name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionHom._default | Mathlib.CategoryTheory.Monoidal.Action.Basic | [
"CategoryTheory.MonoidalCategoryStruct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"id",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | false |
Lean.Lsp.instFileSourceSignatureHelpParams | Lean.Server.FileSource | [
"Lean.Lsp.instFileSourceTextDocumentIdentifier",
"Lean.Lsp.FileSource.mk",
"Lean.Lsp.TextDocumentIdentifier",
"Lean.Lsp.SignatureHelpParams.toTextDocumentPositionParams",
"Lean.Lsp.SignatureHelpParams",
"Lean.Lsp.FileSource",
"Lean.Lsp.TextDocumentPositionParams.textDocument",
"Lean.Lsp.FileSource.fil... | true |
_private.Mathlib.Computability.TuringDegree.0.instPreorderPFunNat | Mathlib.Computability.TuringDegree | [
"LT.mk",
"PFun",
"_private.Mathlib.Computability.TuringDegree.0.instPreorderPFunNat._proof_1",
"Preorder.mk",
"TuringReducible.refl",
"TuringReducible.trans",
"And",
"TuringReducible",
"Nat",
"LE.mk",
"Not",
"Preorder"
] | true |
Lean.IR.Checker.markIndex | Lean.Compiler.IR.Checker | [
"Pure.pure",
"Lean.IR.Checker.M",
"Lean.Core.instMonadLiftIOCoreM",
"IO.instMonadLiftSTRealWorldBaseIO",
"modify",
"String",
"Lean.IR.Checker.CheckerContext",
"instMonadLiftT",
"MonadState.get",
"IO",
"StateRefT'.instMonadStateOfOfMonadLiftTST",
"ReaderT.instMonad",
"Std.TreeSet.insert",
"... | true |
Option.filter_some | Init.Data.Option.Lemmas | [
"Option.some",
"instDecidableEqBool",
"Bool.true",
"Option.none",
"Option.filter",
"Bool",
"Eq",
"rfl",
"Option",
"ite"
] | true |
MvPowerSeries.instInv | Mathlib.RingTheory.MvPowerSeries.Inverse | [
"Inv",
"MvPowerSeries",
"Inv.mk",
"MvPowerSeries.inv",
"Field"
] | true |
Lean.Elab.Tactic.closeMainGoal | Lean.Elab.Tactic.Basic | [
"Pure.pure",
"Lean.MessageData",
"Lean.Elab.Tactic.ensureHasNoMVars",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"String",
"Lean.Elab.Tactic.getMainGoal",
"Lean.Meta.State",
"instMonadLiftT",
"Lean.MessageData.instAppend",
"Option.some",
"Lean.Elab.Tactic.Context",
"Lean.MVarId",
"Lea... | true |
Lean.Elab.GoalsAtResult | Lean.Server.InfoUtils | [
"Lean.Elab.GoalsAtResult.mk"
] | true |
_private.Mathlib.Algebra.Group.Pointwise.Set.ListOfFn.0.Set.mem_list_prod._simp_1_2 | Mathlib.Algebra.Group.Pointwise.Set.ListOfFn | [
"List.ofFn",
"Exists",
"List.exists_iff_exists_tuple",
"List",
"Nat",
"propext",
"Fin",
"Eq"
] | false |
FirstOrder.Language.BoundedFormula.all_iff_not_ex_not | Mathlib.ModelTheory.Equivalence | [
"not_exists._simp_1",
"FirstOrder.Language.Theory.ModelType",
"FirstOrder.Language.BoundedFormula.realize_ex._simp_1",
"Classical.not_not._simp_1",
"FirstOrder.Language.Theory.ModelType.struc",
"congrArg",
"FirstOrder.Language.BoundedFormula.realize_not._simp_1",
"Exists",
"FirstOrder.Language.Bound... | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.derivedLitsInvariant_confirmRupHint._proof_1_14 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult | [
"Lean.Grind.Nat.lt_eq",
"instOfNatNat",
"LE.le",
"instLENat",
"Fin.val",
"Array",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Eq.substr",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Fin",
