsmul_mk | Mathlib.GroupTheory.DivisibleHull | [
"Nat.recAux",
"instHSMul",
"DivisibleHull.mk_add_mk_left",
"congrArg",
"CommSemiring.toSemiring",
"Nat.instMonoid",
"AddMonoid.toAddZeroClass",
"AddMonoid.toNSMul",
"DivisibleHull",
"nonZeroDivisors",
"AddZeroClass.toAddZero",
"instOfNatNat",
"AddCommMonoid",
"one_smul",
"AddZero.toZero"... | true |
CategoryTheory.PreservesFiniteLimitsOfFlat.uniq | Mathlib.CategoryTheory.Functor.Flat | [
"CategoryTheory.Bicone.right",
"CategoryTheory.StructuredArrow.homMk",
"Eq.mpr",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"Trans.trans",
"CategoryTheory.Comma.right",
"CategoryTheory.Limits.Cone.toStructuredArrow._proof_2",
"CategoryTheory.CommaMorphi... | true |
CategoryTheory.Limits.Cocone.whisker_ι | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.whiskerLeft",
"CategoryTheory.Limits.Cocone.whisker",
"CategoryTheory.Limits.Cocone.ι",
"Eq.re... | true |
Lean.Syntax.decodeStrLitAux._unsafe_rec | Init.Meta.Defs | [
"String.Internal.get",
"Pure.pure",
"Lean.Syntax.decodeStringGap",
"instAlternativeOption",
"String.Internal.next",
"String",
"String.push",
"_private.Init.Meta.Defs.0.Lean.Syntax.decodeStrLitAux.match_3",
"instDecidableEqBool",
"Applicative.toPure",
"instBEqOfDecidableEq",
"String.Pos.Raw",
... | false |
ProbabilityTheory.IsRatCondKernelCDFAux.isRatCondKernelCDF | Mathlib.Probability.Kernel.Disintegration.CDFToKernel | [
"Real",
"ProbabilityTheory.IsFiniteKernel",
"ProbabilityTheory.IsRatCondKernelCDFAux.measurable",
"ProbabilityTheory.IsRatCondKernelCDF",
"Rat",
"MeasurableSpace",
"ProbabilityTheory.IsRatCondKernelCDFAux.integrable",
"Real.measurableSpace",
"ProbabilityTheory.IsRatCondKernelCDFAux",
"ProbabilityT... | true |
LocallyConstant.piecewise._proof_3 | Mathlib.Topology.LocallyConstant.Basic | [
"Membership.mem",
"Set.instInter",
"Inter.inter",
"And.right",
"Set.instMembership",
"Set"
] | false |
_private.Aesop.BuiltinRules.0.Aesop.BuiltinRules.pEmpty_false.match_1_1 | Aesop.BuiltinRules | [
"False",
"False.elim",
"PEmpty",
"PEmpty.casesOn"
] | false |
instCompleteLinearOrderENat._proof_6 | Mathlib.Data.ENat.Lattice | [
"Lattice.toSemilatticeSup",
"instLinearOrderENat",
"PartialOrder.toPreorder",
"Preorder.toLE",
"InfSet.mk",
"DistribLattice.toLattice",
"instCompleteLinearOrderENat._aux_4",
"WithTop.isGLB_sInf",
"IsGLB",
"Nat",
"ENat",
"SemilatticeSup.toPartialOrder",
"InfSet.sInf",
"instDistribLatticeOfL... | false |
Std.Time.Millisecond.instLawfulEqOrdOffset | Std.Time.Time.Unit.Millisecond | [
"Std.Time.Millisecond.instOrdOffset",
"Std.Time.Millisecond.Offset",
"_private.Std.Time.Time.Unit.Millisecond.0.Std.Time.Millisecond.instLawfulEqOrdOffset._proof_1",
"Std.LawfulEqOrd"
] | true |
Lean.LocalDecl.replaceFVarId | Lean.LocalContext | [
"Lean.instBEqFVarId",
"Lean.LocalDecl.cdecl",
"Lean.LocalDecl.ldecl",
"Lean.LocalDeclKind",
"Lean.Expr.replaceFVarId",
"Lean.Expr",
"Lean.FVarId",
"instDecidableEqBool",
"Bool.true",
"BEq.beq",
"Lean.LocalDecl.fvarId",
"Nat",
"_private.Lean.LocalContext.0.Lean.LocalDecl.index.match_1",
"Bo... | true |
MeasureTheory.JordanDecomposition.instSMul._proof_4 | Mathlib.MeasureTheory.VectorMeasure.Decomposition.Jordan | [
"MeasureTheory.JordanDecomposition.posPart",
"ENNReal.ofNNReal",
"instHSMul",
"MeasureTheory.Measure",
"instSMulOfMul",
"IsScalarTower.right",
"CommSemiring.toSemiring",
"MeasureTheory.Measure.MutuallySingular.smul",
"Algebra.id",
"MeasureTheory.Measure.instSMul",
"NNReal",
"MeasureTheory.Jord... | false |
SaturatedAddSubmonoid._sizeOf_1 | Mathlib.Algebra.Group.Submonoid.Saturation | [
"AddSubmonoid",
"instOfNatNat",
"instHAdd",
"AddZeroClass",
"AddSubmonoid.AddSaturated",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"SaturatedAddSubmonoid.rec",
"instAddNat",
"SizeOf",
"OfNat.ofNat",
"AddSubmonoid._sizeOf_inst",
"SaturatedAddSubmonoid"
] | false |
FirstOrder.Language.Term.restrictVar | Mathlib.ModelTheory.Syntax | [
"FirstOrder.Language.Term.brecOn",
"Finset",
"Membership.mem",
"FirstOrder.Language.Term",
"Subtype",
