name string | module string | deps list |
|---|---|---|
CategoryTheory.MonoidalCategory.DayConvolution.unit_naturality | Mathlib.CategoryTheory.Monoidal.DayConvolution | [
"CategoryTheory.MonoidalCategory.DayConvolution.convolution",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategory.DayConvolution",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg"... |
CategoryTheory.BasedFunctor.mk | Mathlib.CategoryTheory.FiberedCategory.BasedCategory | [
"CategoryTheory.Functor",
"CategoryTheory.BasedFunctor",
"CategoryTheory.BasedCategory.p",
"CategoryTheory.Functor.comp",
"CategoryTheory.instCategoryObj",
"CategoryTheory.BasedCategory.obj",
"autoParam",
"CategoryTheory.BasedFunctor.w._autoParam",
"CategoryTheory.BasedFunctor.mk",
"CategoryTheory... |
ExpChar.congr | Mathlib.Algebra.CharP.Defs | [
"ExpChar",
"Eq.rec",
"Nat",
"Eq",
"AddMonoidWithOne"
] |
Std.HashMap.getElem_filterMap'._proof_1 | Std.Data.HashMap.Lemmas | [
"Std.HashMap.getKey",
"GetElem?.toGetElem",
"instLawfulHashableOfLawfulBEq",
"congrArg",
"LawfulBEq",
"Membership.mem",
"Eq.mp",
"Std.HashMap",
"GetElem.getElem",
"Bool.true",
"Std.HashMap.getKey_eq",
"Std.HashMap.filterMap",
"Std.HashMap.mem_of_mem_filterMap",
"Bool",
"congrFun'",
"Ha... |
CategoryTheory.Enriched.Functor.functorHom_whiskerLeft_natTransEquiv_symm_app | Mathlib.CategoryTheory.Functor.FunctorHom | [
"CategoryTheory.Functor.HomObj.ofNatTrans",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.coyoneda",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"Quiver.Hom",
"Categor... |
String.utf8Len_le_of_infix | Batteries.Data.String.Lemmas | [
"String.utf8Len_le_of_sublist",
"String.utf8Len",
"LE.le",
"instLENat",
"List.IsInfix",
"List",
"Nat",
"Char",
"List.IsInfix.sublist"
] |
FiniteAddGrp.of.eq_1 | Mathlib.Algebra.Category.Grp.FiniteGrp | [
"Finite",
"FiniteAddGrp.mk",
"FiniteAddGrp",
"AddGroup",
"FiniteAddGrp.of",
"AddGrpCat.of",
"Eq.refl",
"Eq"
] |
_private.Mathlib.Order.Partition.Finpartition.0.Finpartition.mem_part_ofSetSetoid_iff_rel._simp_1_1 | Mathlib.Order.Partition.Finpartition | [
"Finset",
"Finpartition.part",
"Membership.mem",
"Exists",
"Finpartition.mem_part_iff_exists",
"Finpartition.parts",
"And",
"Finset.instSetLike",
"Finset.instLattice",
"propext",
"Finset.instOrderBot",
"Eq",
"Finpartition",
"SetLike.instMembership",
"DecidableEq"
] |
Lean.Meta.Grind.Arith.Cutsat.ToIntInfo.negThm?._default | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToIntInfo | [
"Lean.Expr",
"id",
"Option.none",
"Option"
] |
MonoidHom.inr_apply | Mathlib.Algebra.Group.Prod | [
"MulOne.toOne",
"MonoidHom.instFunLike",
"MonoidHom.inr",
"MonoidHom",
"Prod.instMulOneClass",
"Prod.mk",
"MulOneClass.toMulOne",
"One.toOfNat1",
"MulOneClass",
"Prod",
"OfNat.ofNat",
"Eq",
"DFunLike.coe",
"rfl"
] |
Lean.Meta.Grind.Arith.Linear.IneqCnstrProof.ringEq.inj | Lean.Meta.Tactic.Grind.Arith.Linear.Types | [
"Lean.Meta.Grind.Arith.Linear.LinExpr",
"Lean.Meta.Grind.Arith.Linear.IneqCnstrProof.ringEq",
"Lean.Meta.Grind.Arith.Linear.IneqCnstrProof",
"Lean.Meta.Grind.Arith.Linear.RingEqCnstr",
"And",
"And.intro",
"Lean.Meta.Grind.Arith.Linear.IneqCnstrProof.ringEq.noConfusion",
"Eq"
] |
Std.DTreeMap.Internal.Impl.Equiv.minEntry_eq | Std.Data.DTreeMap.Internal.Lemmas | [
"Std.DTreeMap.Internal.Impl.Equiv.minEntry?_eq",
"Ord",
"congrArg",
"Std.TransOrd",
"Option.get.congr_simp",
"Std.DTreeMap.Internal.Impl.WF",
"Bool.true",
"Std.DTreeMap.Internal.Impl.minEntry?",
"Std.DTreeMap.Internal.Impl.Equiv",
"Option.get",
"Std.DTreeMap.Internal.Impl.isEmpty",
"congr",
... |
constFormalMultilinearSeries.match_1 | Mathlib.Analysis.Calculus.FormalMultilinearSeries | [
"Unit.unit",
"instOfNatNat",
"dite",
"Unit",
"Nat",
"Eq.ndrec_symm",
"instDecidableEqNat",
"OfNat.ofNat",
"Eq",
"Not"
] |
Lean.Doc.Block.rec_5 | Lean.DocString.Types | [
"Lean.Doc.Block.blockquote",
"String",
"Lean.Doc.Block",
"Lean.Doc.Block.concat",
"Lean.Doc.DescItem",