"Array.size"
] | false |
Lean.Lsp.instToJsonChangeAnnotation.toJson | Lean.Data.Lsp.Basic | [
"Lean.Json",
"Lean.Json.mkObj",
"Lean.Json.opt",
"String",
"Lean.instToJsonBool",
"Lean.instToJsonString",
"Lean.ToJson.toJson",
"Prod.mk",
"List.cons",
"Lean.Lsp.ChangeAnnotation",
"List",
"Lean.Lsp.ChangeAnnotation.description?",
"Bool",
"Lean.Lsp.ChangeAnnotation.needsConfirmation",
"... | true |
Lean.Lsp.instFromJsonCallHierarchyPrepareParams.fromJson | Lean.Data.Lsp.LanguageFeatures | [
"Pure.pure",
"Lean.Json",
"Lean.Lsp.CallHierarchyPrepareParams.mk",
"Monad.toApplicative",
"String",
"Lean.Lsp.instFromJsonPosition",
"Lean.Name.mkStr3",
"Lean.Json.getObjValAs?",
"Applicative.toPure",
"ToString.toString",
"Except.instMonad",
"Lean.Lsp.TextDocumentIdentifier",
"instAppendStr... | true |
HomologicalComplex.homotopyCofiber.XIsoBiprod.congr_simp | Mathlib.Algebra.Homology.HomotopyCofiber | [
"HomologicalComplex.instCategory",
"HomologicalComplex.homotopyCofiber.X",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"DecidableRel",
"HomologicalComplex",
"CategoryTheory.Limits.HasBinaryBiproduct",
"CategoryTheory.Iso",
"ComplexShape",
"CategoryTheory.Limits.biprod",
"CategoryTheo... | true |
AntitoneOn.Ico | Mathlib.Order.Interval.Set.Monotone | [
"AntitoneOn.Ici",
"Preorder.toLT",
"Set.Ici",
"MonotoneOn.Iio",
"PartialOrder.toPreorder",
"CompleteLattice.toConditionallyCompleteLattice",
"MonotoneOn.inter",
"Set.Ico",
"MonotoneOn",
"CompleteBooleanAlgebra.toCompleteLattice",
"AntitoneOn",
"ConditionallyCompletePartialOrderSup.toPartialOrd... | true |
List.reduceOption_cons_of_some | Mathlib.Data.List.ReduceOption | [
"congrArg",
"Option.some",
"Membership.mem",
"List.filterMap_congr",
"id",
"List.cons",
"List",
"List.instMembership",
"congr",
"True",
"eq_self",
"of_eq_true",
"Eq.refl",
"List.reduceOption",
"List.filterMap",
"Eq",
"Eq.trans",
"Option"
] | true |
Ordinal.invVeblen₂_gamma | Mathlib.SetTheory.Ordinal.Veblen | [
"Ordinal.veblen",
"Eq.mpr",
"Ordinal.gamma_ne_zero",
"congrArg",
"Ordinal.veblen_gamma_zero",
"id",
"Ordinal.invVeblen₂",
"Ordinal.zero",
"Zero.toOfNat0",
"Eq.refl",
"Ordinal.gamma",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"Ordinal.veblen_pos",
"Ordinal",
"Ordinal.invVeblen₂_veblen"
] | true |
IsJordan.mk._flat_ctor | Mathlib.Algebra.Jordan.Basic | [
"HMul.hMul",
"IsJordan.mk",
"Mul",
"IsJordan",
"Eq",
"instHMul"
] | false |
_private.Mathlib.Data.Nat.ChineseRemainder.0.Nat.modEq_list_map_prod_iff._simp_1_2 | Mathlib.Data.Nat.ChineseRemainder | [
"Nat.Coprime",
"Nat.instOne",
"Membership.mem",
"instMulNat",
"List",
"List.instMembership",
"Nat",
"propext",
"Nat.coprime_list_prod_right_iff",
"Eq",
"List.prod"
] | false |
_private.Mathlib.RingTheory.Coalgebra.GroupLike.0.isGroupLikeElem_self._simp_1_1 | Mathlib.RingTheory.Coalgebra.GroupLike | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Coalgebra.toCoalgebraStruct",
"Semiring.toModule",
"Coalgebra",
"IsGroupLikeElem",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"isGroupLikeElem_iff",
"LinearMap.instFunLike",
"CoalgebraStruct.counit",
"AddCommMonoidWithOne.toAddMonoidWith... | false |