"FirstOrder.Language.Term.restrictVar._f",
"Finset.instSetLike",
"FirstOrder.Language.Term.varFinset",
"FirstOrder.Language",
"SetLike.instMembership",
"DecidableEq"
] | true |
ENNReal.nnreal_smul_lt_top_iff | Mathlib.Data.ENNReal.Action | [
"Eq.mpr",
"instHSMul",
"Preorder.toLT",
"congrArg",
"CommSemiring.toSemiring",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"id",
"NNReal",
"Ne",
"ENNReal.instCommSemiring",
"lt_top_iff_ne_top",
"NNReal.instZero",
"Iff",
"OrderTop.toTop",
"ENNReal.nnreal_smul_ne_top_iff",
... | true |
_private.Lean.Compiler.LCNF.Simp.ConstantFold.0.Lean.Compiler.LCNF.Simp.ConstantFold.getFolder | Lean.Compiler.LCNF.Simp.ConstantFold | [
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Core.instMonadRefCoreM",
"String",
"Lean.Core.instMonadEnvCoreM",
"_private.Lean.Compiler.LCNF.Simp.ConstantFold.0.Lean.Compiler.LCNF.Simp.ConstantFold.getFolderCore",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean... | true |
SmoothBumpCovering.mk.inj | Mathlib.Geometry.Manifold.PartitionOfUnity | [
"SmoothBumpCovering",
"Real",
"SmoothBumpCovering.mk",
"NormedSpace",
"Real.denselyNormedField",
"Real.instZero",
"NormedSpace.toModule",
"SmoothBumpCovering.mk.noConfusion",
"Membership.mem",
"Exists",
"nhds",
"Filter.EventuallyEq",
"LocallyFinite",
"Real.instOne",
"SmoothBumpFunction.t... | true |
CategoryTheory.ObjectProperty.fullSubcategoryCongr_functor | Mathlib.CategoryTheory.Equivalence | [
"CategoryTheory.Functor",
"CategoryTheory.ObjectProperty.ιOfLE",
"CategoryTheory.ObjectProperty.fullSubcategoryCongr",
"CategoryTheory.Equivalence.functor",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ObjectProperty.FullSubcategory",
"CategoryTheory.ObjectProperty.FullSubcat... | true |
Filter.comap_embedding_atBot | Mathlib.Order.Filter.AtTopBot.Tendsto | [
"Filter.instMembership",
"Iff.mpr",
"Monotone._to_dual_cast_2",
"Filter.Tendsto.le_comap",
"Filter.le_principal_iff",
"Filter.instCompleteLatticeFilter",
"PartialOrder.toPreorder",
"Monotone",
"le_iInf",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Eq.mp",
"HasSubset.Subset",
"LE.le",
... | true |
Lean.Compiler.LCNF.initFn._@.Lean.Compiler.LCNF.ConfigOptions.583794373._hygCtx._hyg.4 | Lean.Compiler.LCNF.ConfigOptions | [
"Lean.Option",
"Lean.Name.mkStr5",
"IO",
"Lean.Option.Decl.mk",
"Bool.true",
"Lean.KVMap.instValueBool",
"Lean.Option.register",
"Bool",
"Lean.Name.mkStr2"
] | false |
LieSubmodule.instAddCommMonoid._proof_1 | Mathlib.Algebra.Lie.Submodule | [
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieSubmodule",
"AddCommGroup",
"instOfNatNat",
"LieSubmodule.instZero",
"LieRing",
"CommRing.toCommSemiring",
"nsmulRec",
"Nat",
"LieRingModule",
"Zero.toOfNat0",
"Eq.refl",
"LieSubmodule.instAdd",
"Module",
"OfN... | false |
LocalizedModule.liftOn._proof_2 | Mathlib.Algebra.Module.LocalizedModule.Basic | [
"LocalizedModule.r",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"LocalizedModule.r.setoid._proof_1",
"LocalizedModule.r.setoid",
"Membership.mem",
"Setoid.mk.congr_simp",
"Equivalence",
"Eq.mp",
"Subtype",
"Setoid",
"AddCommMonoid",
"MulZeroOneClass.toMulOneClass",
"i... | false |
SemiNormedGrp.Hom.mk.injEq | Mathlib.Analysis.Normed.Group.SemiNormedGrp | [
"NormedAddGroupHom",
"Eq.propIntro",
"SemiNormedGrp.Hom.mk.inj",
"SemiNormedGrp.Hom",
"SemiNormedGrp.carrier",
"SemiNormedGrp.Hom.mk",
"Eq.ndrec",
"Eq.refl",
"SemiNormedGrp.str",
"Eq",
"SemiNormedGrp"
] | true |
CategoryTheory.GrothendieckTopology.Cover.preOneHypercover_p₂ | Mathlib.CategoryTheory.Sites.Hypercover.One | [
"CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation",
"CategoryTheory.GrothendieckTopology.Cover.preOneHypercover",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.GrothendieckTopology.Cover.Arrow.Relation.Z",
"CategoryTheory.GrothendieckTopology.Cover.Arrow",
"CategoryTheo... | true |
Std.ExtHashMap.getD_diff_of_mem_right | Std.Data.ExtHashMap.Lemmas | [
"Std.ExtHashMap.getD",
"Std.ExtHashMap.inner",
"Membership.mem",
"Std.ExtHashMap.instSDiffOfEquivBEqOfLawfulHashable",