"Int",
"Lean.Doc.Block.dl",
"Lean.Doc.Block.ul",
"List.cons",
"Array",
"List",
"Lean.Doc.Block.ol",
"Lean.Doc.DescItem.mk",
"Lean.Doc.Block.code",
"Lean.Doc.Block.para",
"Lean.Doc.Lis... |
_private.Lean.Server.InfoUtils.0.Lean.Elab.Info.type?._sparseCasesOn_1 | Lean.Server.InfoUtils | [
"Lean.Elab.PartialTermInfo",
"Lean.Elab.Info.ofOptionInfo",
"Nat.ne_of_beq_eq_false",
"Lean.Elab.Info.ofTacticInfo",
"Lean.Elab.FieldRedeclInfo",
"Lean.Elab.CompletionInfo",
"Lean.Elab.OptionInfo",
"Nat.shiftRight",
"Lean.Elab.Info.rec",
"Lean.Elab.MacroExpansionInfo",
"Nat.hasNotBit",
"instOf... |
Std.DTreeMap.getKey!_eq_get!_getKey? | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap.Internal.Impl.getKey!_eq_get!_getKey?",
"Std.DTreeMap",
"Std.DTreeMap.getKey!",
"Ord.mk",
"Ordering",
"Option.get!",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Std.DTreeMap.getKey?",
"Std.DTreeMap.wf",
"Inhabited",
"Eq"
] |
NormedGroup.toENormedMonoid._proof_4 | Mathlib.Analysis.Normed.Group.Continuity | [
"Semigroup.toMul",
"ENNReal.ofNNReal",
"HMul.hMul",
"CommSemiring.toSemiring",
"NormedGroup",
"NNNorm.nnnorm",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"SeminormedGroup.toPseudoMetricSpace",
"Preorder.toLE",
"Distrib.toAdd",
"DivInvMonoid.toMonoid",
"NNReal",
"ENNReal... |
IsLocalization.IsInteger.eq_1 | Mathlib.RingTheory.Localization.Rat | [
"IsLocalization.IsInteger",
"Subsemiring.instSetLike",
"CommSemiring.toSemiring",
"Algebra",
"Membership.mem",
"algebraMap",
"Subsemiring",
"CommSemiring",
"Eq.refl",
"Semiring.toNonAssocSemiring",
"Eq",
"SetLike.instMembership",
"RingHom.rangeS"
] |
CategoryTheory.Limits.equalizerSubobject_arrow | Mathlib.CategoryTheory.Subobject.Limits | [
"CategoryTheory.Subobject.arrow",
"CategoryTheory.Subobject.underlying",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.equalizer",
"PartialOrder.toPreorder",
"CategoryTheory.Limits.equalizerSubobject",
"CategoryTheory.Limits.HasEqualizer",
"Preorder.sma... |
MeasureTheory.AECover.integral_tendsto_of_countably_generated | Mathlib.MeasureTheory.Integral.IntegralEqImproper | [
"MeasureTheory.ae",
"MeasureTheory.Integrable.aestronglyMeasurable",
"Norm.norm",
"Eq.mpr",
"MeasureTheory.integral_indicator",
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"congrArg",
"Set.indicator",
"HEq.refl",
"Filter.Eventually",
"MeasureTheory.tendsto_integral_filte... |
ScottContinuous.comp | Mathlib.Order.ScottContinuity | [
"Eq.mpr",
"ScottContinuousOn.comp",
"congrArg",
"scottContinuousOn_univ",
"Set.mem_univ._simp_1",
"Set.univ",
"ScottContinuous",
"Preorder.toLE",
"Function.comp",
"Membership.mem",
"Eq.mp",
"Set.instSingletonSet",
"id",
"Insert.insert",
"LE.le",
"imp_self._simp_1",
"Set.instInsert",
... |
FiniteField.exists_nonsquare | Mathlib.FieldTheory.Finite.Basic | [
"Eq.mpr",
"not_exists._simp_1",
"NegZeroClass.toNeg",
"Ring.neg_one_ne_one_of_char_ne_two",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"congrArg",
"Finite",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddGroupWithOne.toAddMonoidWithOne",
"Functio... |
_private.Batteries.Data.String.Lemmas.0.Substring.Raw.ValidFor.toString.match_1_1 | Batteries.Data.String.Lemmas | [
"Unit.unit",
"Substring.Raw.mk",
"HEq.refl",
"String.utf8Len",
"Substring.Raw.ValidFor",
"Substring.Raw",
"Substring.Raw.ValidFor.mk",
"instHAppendOfAppend",
"List",
"instHAdd",
"Unit",
"String.Pos.Raw.mk",
"HAdd.hAdd",
"Nat",
"eq_of_heq",
"Eq.ndrec",
"instAddNat",
"Eq.refl",
"HE... |
Lean.Meta.ArgsPacker.noConfusionType | Lean.Meta.ArgsPacker.Basic | [
"Lean.Meta.ArgsPacker",
"Array",
"Lean.Name",
"Lean.Meta.ArgsPacker.casesOn",
"Eq"
] |
Interval.recBotCoe | Mathlib.Order.Interval.Basic | [
"WithBot.some",
"WithBot",
"Bot.bot",
"Interval",
"LE",
"WithBot.recBotCoe",
"WithBot.bot",
"NonemptyInterval"
] |
Fin.univ_def | Mathlib.Data.Fintype.Basic | [
"Finset.univ",
"Finset",
"Fin.fintype",
"Multiset.ofList",
"Nat",
"List.nodup_finRange",