Combinatorics.Line._sizeOf_inst | Mathlib.Combinatorics.HalesJewett | [
"Combinatorics.Line._sizeOf_1",
"Combinatorics.Line",
"SizeOf.mk",
"SizeOf"
] | false |
iSup_subtype' | Mathlib.Order.CompleteLattice.Basic | [
"iSup",
"iSup_subtype",
"Subtype",
"Subtype.mk",
"CompleteSemilatticeSup.toSupSet",
"CompleteLattice.toCompleteSemilatticeSup",
"Eq.symm",
"CompleteLattice",
"Subtype.val",
"Eq",
"Subtype.property"
] | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_430 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Equiv.instEquivLike",
"Finset",
"Lean.Grind.Nat.lt_eq",
"List.getElem_filter_eq_getElem_getElem_findIdxs._proof_2",
"Equiv",
"instOfNatNat",
"LE.le",
"instLENat",
"instBEqOfDecidableEq",
"List.cons",
"List.idxOfNth",
"List.findIdxs",
"instHAdd",
"HAdd.hAdd",
"Equiv.Perm",
"Nat",
"Li... | false |
BitVec.msb_twoPow | Init.Data.BitVec.Lemmas | [
"Eq.mpr",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.msb_twoPow._proof_1_3",
"BitVec.getMsbD",
"congrArg",
"BitVec.getMsbD_eq_getLsbD",
"HSub.hSub",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.msb_twoPow._simp_1_2",
"BitVec.getLsbD",
"id",
"Bool.and",
"instSubNat",
"instOfNatNat",
"Bool.true"... | true |
GrpCat.SurjectiveOfEpiAuxs.tau._proof_1 | Mathlib.Algebra.Category.Grp.EpiMono | [
"MonoidHom.range",
"instHSMul",
"GrpCat",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"CategoryTheory.CategoryStruct.toQuiver",
"one_leftCoset",
"Quiver.Hom",
"GrpCat.str",
"GrpCat.Hom.hom",
"DivInvOneMonoid.toDivInvMonoid",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMono... | false |
MulAction.isPreprimitive_stabilizer_of_surjective | Mathlib.GroupTheory.Perm.MaximalSubgroups | [
"Equiv.Perm.applyMulAction",
"Eq.mpr",
"instHSMul",
"Function.bijective_id",
"congrArg",
"Group",
"Membership.mem",
"inferInstance",
"Set.Elem",
"id",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
"MulActionHom.mk",
"MulAction.toPerm",
"instFunLikeMulActionHom",
"Group.toDivInvMono... | true |
HomologicalComplex.dFrom_eq | Mathlib.Algebra.Homology.HomologicalComplex | [
"HomologicalComplex.xNext",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex",
"CategoryTheory.CategoryStruct.id",
"HomologicalComplex.xNextIso",
"CategoryTheory.Category.comp_id",
"ComplexShape",
"HomologicalComplex.dFrom",
"C... | true |
Lean.Widget.RpcEncodablePacket.«_@».Lean.Widget.UserWidget.577854155._hygCtx._hyg.1.recOn | Lean.Widget.UserWidget | [
"Lean.Json",
"Lean.Widget.RpcEncodablePacket._@.Lean.Widget.UserWidget.577854155._hygCtx._hyg.1",
"Lean.Widget.RpcEncodablePacket.«_@».Lean.Widget.UserWidget.577854155._hygCtx._hyg.1.rec",
"Lean.Widget.RpcEncodablePacket.mk._@.Lean.Widget.UserWidget.577854155._hygCtx._hyg.1"
] | false |
_private.Mathlib.ModelTheory.Semantics.0.FirstOrder.Language.model_distinctConstantsTheory._simp_1_1 | Mathlib.ModelTheory.Semantics | [
"Set.mem_image",
"Membership.mem",
"Exists",
"And",
"propext",
"Set.image",
"Eq",
"Set.instMembership",
"Set"
] | false |
Ordinal.omega | Mathlib.SetTheory.Cardinal.Aleph | [
"Ordinal.instLinearOrder",
"Ordinal.omega0",
"Ordinal.partialOrder",