"LawfulHashable",
"Std.ExtHashMap",
"SDiff.sdiff",
"EquivBEq",
"Hashable",
"Std.ExtDHashMap.Const.getD_diff_of_mem_right",
"Std.ExtHashMap.instMembershipOfEquivBEqOfLawfulHashab... | true |
OrderAddMonoidHom.coe_comp_orderHom | Mathlib.Algebra.Order.Hom.Monoid | [
"OrderAddMonoidHom.comp",
"OrderHom.comp",
"OrderAddMonoidHom.instFunLike",
"AddZeroClass",
"OrderHomClass.toOrderHom",
"OrderAddMonoidHom.instOrderHomClass",
"OrderAddMonoidHom",
"Eq",
"OrderHom",
"rfl",
"Preorder"
] | true |
CategoryTheory.CostructuredArrow.homMk'_id._proof_2 | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CostructuredArrow.hom",
"CategoryTheory.CategoryStruct.id",
"id",
"CategoryTheory.CostructuredArrow",
"CategoryTheory.Functor.map",
"CategoryTheory.Functor.map_id",
"Category... | false |
Set.pairwise_iUnion₂_iff | Mathlib.Data.Set.Pairwise.Lattice | [
"Set.subset_iUnion₂_of_subset",
"DirectedOn",
"Set.Pairwise.mono",
"Membership.mem",
"Set.instReflSubset",
"HasSubset.Subset",
"subset_refl",
"Set.Pairwise",
"Iff",
"Set.pairwise_iUnion₂",
"Iff.intro",
"Set.instMembership",
"Set.iUnion",
"Set.instHasSubset",
"Set"
] | true |
_private.Lean.Server.AsyncList.0.IO.AsyncList.getFinishedPrefix.match_5 | Lean.Server.AsyncList | [
"IO.AsyncList.delayed",
"Unit.unit",
"IO.AsyncList.nil",
"IO.AsyncList.casesOn",
"Unit",
"Lean.Server.ServerTask",
"IO.AsyncList.cons",
"Except",
"IO.AsyncList"
] | false |
Lean.Meta.forallMetaTelescopeReducingUntilDefEq | Mathlib.Lean.Meta.Basic | [
"Pure.pure",
"Lean.Meta.ppExpr",
"Lean.MessageData",
"Array.instAppend",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.MetavarKind.natural",
"Bool.not",
"ReaderT",
"String",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.MessageDat... | true |
CategoryTheory.CommSq.mk._flat_ctor | Mathlib.CategoryTheory.CommSq | [
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.CommSq.w._autoParam",
"Quiver.Hom",
"CategoryTheory.CommSq",
"CategoryTheory.CommSq.mk",
"autoParam",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Category"
] | false |
surjective_of_isLocalized_span | Mathlib.RingTheory.LocalProperties.Exactness | [
"Iff.mpr",
"Submodule",
"RingHomSurjective.ids",
"Semiring.toModule",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"Membership.mem",
"Submodule.eq_top_of_isLocalized₀_span",
"LinearMap.range",
"Set.Elem",
"Submodule.instTop",
"Ideal",
"LinearMap.module",
"LinearMap",
"LinearMap.ra... | true |
_private.Mathlib.SetTheory.Cardinal.CountableCover.0.Cardinal.mk_subtype_le_of_countable_eventually_mem._simp_1_1 | Mathlib.SetTheory.Cardinal.CountableCover | [
"Membership.mem",
"Set.preimage",
"propext",
"Eq",
"Set.instMembership",
"Set.mem_preimage",
"Set"
] | false |
CategoryTheory.IsCardinalFiltered.coeq_condition | Mathlib.CategoryTheory.Presentable.IsCardinalFiltered | [
"CategoryTheory.Limits.WalkingParallelFamily.one",
"CategoryTheory.IsCardinalFiltered.cocone",
"CategoryTheory.IsCardinalFiltered",
"HasCardinalLT",
"Cardinal.IsRegular",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Cardinal",
"CategoryTheory.IsCardinalFiltered.toCoeq",
"CategoryTheory... | true |
List.TProd.elim._proof_1 | Mathlib.Data.Prod.TProd | [
"Membership.mem",
"Or.resolve_left",
"List.cons",
"List",
"List.instMembership",
"Iff.mp",
"Or",
"List.mem_cons",
"Eq",
"Not"
] | false |
BooleanSubalgebra.instTopCoe | Mathlib.Order.BooleanSubalgebra | [
"BooleanAlgebra",
"BooleanSubalgebra",
"BooleanSubalgebra.top_mem",
"Membership.mem",
"Subtype",
"Top.mk",
"Subtype.mk",
"BooleanAlgebra.toTop",
"BooleanSubalgebra.instSetLike",
"Top.top",
"SetLike.instMembership",
"Top"
] | true |
MeasureTheory.Measure.tprod | Mathlib.MeasureTheory.Constructions.Pi | [
"MeasureTheory.Measure",
"List.rec",
"MeasureTheory.Measure.dirac",
"MeasurableSpace",
"List",
"TProd.instMeasurableSpace",
"MeasureTheory.Measure.prod",
"PUnit",
"List.TProd",
"PUnit.unit",
"Prod",
"List.foldr",
"List.nil"
] | true |
Polynomial.Chebyshev.C_add_two | Mathlib.RingTheory.Polynomial.Chebyshev | [
"neg_add_rev",