"Finset.mk",
"Fin",
"List.finRange",
"Eq",
"rfl"
] |
EuclideanGeometry.Sphere.isIntTangent_self_iff | Mathlib.Geometry.Euclidean.Sphere.Tangent | [
"Nontrivial",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real.instLE",
"Real",
"EuclideanGeometry.Sphere.isIntTangentAt_self_iff_mem._simp_1",
"Real.instZero",
"Real.instRCLike",
"congrArg",
"EuclideanGeometry.Sphere.nonempty_iff",
"EuclideanGeometry.Sphere",
"EuclideanGeometry.Sphere.IsInt... |
Lean.Meta.reduceBoolNativeUnsafe | Lean.Meta.WHNF | [
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.Core.instMonadOptionsCoreM",
"Lean.MonadQuotation.toMonadRef",
"Lean.instMonadOptionsOfMonadLift",
"Lean.Meta.MetaM",
"IO.RealWorld",
"StateRefT'.inst... |
Lean.Elab.Command.Scope.levelNames._default | Lean.Elab.Command.Scope | [
"id",
"List",
"Lean.Name",
"List.nil"
] |
Polynomial.div_tendsto_atBot_zero_iff_degree_lt | Mathlib.Analysis.Polynomial.Basic | [
"NormedCommRing.toNormedRing",
"WithBot.instPreorder",
"Eq.mpr",
"Polynomial.C",
"Polynomial.eval",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"RingHom.instRingHomClass",
"False",
"OrderTopology",
"WithBot",
"Preorder.toLT",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAs... |
CategoryTheory.Deterministic | Mathlib.CategoryTheory.CopyDiscardCategory.Deterministic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsComonHom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.CopyDiscardCategory.comonObj",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.CopyDiscardCategory",
"CategoryTheory.Category"
] |
_private.Batteries.Data.RBMap.Depth.0.Batteries.RBNode.Balanced.le_size.match_1_7 | Batteries.Data.RBMap.Depth | [
"instPowNat",
"Batteries.RBNode",
"Unit.unit",
"HEq.refl",
"Batteries.RBNode.Balanced.below.nil",
"Batteries.RBNode.nil",
"instOfNatNat",
"LE.le",
"instLENat",
"Batteries.RBNode.size",
"Batteries.RBNode.Balanced.nil",
"instNatPowNat",
"Batteries.RBNode.Balanced.black",
"instHAdd",
"Batte... |
OrderIso.map_ciSup_set_of_directedOn | Mathlib.Order.ConditionallyCompletePartialOrder.Indexed | [
"iSup",
"PartialOrder.toPreorder",
"GaloisConnection.l_ciSup_set_of_directedOn",
"OrderIso.to_galoisConnection",
"Preorder.toLE",
"DirectedOn",
"Membership.mem",
"Set.Elem",
"OrderIso",
"LE.le",
"OrderIso.symm",
"BddAbove",
"Set.Nonempty",
"instFunLikeOrderIso",
"Set.image",
"Condition... |
Subgroup.exists_pow_mem_of_index_ne_zero | Mathlib.GroupTheory.Index | [
"zpow_natCast",
"Eq.mpr",
"Fintype.card_ofFinset",
"Nat.card_le_card_of_injective",
"Nat.instCanonicallyOrderedAdd",
"False",
"Nat.instOrderedSub",
"Preorder.toLT",
"zpow_add",
"Nat.instIsOrderedAddMonoid",
"HMul.hMul",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"DivInvOneMonoid.toInvOneCla... |
CategoryTheory.ShortComplex.SnakeInput.mono_v₀₁_τ₂ | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.Mono",
"CategoryTheory.ShortComplex.SnakeInput.L₂",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.SnakeInput.L₀",
"CategoryTheory.ShortComplex.SnakeInput",
"Category... |
Nat.fact_prime_two | Mathlib.Data.Nat.Prime.Defs | [
"Nat.Prime",
"Fact",
"instOfNatNat",
"Nat.prime_two",
"Fact.mk",
"Nat",
"OfNat.ofNat"
] |
DirichletCharacter.isPrimitive_one_level_one | Mathlib.NumberTheory.DirichletCharacter.Basic | [
"DirichletCharacter.conductor",
"Dvd.dvd",
"ZMod.commRing",
"MulChar.hasOne",
"DirichletCharacter.conductor_dvd_level",
"Nat.dvd_one",
"instOfNatNat",
"ZMod",
"Nat.instDvd",
"CommMonoidWithZero",
"Nat",
"DirichletCharacter",
"Iff.mp",
"DirichletCharacter.IsPrimitive",
"One.toOfNat1",
"... |
Std.ExtDTreeMap.le_minKey? | Std.Data.ExtDTreeMap.Lemmas | [
"Std.DTreeMap",
"Option.some",
"Membership.mem",
"Ordering",
"Std.ExtDTreeMap.minKey?",
"Std.TransCmp",
"Bool.true",
"Iff",
"Std.ExtDTreeMap.inductionOn",
"Std.ExtDTreeMap",
"Bool",
"Ordering.isLE",
"Eq",
"Std.ExtDTreeMap.instMembershipOfTransCmp",
"Std.DTreeMap.le_minKey?",
"Option"
] |
lp.singleAddMonoidHom | Mathlib.Analysis.Normed.Lp.lpSpace | [
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"instAddCommGroupPreLp",
"AddCommGroup.toAddGroup",
"lp.single",
"AddSubgroup.toAddGroup",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddMonoidHom.mk",
"lp.single_zero",
"Subtype",
"ESeminormedAddMonoid.toAddMonoid",
"ZeroHom.... |
UpperSet.coe_zero | Mathlib.Algebra.Order.UpperLower | [
"Set.Ici",
"UpperSet",
"UpperSet.instSetLike",
"Preorder.toLE",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"SetLike.coe",
"UpperSet.instZero",
"Zero.toOfNat0",
"AddCommGroup.toDivisionAddCommMonoid",
... |
isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Instances | [
"cfcₙ",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"IsSelfAdjoint",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"RCLike.toNormedAlgebra",
"Complex.instNormedAddCommGroup",
"IsStarNormal",
"IsTopologicalRing.toIsTopologicalSemiring",
"Real.instRCLike",
"congrArg",
"CommSemi... |
ProbabilityTheory.lintegral_condCDF | Mathlib.Probability.Kernel.Disintegration.CondCDF | [
"Set.instSProd",
"Unit.unit",
"Real",
"MeasureTheory.Measure",
"ProbabilityTheory.Kernel.const.instIsFiniteKernel",
"ENNReal.ofReal",
"SProd.sprod",
"Set.univ",
"PseudoMetricSpace.toUniformSpace",
"StieltjesFunction.toFun",
"MeasurableSpace",
"Unit",
"Real.measurableSpace",
"MeasureTheory.... |
Filter.boundedFilterSubalgebra._proof_2 | Mathlib.Order.Filter.ZeroAndBoundedAtFilter | [
"Filter.boundedFilterSubmodule",
"Submodule",
"Filter.BoundedAtFilter.mul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"SeminormedCommRing",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"SeminormedCommRing.toCommRing",
"Algebra",
"NonUnitalNonAssocSemiring.toMulZeroClass"... |
_private.Init.Data.SInt.Lemmas.0.ISize.ofNat_mul._simp_1_1 | Init.Data.SInt.Lemmas | [
"ISize.ofInt",
"ISize.ofNat",
"Int",
"Nat.cast",
"ISize.ofInt_eq_ofNat",
"Nat",
"instNatCastInt",
"Eq.symm",
"ISize",
"Eq"
] |
TrivSqZeroExt.snd_mul | Mathlib.Algebra.TrivSqZeroExt.Basic | [
"TrivSqZeroExt.mul",
"TrivSqZeroExt.snd",
"instHSMul",
"TrivSqZeroExt",
"HMul.hMul",
"SMul",
"MulOpposite",
"Mul",
"TrivSqZeroExt.fst",
"instHAdd",
"HAdd.hAdd",
"HSMul.hSMul",
"Eq",
"Add",
"rfl",
"MulOpposite.op",
"instHMul"
] |
AddSubgroup.nontrivial_iff_exists_ne_zero | Mathlib.Algebra.Group.Subgroup.Lattice | [
"Nontrivial",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Subtype.nontrivial_iff_exists_ne",
"Iff.of_eq",
"congrArg",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"id",
"Subtype",
"Ne",
"SubtractionMonoid.toSubNegZeroMonoid",
"exists_prop",
"SubNegZe... |
ByteArray.Iterator.casesOn | Init.Data.ByteArray.Basic | [
"ByteArray.Iterator.rec",
"ByteArray.Iterator",
"Nat",
"ByteArray.Iterator.mk",
"ByteArray"
] |
BitVec.hash._unary.eq_def | Init.Data.BitVec.Basic | [
"instPowNat",
"Eq.mpr",
"BitVec.setWidth",
"BitVec.instHShiftRightNat",
"mixHash",
"congrArg",
"UInt64",
"InvImage",
"HSub.hSub",
"WellFounded.Nat.fix",
"WellFounded.Nat.fix_eq",
"BitVec",
"BitVec.toFin",
"PSigma.casesOn",
"id",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",... |
Std.DTreeMap.Internal.Unit.RoiSliceData.mk | Std.Data.DTreeMap.Internal.Zipper | [
"Std.DTreeMap.Internal.Unit.RoiSliceData",
"Ord",
"Std.DTreeMap.Internal.Unit.RoiSliceData.mk",
"Unit",
"Std.Roi",
"Std.DTreeMap.Internal.Impl"
] |
Complex.norm_ofNat | Mathlib.Analysis.Complex.Norm | [
"Norm.norm",
"Real",
"Complex.norm_natCast",
"Complex.instNorm",
"Complex.instNatCast",
"Nat",
"Complex",
"OfNat.ofNat",
"Eq",
"instOfNatAtLeastTwo",
"Nat.AtLeastTwo",
"Real.instNatCast"
] |
_private.Mathlib.Tactic.Ring.Common.0.Mathlib.Tactic.Ring.ExProd.evalInv.match_13 | Mathlib.Tactic.Ring.Common | [
"Mathlib.Tactic.Ring.Result",
"Mathlib.Tactic.Ring.Result.mk",
"Lean.Expr.const",
"Mathlib.Tactic.Ring.ExProd",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Lean.Literal.natVal",