"Int.instAddCommGroup",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"AddGroup.toSubtractionMonoid",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Mathlib.Tactic.RingNF.add_assoc_... | true |
Lean.Import._sizeOf_1 | Lean.Setup | [
"Lean.Import.rec",
"Lean.Import",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"SizeOf.sizeOf",
"Bool",
"instAddNat",
"Lean.Name",
"OfNat.ofNat",
"Bool._sizeOf_inst"
] | false |
CommGrpCat.id_apply | Mathlib.Algebra.Category.Grp.Basic | [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"CategoryTheory.ConcreteCategory.hom",
"CommGrpCat.instCategory",
"CategoryTheory.CategoryStruct.id",
"CommGrpCat.str",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"CommGrpCat.carrier",
"CommGrpCat.instC... | true |
HasProd.mul_isCompl | Mathlib.Topology.Algebra.InfiniteSum.Basic | [
"MulOne.toOne",
"Set.mulIndicator_self_mul_compl_apply",
"HMul.hMul",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Monoid.toMulOneClass",
"congrArg",
"Compl.compl",
"SummationFilter",
"Set.mulIndicator",
"hasProd_subtype_iff_mulIndicator",
"HasProd",
"Function.comp",
"Membership.mem",... | true |
Interval.«_aux_Mathlib_Order_Interval_Set_UnorderedInterval___macroRules_Interval_term[[_,_]]_1» | Mathlib.Order.Interval.Set.UnorderedInterval | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMonad"... | false |
MonomialOrder.degree_smul_of_mem_nonZeroDivisors | Mathlib.RingTheory.MvPolynomial.MonomialOrder | [
"Iff.mpr",
"Finsupp.instAddZeroClass",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"False",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"instHSMul",
"HMul.hMul",
"eq_false",
"MulZeroClass.toMul",
"mem_nonZeroDivisors_iff",
"congrArg",
"CommSemiring.toSemiring",
"instDis... | true |
RatFunc.laurent_laurent | Mathlib.FieldTheory.Laurent | [
"Eq.mpr",
"IsDomain",
"CommRing",
"instHDiv",
"Semiring.toModule",
"RatFunc.laurent_div",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"RatFunc.laurent",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"Polynomial.taylor",
"LinearMap.instFunLike",
"RatFunc.in... | true |
MeasurableEquiv.mulLeft.congr_simp | Mathlib.MeasureTheory.Group.LIntegral | [
"MeasurableEquiv.mulLeft",
"Monoid.toMulOneClass",
"Group",
"Eq.rec",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"MeasurableMul",
"Group.toDivInvMonoid",
"MeasurableSpace",
"MulOneClass.toMulOne",
"Eq.refl",
"MeasurableEquiv",
"Eq"
] | true |
Filter.lift_lift_same_le_lift | Mathlib.Order.Filter.Lift | [
"Filter.instMembership",
"Iff.mpr",
"le_rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Filter.lift_le",
"Filter.le_lift",
"LE.le",
"Filter.lift",
"Filter",
"Filter.instPartialOrder",
"Set"
] | true |
BooleanSubalgebra.copy | Mathlib.Order.BooleanSubalgebra | [
"Sublattice",
"BooleanAlgebra",
"BooleanSubalgebra",
"BooleanSubalgebra.copy._proof_3",
"BiheytingAlgebra.toCoheytingAlgebra",
"BooleanSubalgebra.mk",
"BooleanSubalgebra.copy._proof_1",
"BooleanSubalgebra.toSublattice",
"BooleanAlgebra.toBiheytingAlgebra",
"BooleanSubalgebra.copy._proof_2",
"Set... | true |
FirstOrder.Language.partialOrderTheory.eq_1 | Mathlib.ModelTheory.Order | [
"FirstOrder.Language.partialOrderTheory",
"FirstOrder.Language.preorderTheory",
"FirstOrder.Language.Theory",
"Insert.insert",
"FirstOrder.Language.Relations.antisymmetric",
"FirstOrder.Language.IsOrdered.leSymb",
"Set.instInsert",
"FirstOrder.Language.IsOrdered",
"Eq.refl",
"FirstOrder.Language",... | true |
_private.Mathlib.Order.Category.DistLat.0.DistLat.Hom.mk.inj | Mathlib.Order.Category.DistLat | [
"_private.Mathlib.Order.Category.DistLat.0.DistLat.Hom.mk",
"DistLat.str",
"_private.Mathlib.Order.Category.DistLat.0.DistLat.Hom.mk.noConfusion",
"DistribLattice.toLattice",
"LatticeHom",
"eq_of_heq",
"HEq",
"Eq",
"DistLat.Hom",
"DistLat.carrier",
"DistLat"
] | true |
CompactlySupportedContinuousMap.coeFnMonoidHom._proof_2 | Mathlib.Topology.ContinuousMap.CompactlySupported | [
"AddMonoid.toAddSemigroup",
"CompactlySupportedContinuousMap",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"TopologicalSpace",
"AddZero.toZero",
"instHAdd",
"AddSemigroup.toAdd",
"Pi.instAdd",
"CompactlySupportedContinuousMap.instFunLike",
"HAdd.hAdd",
"AddMonoid",
"AddZero.toAdd",... | false |
IsIntegralClosure.equiv.congr_simp | Mathlib.Topology.Algebra.Valued.WithVal | [
"IsIntegralClosure",
"CommRing",
"IsIntegralClosure.equiv",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra",
"Algebra.toSMul",
"CommRing.toCommSemiring",
"AlgEquiv",
"Eq.refl",
"Eq"
] | true |
Std.ExtDTreeMap.instDecidableMem | Std.Data.ExtDTreeMap.Basic | [
"Bool.decEq",
"Decidable",
"Membership.mem",
"Ordering",
"Std.TransCmp",
"Std.ExtDTreeMap.contains",
"Bool.true",
"Std.ExtDTreeMap",
"Std.ExtDTreeMap.instMembershipOfTransCmp"
] | true |
Std.DHashMap.Raw | Std.Data.DHashMap.RawDef | [
"Std.DHashMap.Raw.mk"
] | true |
Ideal.quotientEquiv._proof_6 | Mathlib.RingTheory.Ideal.Quotient.Operations | [
"RingHom.instRingHomClass",
"RingHom",
"RingHom.instFunLike",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Ring",
"RingHomClass"
] | false |
CategoryTheory.GlueData'.t''._proof_14 | Mathlib.CategoryTheory.GlueData | [
"CategoryTheory.GlueData'",
"CategoryTheory.GlueData'.U",
"CategoryTheory.GlueData'.J",
"eq_self",
"of_eq_true",
"Eq",
"CategoryTheory.Category"
] | false |
_private.Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne.0.NumberField.mixedEmbedding.fundamentalCone.expMap_smul._simp_1_1 | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.NormLeOne | [
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"mul_assoc",
"Eq.symm",
"Eq",
"instHMul"
] | false |
Std.ExtTreeMap.getKey!_minKey! | Std.Data.ExtTreeMap.Lemmas | [
"Std.ExtTreeMap.minKey!",
"Std.ExtTreeMap.mk",
"Ordering",
"mt",
"Ne",
"Std.ExtDTreeMap.instEmptyCollection",
"Std.TransCmp",
"Std.ExtTreeMap.getKey!",
"Std.ExtTreeMap",
"_private.Std.Data.ExtTreeMap.Lemmas.0.Std.ExtTreeMap.ext",
"Std.ExtTreeMap.inner",
"Std.ExtDTreeMap",
"Inhabited",
"Emp... | true |
MeasureTheory.quasiMeasurePreserving_sub_left | Mathlib.MeasureTheory.Group.Prod | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"NegZeroClass.toNeg",
"MeasureTheory.Measure",
"MeasureTheory.Measure.QuasiMeasurePreserving._auto_3",
"congrArg",
"AddMonoid.toAddZeroClass",
"sub_eq_add_neg",
"HSub.hSub",
"AddZeroClass.toAddZero",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"Mea... | true |
Std.DTreeMap.Internal.Impl.Const.isSome_apply_of_contains_filterMap! | Std.Data.DTreeMap.Internal.Lemmas | [
"Std.DTreeMap.Internal.Impl.filterMap_eq_filterMap!",
"Std.DTreeMap.Internal.Impl.contains_of_contains_filterMap",
"Ord",
"congrArg",
"Std.DTreeMap.Internal.Impl.getKey",
"Std.TransOrd",
"Eq.mp",
"Std.DTreeMap.Internal.Impl.WF",
"Std.DTreeMap.Internal.Impl.Const.get",
"Std.DTreeMap.Internal.Impl.W... | true |
ProbabilityTheory.measure_condCDF_univ | Mathlib.Probability.Kernel.Disintegration.CondCDF | [
"Eq.mpr",
"Real.partialOrder",
"ConditionallyCompleteLinearOrder.toCompactIccSpace",
"Real",
"ProbabilityTheory.tendsto_condCDF_atBot",
"MeasureTheory.Measure",
"MulZeroClass.toMul",
"ENNReal.ofReal",
"congrArg",
"sub_zero",
"StieltjesFunction.measure_univ",
"Set.univ",
"HSub.hSub",
"Pseud... | true |
_private.Mathlib.RingTheory.LocalRing.Module.0.IsLocalRing.map_tensorProduct_mk_eq_top._proof_1_4 | Mathlib.RingTheory.LocalRing.Module | [
"Submodule",
"MulOne.toOne",
"CommRing",
"instHSMul",
"Module.isTorsionBySet_quotient_ideal_smul",
"Semiring.toModule",
"Monoid.toMulOneClass",
"Submodule.Quotient.addCommGroup",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"IsLocalRing.maximalIdeal",
"Submodule.hasQuotient",
"... | false |
CategoryTheory.Limits.hasProducts_opposite | Mathlib.CategoryTheory.Limits.Shapes.Opposites.Products | [
"Opposite",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.Limits.HasProducts",
"inferInstance",
"CategoryTheory.Limits.HasCoproducts",
"CategoryTheory.Limits.hasProductsOfShape_opposite",
"CategoryTheory.discreteCategory",
"CategoryTheory.Category.opposite",