"Qq.Quoted",
"Lean.Level.zero",
"Qq.Quoted.unsafeMk",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean.Level.succ",
... |
CategoryTheory.Mon_Class.one_eq_one | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon_ | [
"MulOne.toOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Monoid.toMulOneClass",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.MonObj.one",
"MulOneClass.toMulOne",
"CategoryTheory.Hom.monoid",
"Category... |
Lean.Lsp.instFromJsonSignatureHelpTriggerKind | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Json",
"Except.ok",
"String",
"Lean.Lsp.instFromJsonSignatureHelpTriggerKind.match_1",
"Lean.Lsp.SignatureHelpTriggerKind.triggerCharacter",
"Except.error",
"Lean.Lsp.SignatureHelpTriggerKind",
"Lean.Lsp.SignatureHelpTriggerKind.contentChange",
"Lean.Lsp.SignatureHelpTriggerKind.invoked",
"U... |
iterate_map_sub | Mathlib.Algebra.Group.Hom.Defs | [
"AddGroup.toSubtractionMonoid",
"map_sub",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"Nat.iterate",
"SubNegMonoid.toSub",
"Function.Semiconj₂.iterate",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"Nat",
"SubNegMonoid.toAddMonoid",
"Eq"... |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_495 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Equiv.instEquivLike",
"Finset",
"Lean.Grind.Nat.lt_eq",
"Equiv",
"Insert.insert",
"instOfNatNat",
"LE.le",
"instLENat",
"instBEqOfDecidableEq",
"Finset.instInsert",
"List.cons",
"List.idxOfNth",
"instHAdd",
"HAdd.hAdd",
"Equiv.Perm",
"Nat",
"List.filter",
"LT.lt",
"Eq.substr",
... |
_private.Mathlib.LinearAlgebra.Basis.VectorSpace.0.nonzero_span_atom._simp_1_1 | Mathlib.LinearAlgebra.Basis.VectorSpace | [
"Submodule",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Set.instSingletonSet",
"Submodule.instPartialOrder",
"LE.le",
"AddCommMonoid",
"Submodule.setLike",
"propext",
"Submodule.span",
"Semiring",
"Submodule.span_singleton_le_iff_mem",
"Module",
"Singleton.singleton",... |
Sigma.Lex.linearOrder._proof_4 | Mathlib.Data.Sigma.Order | [
"instTrichotomousLt",
"Preorder.toLT",
"Sigma.Lex",
"LinearOrder",
"Sigma.instTotalLexOfTrichotomous",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"LE.le",
"total_of",
"LT.lt",
"Or",
"instDistribLatticeOfLinearOrder",
"Sigma",
... |
ContDiffMapSupportedIn.instSMul | Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | [
"Real",
"instHSMul",
"NormedSpace",
"ContDiffMapSupportedIn.instSMul._proof_2",
"ContDiffMapSupportedIn.mk",
"DistribMulAction.toDistribSMul",
"SMul",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddZeroClass.toAddZero",
"Real.semiring",
"Function.... |
Lean.Expr.foldRelevantConstants | Lean.LibrarySuggestions.Basic | [
"Pure.pure",
"Lean.Meta.State",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Applicative.toPure",
"Lean.Core.CoreM",
"StateRefT'",
"StateRefT'.instMonad",
"Lean.Name",
"Lean.Core.instMonadCoreM",
"ReaderT.instApplicativeOfMonad",
"Lean.Meta.Context"
] |
NormedField.instRankOneNNRealValuation._proof_4 | Mathlib.Topology.Algebra.Valued.NormedValued | [
"NormedCommRing.toNormedRing",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"NormedCommRing.toSeminormedCommRing",
"NormedRing.toRing",
"StrictMono",
"Monoid.toMulOneClass",
"PartialOrder.toPreorder",
"LinearOrderedCommMonoidWithZero.toLinearO... |
Subalgebra.involutiveStar._proof_11 | Mathlib.Algebra.Star.Subalgebra | [
"Subalgebra.instSetLike",
"Subalgebra.involutiveStar._proof_7",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"Set.star",
"star_star",
"Subsemigroup.mk",
"CommSemiring.toSemiring",
"SubsemiringClass.toAddSubmonoidClass",
"Subalgebra.involutiveStar._proof_4",
"AddMonoid.toAddZeroClas... |
StieltjesFunction.instModuleNNReal._proof_5 | Mathlib.MeasureTheory.Measure.Stieltjes | [
"ContinuousWithinAt.const_smul",
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsOrderedRing.toPosMulMono",
"HMul.hMul",
"Set.Ici",
"CommRing.toNonUnitalCommRing",
"StieltjesFunction.mk",
"IsTopologicalRin... |
BoundedOrder.noConfusionType | Mathlib.Order.BoundedOrder.Basic | [
"OrderBot",
"BoundedOrder.casesOn",
"OrderTop",
"LE",
"HEq",
"BoundedOrder"
] |
_private.Mathlib.Data.Set.Finite.Lattice.0.Set.Finite.bddAbove_biUnion._simp_1_1 | Mathlib.Data.Set.Finite.Lattice | [
"Preorder.toLE",
"BddAbove",
"bddAbove_empty",
"True",
"eq_true",
"Set.instEmptyCollection",
"Nonempty",
"EmptyCollection.emptyCollection",
"Eq",
"Preorder",
"Set"
] |
CategoryTheory.Functor.instEffectiveEpiEffectiveEpiOver | Mathlib.CategoryTheory.EffectiveEpi.Enough | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.EffectivelyEnough.presentation",
"CategoryTheory.Functor.EffectivePresentation",
"CategoryTheory.Functor.EffectivePresentation.effectiveEpi",
"CategoryTheory.Functor.effectiveEpiOverObj",
"Nonempty.some",
"CategoryTheory.EffectiveEpi",
"CategoryTheory.... |
derivWithin_fun_const | Mathlib.Analysis.Calculus.Deriv.Basic | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"NormedRing.toRing",
"NormedSpace",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"PseudoMetricSpace.toUnif... |
CoeOut.mk | Init.Coe | [
"CoeOut.mk",
"CoeOut",
"semiOutParam"
] |
CategoryTheory.Functor.IsCoverDense.sheafYonedaHom | Mathlib.CategoryTheory.Sites.DenseSubsite.Basic | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Functor.IsCoverDense",
"Opposite",
"CategoryTheory.coyoneda",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.yoneda",
"CategoryTheory.... |
_private.Mathlib.Topology.UniformSpace.Closeds.0.IsCompact.nhds_hausdorff_eq_nhds_vietoris._simp_1_2 | Mathlib.Topology.UniformSpace.Closeds | [
"Filter.instMembership",
"Filter.le_principal_iff",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"propext",
"Filter.principal",
"Eq",
"Filter",
"Filter.instPartialOrder",
"Set"
] |
_private.Mathlib.AlgebraicTopology.SimplicialObject.II.0.SimplexCategory.II.last_mem_finset._simp_1_1 | Mathlib.AlgebraicTopology.SimplicialObject.II | [
"SimplexCategory.II.finset",
"Finset",
"PartialOrder.toPreorder",
"Membership.mem",
"Exists",
"Fin.castPred",
"Ne",
"instOfNatNat",
"LE.le",
"instLEFin",
"instHAdd",
"OrderHom.instFunLike",
"Fin.instPartialOrder",
"Finset.instSetLike",
"HAdd.hAdd",
"SimplexCategory.II.mem_finset_iff",
... |
Stream'.Seq1.bind_assoc | Mathlib.Data.Seq.Basic | [
"Eq.mpr",
"Stream'.Seq",
"congrArg",
"Function.comp",
"Stream'.Seq.map",
"Stream'.Seq.join_append",
"id",
"Prod.mk",
"Stream'.Seq.join",
"Stream'.Seq1.map",
"Stream'.Seq.append_nil",
"Stream'.Seq.nil",
"Stream'.Seq1.bind",
"Stream'.Seq.map_comp",
"Stream'.Seq.recOn",
"Stream'.Seq.appen... |
Std.Time.Month.instInhabitedOrdinal | Std.Time.Date.Unit.Month | [
"Inhabited",
"OfNat.ofNat",
"Std.Time.Month.Ordinal",
"Std.Time.Month.instOfNatOrdinal",
"Inhabited.mk"
] |
Nat.le_three_of_sqrt_eq_one | Mathlib.Data.Nat.Sqrt | [
"Nat.sqrt_lt",
"HMul.hMul",
"_private.Mathlib.Data.Nat.Sqrt.0.Nat.le_three_of_sqrt_eq_one._proof_1_1",
"instMulNat",
"Nat.sqrt",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.le_of_lt_succ",
"Nat",
"LT.lt",
"Iff.mp",
"instLTNat",
"OfNat.ofNat",
"Eq",
"instHMul"
] |
Derivation.couple._proof_10 | Mathlib.RingTheory.Derivation.Lie | [
"CommRing",
"CommSemiring.toSemiring",
"Algebra.toModule",
"Algebra.id",
"smulCommClass_self",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"CommRing.toCommSemiring",
"CommMonoid.toMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"CommSemiring.toCommMonoid",
"Monoid.toSemigroup",
"Modu... |
_private.Mathlib.Order.ModularLattice.0.Set.Iic.isCompl_inf_inf_of_isCompl_of_le._simp_1_1 | Mathlib.Order.ModularLattice | [
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"OrderBot",
"disjoint_iff",
"SemilatticeInf.toPartialOrder",
"Bot.bot",
"SemilatticeInf.toMin",
"SemilatticeInf",
"propext",
"Eq",
"Min.min"
] |
Lean.Elab.Term.TacticMVarKind.term.sizeOf_spec | Lean.Elab.Term.TermElabM | [