"CategoryTheory.Category",
... | true |
Module.Flat.instPreservesFiniteLimitsModuleCatTensorRightOfCarrier | Mathlib.RingTheory.Flat.CategoryTheory | [
"CommRing",
"CategoryTheory.Limits.PreservesFiniteLimits",
"ModuleCat",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.BraidedCategory.tensorLeftIsoTensorRight",
"Module.Flat",
"CategoryTheory.MonoidalCategory.tensorLeft",
"ModuleCat.monoidalCategory",
"ModuleCat.MonoidalCategory.instBraidedCategor... | true |
ProbabilityTheory.covarianceBilin_real | Mathlib.Probability.Moments.CovarianceBilin | [
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Function.id_def",
"False",
"instTrivialStarReal",
"Semigroup.toMul",
"Real",
"Algebra.to_smulCommClass",
"MeasureTheory.Measure",
"ProbabilityTheory... | true |
Std.Http.CustomStatus.casesOn | Std.Internal.Http.Data.Status | [
"Std.Http.CustomStatus.mk",
"String",
"Std.Http.CustomStatus.rec",
"instLEUInt16",
"LE.le",
"Bool.true",
"And",
"UInt16",
"Std.Http.CustomStatus",
"Bool",
"Std.Http.isKnownStatusCode",
"OfNat.ofNat",
"Eq",
"Not",
"UInt16.instOfNat",
"Std.Http.IsValidReasonPhrase"
] | false |
Std.Roi.eq_succMany?_of_toList_eq_append_cons | Init.Data.Range.Polymorphic.Lemmas | [
"Std.Roi.eq_succMany?_of_toList_eq_append_cons._proof_2",
"Std.Roi.toList",
"Nat.zero_lt_succ._simp_1",
"Std.PRange.UpwardEnumerable",
"Std.Roi.getElem_toList_eq",
"congrArg",
"Std.IsLinearPreorder.toIsPreorder",
"Std.PRange.LawfulUpwardEnumerableLT",
"Nat.lt_add_right_iff_pos._simp_1",
"Std.Roi.l... | true |
Mathlib.TacticAnalysis.ComplexConfig.test | Mathlib.Tactic.TacticAnalysis | [
"Mathlib.TacticAnalysis.ComplexConfig",
"Lean.MVarId",
"Lean.Elab.ContextInfo",
"Mathlib.TacticAnalysis.ComplexConfig.out",
"Mathlib.TacticAnalysis.ComplexConfig.ctx",
"Lean.Elab.Command.CommandElabM",
"Lean.Elab.TacticInfo"
] | true |
Metric.Snowflaking.preimage_toSnowflaking_eball | Mathlib.Topology.MetricSpace.Snowflaking | [
"Eq.mpr",
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Real.instLE",
"Real",
"Equiv.instEquivLike",
"ENNReal.rpow_inv_rpow",
"Metric.Snowflaking.toSnowflaking",
"Real.instZero",
"congrArg",
"Real.instInv",
"ENNReal.instPowReal",
"Metric.Snowflaking.image_toSnowflaking_eball",
"Real.instLT... | true |
List.Shortlex.cons | Mathlib.Data.List.Shortlex | [
"Std.Irrefl",
"Iff.mpr",
"List.cons",
"List.shortlex_cons_iff",
"List",
"List.Shortlex"
] | true |
Min.casesOn | Init.Prelude | [
"Min.mk",
"Min",
"Min.rec"
] | false |
CFC.neg_negPart_le | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.PosPart.Basic | [
"NegZeroClass.toNeg",
"IsSelfAdjoint",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"instSMulOfMul",
"IsTopologicalRing.toIsTopologicalSemiring",
"CFC.neg_negPart_le._auto_1",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScala... | true |
CategoryTheory.Equivalence.mapCommMon_inverse | Mathlib.CategoryTheory.Monoidal.CommMon_ | [
"CategoryTheory.CommMon.instCategory",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Equivalence",
"CategoryTheory.Equivalence.IsMonoidal",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.Equivalence.mapCommMon",
"CategoryTheory.BraidedCategory",
"CategoryTheory.... | true |
Homeomorph.comp_isOpenMap_iff._simp_1 | Mathlib.Topology.Homeomorph.Defs | [
"Function.comp",
"Homeomorph.comp_isOpenMap_iff",
"IsOpenMap",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"propext",
"Homeomorph",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | false |
CategoryTheory.Limits.walkingCospanOpEquiv_inverse_obj | Mathlib.CategoryTheory.Limits.Shapes.Pullback.HasPullback | [
"CategoryTheory.Limits.WalkingSpan",
"Opposite",
"CategoryTheory.Limits.WidePullbackShape",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limits.WalkingPair",
"CategoryTheory.Limits.walkingCospanOpEquiv",
"CategoryTheory.Limits.WidePushoutShape.category",
"Opposite.op",
"Catego... | true |
CategoryTheory.IsSplitMono.casesOn | Mathlib.CategoryTheory.EpiMono | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsSplitMono.rec",
"CategoryTheory.IsSplitMono",
"Nonempty",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.SplitMono",
"CategoryTheory.IsSplitMono.mk",
"CategoryTheory.Category"
] | false |
MultilinearMap.domDomCongr_eq_iff._simp_1 | Mathlib.LinearAlgebra.Multilinear.Basic | [
"Equiv",
"MultilinearMap",
"AddCommMonoid",
"MultilinearMap.domDomCongr_eq_iff",
"propext",
"MultilinearMap.domDomCongr",
"Semiring",
"Module",
"Eq"
] | false |
MeasureTheory.Measure.toOuterMeasure_top | Mathlib.MeasureTheory.Measure.MeasureSpace | [
"MeasureTheory.Measure",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"MeasureTheory.OuterMeasure",
"MeasurableSpace",
"MeasureTheory.Measure.toOuterMeasure",
"OrderTop.toTop",
"BoundedOrder.toOrderTop",
... | true |
_private.Mathlib.Analysis.ConstantSpeed.0.unique_unit_speed_on_Icc_zero._simp_1_1 | Mathlib.Analysis.ConstantSpeed | [
"Preorder.toLE",
"Membership.mem",
"LE.le",
"And",
"Set.Icc",
"propext",
"Set.mem_Icc",
"Eq",
"Set.instMembership",
"Preorder",
"Set"
] | false |
instIsLocalizationAlgebraMapSubmonoidPrimeComplLocalization | Mathlib.RingTheory.DedekindDomain.Instances | [
"Algebra.algebraMapSubmonoid_map_map",
"Eq.mpr",
"CommRing",
"IsLocalization",
"OreLocalization.instAlgebra",
"congrArg",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra",
"Algebra.toSMul",
"Algebra.id",
"id",
"Localization",
"Ideal",
"MulZeroOneClass.toMulOneClass",
"instMulZeroO... | true |
List.zipWithM'._sunfold | Init.Data.List.Monadic | [
"Pure.pure",
"Monad.toApplicative",
"Applicative.toPure",
"List.cons",
"List",
"List.zipWithM'",
"List.zipWithM'.match_1",
"Monad.toBind",
"Bind.bind",
"Monad",
"List.nil"
] | false |
_private.Lean.Meta.Eqns.0.Lean.Meta.mkSimpleEqThm.match_1 | Lean.Meta.Eqns | [
"Lean.ConstantInfo.defnInfo",
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Lean.ConstantInfo.ctorIdx",
"_private.Lean.Meta.Eqns.0.Lean.Meta.initFn._sparseCasesOn_1._@.Lean.Meta.Eqns.758090479._hygCtx._hyg.2",
"Lean.ConstantInfo",
"_private.Lean.Meta.Eqns.0.Lean.Meta.mkSimpleEqThm._sparseCasesOn_... | false |
Function.smulCommClass | Mathlib.Algebra.Group.Action.Pi | [
"SMul",
"Function.hasSMul",
"Pi.smulCommClass",
"SMulCommClass"
] | true |
CategoryTheory.LiftableCone.validLift | Mathlib.CategoryTheory.Limits.Creates | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.LiftableCone",
"CategoryTheory.Functor.comp",
"CategoryTheory.Iso",
"CategoryTheory.Functor.mapCone",
"CategoryTheory.Limits.Cone.category",
"CategoryTheory.LiftableCone.liftedCone",
"CategoryTheory.Category"
] | true |
FiniteGaloisIntermediateField.finGaloisGroup._proof_2 | Mathlib.FieldTheory.Galois.Profinite | [
"FiniteGaloisIntermediateField.finGaloisGroup._proof_1",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"Finite.algHom",
"IntermediateField",
"Finite",
"IntermediateField.toField",
"Algebra",
"Membership.mem",
"Field.toDivisionRing",
"Algebra.... | false |
Mathlib.Tactic.LibrarySearch.observe | Mathlib.Tactic.Observe | [
"Lean.ParserDescr.nonReservedSymbol",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.sepBy1",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.const",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Bool.false",
... | true |
List.flatten._sunfold | Init.Prelude | [
"List.append",
"List",
"Unit",
"List.flatten",
"List.flatten.match_1",
"List.nil"
] | false |
CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₃.congr_simp | Mathlib.CategoryTheory.Presentable.Directed | [
"CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram",
"Cardinal.IsRegular",
"Cardinal",
"Fact",
"Eq.rec",
"CategoryTheory.SmallCategory",
"CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.DiagramWithUniqueTerminal",
"Eq.refl",
"CategoryTheory.IsCardinalFiltered.exists_cardi... | true |
continuousAt_codRestrict_iff | Mathlib.Topology.Constructions | [
"Topology.IsInducing.continuousAt_iff",
"ContinuousAt",
"Membership.mem",
"Set.Elem",
"Subtype",
"TopologicalSpace",
"Iff",
"Set.codRestrict",
"instTopologicalSpaceSubtype",
"Subtype.val",
"Set.instMembership",