"Lean.Elab.Term.TacticMVarKind.term",
"instOfNatNat",
"Lean.Elab.Term.TacticMVarKind",
"Nat",
"SizeOf.sizeOf",
"Lean.Elab.Term.TacticMVarKind._sizeOf_inst",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] |
Lean.PrettyPrinter.Delaborator.delabHOrElse._regBuiltin.Lean.PrettyPrinter.Delaborator.delabHOrElse_1 | Lean.PrettyPrinter.Delaborator.Builtins | [
"IO",
"Lean.PrettyPrinter.Delaborator.Delab",
"Lean.Name.mkStr3",
"Lean.PrettyPrinter.Delaborator.delabHOrElse",
"Unit",
"Lean.Name.mkStr4",
"Lean.PrettyPrinter.Delaborator.delabAttribute",
"Lean.KeyedDeclsAttribute.addBuiltin"
] |
Lean.Parser.Term.app._regBuiltin.Lean.Parser.Term.ellipsis.formatter_11 | Lean.Parser.Term | [
"Lean.PrettyPrinter.Formatter",
"Lean.Name.mkStr5",
"IO",
"Unit",
"Lean.Parser.Term.ellipsis.formatter",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] |
_private.Mathlib.Analysis.Normed.Field.Dense.0.IsAlgClosed.of_denseRange._simp_1_3 | Mathlib.Analysis.Normed.Field.Dense | [
"Finset",
"Finset.not_nonempty_iff_eq_empty",
"Finset.instEmptyCollection",
"propext",
"Finset.Nonempty",
"EmptyCollection.emptyCollection",
"Eq",
"Not"
] |
CategoryTheory.Functor.WellOrderInductionData.Extension.limit._proof_3 | Mathlib.CategoryTheory.SmallObject.WellOrderInductionData | [
"CategoryTheory.Functor.op",
"Eq.mpr",
"CategoryTheory.Functor",
"Preorder.toLT",
"isMin_iff_eq_bot._simp_1",
"CategoryTheory.Functor.WellOrderInductionData",
"Opposite",
"CategoryTheory.Functor.WellOrderInductionData.Extension.map_zero",
"OrderHom.monotone",
"CategoryTheory.CategoryStruct.toQuive... |
Partition.mk._flat_ctor | Mathlib.Order.Partition.Basic | [
"sSupIndep",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"CompleteLattice.toBoundedOrder",
"Bot.bot",
"Partition",
"BoundedOrder.toOrderBot",
"Condit... |
instCStarAlgebraSubtypeMemStarSubalgebraComplexElemental._proof_5 | Mathlib.Analysis.CStarAlgebra.Classes | [
"CStarAlgebra.toNonUnitalCStarAlgebra",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"SeminormedAddGroup.toAddGroup",
"NormedRing.toRing",
"Ring.toNonAssocRing",
"ContinuousStar",
"PseudoMetricSpace.toUniformSpace",
"NormedStarGroup.to_continuousStar",
"CStarAlgebra.toNormedRing",
"CStarAlgebra.... |
MvPolynomial.degrees_neg | Mathlib.Algebra.MvPolynomial.CommRing | [
"Finsupp.instAddZeroClass",
"Eq.mpr",
"NegZeroClass.toNeg",
"Nat.instMulZeroClass",
"CommRing",
"Lattice.toSemilatticeSup",
"Finsupp.toMultiset",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"Multiset.instAddCancelCommMonoid",
"Multiset.instLattice",
"Nat.instAddMonoid",
"AddZeroClass... |
Mathlib.Tactic.BicategoryLike.MkMor₂.casesOn | Mathlib.Tactic.CategoryTheory.Coherence.Datatypes | [
"Mathlib.Tactic.BicategoryLike.Mor₂",
"Lean.Expr",
"Mathlib.Tactic.BicategoryLike.MkMor₂",
"Mathlib.Tactic.BicategoryLike.MkMor₂.mk",
"Mathlib.Tactic.BicategoryLike.MkMor₂.rec"
] |
_private.Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody.0.NumberField.mixedEmbedding.convexBodyLT'_mem._simp_1_5 | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody | [
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Real",
"SeminormedAddGroup.toAddGroup",
"SeminormedAddGroup",
"Real.instLT",
"Membership.mem",
"Metric.ball",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SeminormedAddGroup.toPseudoMetric... |
CategoryTheory.RightRigidCategory.noConfusionType | Mathlib.CategoryTheory.Monoidal.Rigid.Basic | [
"CategoryTheory.HasRightDual",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.RightRigidCategory",
"CategoryTheory.RightRigidCategory.casesOn",
"HEq",
"CategoryTheory.Category"
] |
AlgebraicGeometry.SheafedSpace.mk.injEq | Mathlib.Geometry.RingedSpace.SheafedSpace | [
"AlgebraicGeometry.SheafedSpace",
"AlgebraicGeometry.PresheafedSpace.carrier",
"Eq.propIntro",
"TopCat.Presheaf.IsSheaf",
"AlgebraicGeometry.SheafedSpace.mk",
"AlgebraicGeometry.SheafedSpace.mk.inj",