"Topology.IsInducing.subtypeVal",
"Set"
] | true |
_private.Mathlib.Data.Set.Insert.0.HasSubset.Subset.ssubset_of_mem_notMem._proof_1_1 | Mathlib.Data.Set.Insert | [
"False",
"eq_false",
"Set.ssubset_def",
"Set.subset_def",
"Classical.byContradiction",
"Lean.Grind.eq_false_of_imp_eq_true",
"HasSSubset.SSubset",
"Lean.Grind.and_eq_of_eq_true_left",
"Set.instHasSSubset",
"Membership.mem",
"Eq.mp",
"id",
"HasSubset.Subset",
"And",
"True",
"Lean.Grind.... | false |
SetRel.IsSeparated.empty | Mathlib.Data.Rel.Separated | [
"SetRel",
"Set.pairwise_empty",
"Membership.mem",
"Prod.mk",
"SetRel.IsSeparated",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Prod",
"Set.instMembership",
"Not",
"Set"
] | true |
Matrix.isRepresentation.toEnd._proof_8 | Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap | [
"Subalgebra.instSetLike",
"CommRing",
"CommSemiring.toSemiring",
"Matrix",
"SubsemiringClass.toAddSubmonoidClass",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"AddZeroClass.toAddZero",
"Matrix.instAlgebra",
"Algebra.id",
"ZeroMemClass",
"Matrix.nonAssocSemiring",
"AddZe... | false |
Finset.Ioc_subset_Ioc_left | Mathlib.Order.Interval.Finset.Basic | [
"le_rfl",
"Finset",
"Preorder.toLE",
"HasSubset.Subset",
"LE.le",
"Finset.instHasSubset",
"Finset.Ioc_subset_Ioc",
"LocallyFiniteOrder",
"Preorder",
"Finset.Ioc"
] | true |
CategoryTheory.CoreSmallCategoryOfSet.homEquiv | Mathlib.CategoryTheory.SmallRepresentatives | [
"CategoryTheory.CoreSmallCategoryOfSet.objEquiv",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Set.Elem",
"Equiv",
"CategoryTheory.CoreSmallCategoryOfSet.obj",
"CategoryTheory.CoreSmallCategoryOfSet",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Co... | true |
_private.Lean.Meta.Tactic.Subst.0.Lean.Meta.substVar.match_4 | Lean.Meta.Tactic.Subst | [
"Option.ctorIdx",
"Option.some",
"Lean.FVarId",
"Nat.hasNotBit",
"Prod.mk",
"_private.Lean.Meta.Tactic.Subst.0.Lean.Meta.substVar._sparseCasesOn_1",
"Bool",
"Prod",
"Prod.casesOn",
"Option"
] | false |
DistribMulActionHom.mk.congr_simp | Mathlib.Algebra.Algebra.Unitization | [
"Monoid",
"DistribMulActionHom.mk",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"DistribMulActionHom",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Eq.rec",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"MulActionHom.toFun",
"AddZero.toZero",
... | true |
SubAddAction.closure | Mathlib.GroupTheory.GroupAction.SubMulAction.Closure | [
"setOf",
"VAdd",
"HasSubset.Subset",
"SubAddAction.instInfSet",
"SubAddAction",
"SetLike.coe",
"InfSet.sInf",
"Set.instHasSubset",
"SubAddAction.instSetLike",
"Set"
] | true |
CategoryTheory.Functor.IsStronglyCartesian.domainIsoOfBaseIso._proof_5 | Mathlib.CategoryTheory.FiberedCategory.Cartesian | [
"CategoryTheory.Functor",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.IsStronglyCartesian.map_self",
"CategoryTheory.Functor.IsHomLift",
"CategoryTheory.CategoryStruct.id",
"Eq.rec",
"CategoryTheory.Functor.IsStrongly... | false |
_private.Init.Data.String.Decode.0.Char.toNat_le | Init.Data.String.Decode | [
"Char.toNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Char.valid",
"_private.Init.Data.String.Decode.0.Char.toNat_le._proof_1_1",
"Char.val",
"Nat",
"Decidable.byContradiction",
"Char",
"OfNat.ofNat",
"Not",
"Nat.decLe",
"UInt32.isValidChar"
] | true |
CategoryTheory.MorphismProperty.DescendsAlong.recOn | Mathlib.CategoryTheory.MorphismProperty.Descent | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsPullback",
"CategoryTheory.MorphismProperty.DescendsAlong",
"CategoryTheory.MorphismProperty.DescendsAlong.mk",
"CategoryTheory.MorphismProperty.DescendsAlong.rec",
"CategoryTheory.Category.toC... | false |
CategoryTheory.Functor.whiskerRight_comp | Mathlib.CategoryTheory.Whiskering | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.whiskeringRight",
"CategoryTheory.Functor.whiskerRight",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Functor.map_comp"... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.