"AlgebraicGeometry.PresheafedSpace.presheaf",
"Eq.ndrec",
"Eq.refl",
"AlgebraicGeometry.Presheafed... |
ContDiffMapSupportedIn.fderivLM._proof_10 | Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"ContinuousLinearMap.topologicalSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",... |
EStateM.Backtrackable.recOn | Init.Prelude | [
"EStateM.Backtrackable.rec",
"EStateM.Backtrackable",
"EStateM.Backtrackable.mk"
] |
Mathlib.Tactic.Ring.ExBase.atom.injEq | Mathlib.Tactic.Ring.Common | [
"Eq.propIntro",
"Lean.Expr.const",
"Mathlib.Tactic.Ring.ExBase.atom",
"Mathlib.Tactic.Ring.ExBase",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Nat",
"Eq.ndrec",
"Lean.Expr.app",
"Mathlib.Tactic.Ring.ExBase.atom.inj",
"Eq.refl",
"Lean.Level.succ",
"Lean.Name.mkStr1",
"Eq... |
_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.ChevalleyThm.PolynomialC.induction_aux._simp_1_10 | Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | [
"instHSMul",
"SMul",
"Set.instSingletonSet",
"Set.smul_set_singleton",
"HSMul.hSMul",
"Singleton.singleton",
"Eq.symm",
"Eq",
"Set.smulSet",
"Set"
] |
CategoryTheory.Functor.OplaxMonoidal.whiskeringRight._proof_6 | Mathlib.CategoryTheory.Monoidal.FunctorCategory | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.OplaxMonoidal.δ",
"id",
"CategoryTheory.Monoi... |
Std.Iter.allM_map | Init.Data.Iterators.Lemmas.Combinators.FilterMap | [
"Pure.pure",
"Eq.mpr",
"Std.IterStep",
"Std.Iterators.Types.FilterMap.PlausibleStep.skip",
"congrArg",
"Monad.toApplicative",
"Std.Iter.step_map",
"Std.Iterators.Types.Map.instIterator",
"MonadLiftT.monadLift",
"Std.Iterators.Types.Map.instFinite",
"Std.instLawfulIteratorLoopDefaultImplementatio... |
_private.Std.Data.ExtDHashMap.Lemmas.0.Std.ExtDHashMap.mem_erase._simp_1_1 | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Membership.mem",
"Std.ExtDHashMap.contains",
"LawfulHashable",
"Bool.true",
"EquivBEq",
"propext",
"Std.ExtDHashMap",
"Bool",
"Hashable",
"Eq.symm",
"BEq",
"Eq",
"Std.ExtDHashMap.contains_iff_mem"
] |
PiTensorProduct.map._proof_1 | Mathlib.LinearAlgebra.PiTensorProduct | [
"PiTensorProduct.instModule",
"CommSemiring.toSemiring",
"PiTensorProduct.instAddCommMonoid",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
"CommMonoid.toMonoid",
"CommSemiring.toCommMonoid",
"Monoid.toSemigroup",
"Module.toDistribMulAction",
"SemigroupAction.toSMul",
"AddCommMonoid.t... |
_private.Lean.Elab.DocString.Builtin.Keywords.0.Lean.Doc.isAtoms | Lean.Elab.DocString.Builtin.Keywords | [
"StateT.run",
"String",
"Lean.Syntax",
"Id",
"Prod.fst",
"List.cons",
"List",
"Bool",
"_private.Lean.Elab.DocString.Builtin.Keywords.0.Lean.Doc.isAtoms.go",
"List.nil"
] |
Finset.trop_inf | Mathlib.Algebra.Tropical.BigOperators | [
"Multiset.sum",
"Eq.mpr",
"Multiset.map",
"Tropical.instAddCommMonoidTropical",
"congrArg",
"HEq.refl",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Function.comp",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Multiset",
"DistribLattice.toLattice",
"Eq.c... |
CategoryTheory.Limits.Bicone.IsBilimit.mk.sizeOf_spec | Mathlib.CategoryTheory.Limits.Shapes.Biproducts | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Discrete._sizeOf_inst",
"CategoryTheory.Limits.IsLimit._sizeOf_inst",
"CategoryTheory.Limits.Bicone.toCocone",
"CategoryTheory.Limits.Bicone.toCone",
"CategoryTheory.Discrete.functor",
"CategoryTheory.Limits.Bicone.IsBilimit.mk",
"CategoryTheor... |
ProofWidgets.Html._sizeOf_inst | ProofWidgets.Data.Html | [
"ProofWidgets.Html",
"SizeOf.mk",
"SizeOf",
"ProofWidgets.Html._sizeOf_1"
] |
CategoryTheory.EffectiveEpiStruct.noConfusionType | Mathlib.CategoryTheory.EffectiveEpi.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.EffectiveEpiStruct.casesOn",
"CategoryTheory.CategoryStruct.comp",
"HEq",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.EffectiveEpiStruct",
"Eq",
"CategoryTheory.Category"
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.