"OrderEmbedding.addLeft",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"LE.le",
"Ordinal.instAddLeftStrictMono",
"Ordinal.add",
"OrderEmbedding",
"RelEmbedding.tra... | true |
AddChar.circleEquivComplex._proof_5 | Mathlib.Analysis.Fourier.FiniteAbelian.PontryaginDuality | [
"Iff.mpr",
"NormedCommRing.toNormedRing",
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"NormedCommRing.toSeminormedCommRing",
"Real",
"MonoidHom.instFunLike",
"SeminormedAddGroup.toAddGroup",
"Equiv.instEquivLike",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",... | false |
Batteries.Tactic.Lint.isAutoDecl | Batteries.Tactic.Lint.Basic | [
"Pure.pure",
"Lean.Name.below",
"Lean.Environment.isConstructor",
"String",
"Lean.casesOnSuffix",
"Lean.Core.instMonadEnvCoreM",
"Lean.Environment.find?",
"Membership.mem",
"Lean.isReservedName",
"_private.Batteries.Tactic.Lint.Basic.0.Batteries.Tactic.Lint.isAutoDecl.match_4",
"Lean.isSubobject... | true |
CategoryTheory.Mon.tensorUnit_mul | Mathlib.CategoryTheory.Monoidal.Mon_ | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategoryStruct.leftUnitor",
"CategoryTheory.BraidedCategory",
"CategoryTheory.Mon",
"CategoryTheory.Mon.X",
"CategoryTheory.Mon.instCategory",
"CategoryTheory.MonoidalCategoryStruct.ten... | true |
DirectLimit.instMulDistribMulActionOfMulActionHomClass._proof_4 | Mathlib.Algebra.Colimit.DirectLimit | [
"MulActionHomClass",
"DirectLimit.setoid",
"Monoid",
"MulOne.toOne",
"instHSMul",
"DirectLimit.instSMul",
"Monoid.toMulOneClass",
"DirectLimit.instMonoid",
"Preorder.toLE",
"LE.le",
"DirectLimit",
"DirectLimit.smul_def",
"Quotient.mk",
"MulOneClass.toMulOne",
"Quotient",
"DirectLimit.i... | false |
_private.Mathlib.CategoryTheory.Triangulated.Subcategory.0.CategoryTheory.ObjectProperty.extensionProduct_retractClosure_retractClosure_le._proof_1_3 | Mathlib.CategoryTheory.Triangulated.Subcategory | [
"CategoryTheory.Category.assoc",
"False",
"eq_false",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Classical.byContradiction",
"CategoryTheory.shiftFunctor",
"CategoryTheory.CategoryStruct.id",
"Eq.mp",
"id",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Functor.map",... | false |
Lean.CollectFVars.State.fvarIds._default | Lean.Util.CollectFVars | [
"id",
"Lean.FVarId",
"List.toArray",
"Array",
"List.nil"
] | false |
Lean.Lsp.instDecidableEqCompletionItemKind._proof_2 | Lean.Data.Lsp.LanguageFeatures | [
"False",
"Lean.Lsp.CompletionItemKind.ctorIdx",
"Lean.Lsp.CompletionItemKind",
"absurd",
"Nat",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Not"
] | false |
Lean.Server.Watchdog.WorkerState.ctorIdx | Lean.Server.Watchdog | [
"Lean.Server.Watchdog.WorkerState.casesOn",
"Nat",
"Lean.Server.Watchdog.WorkerState"
] | false |
_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable.go.induct_unfolding | Init.Data.String.Pattern.String | [
"PSigma.snd",
"_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable.go._unary._proof_5",
"Vector",
"Array.push",
"_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable.go._unary._proof_13",
"HSub.hSub",
"String.Slice",
... | true |
HahnSeries.instIsScalarTower | Mathlib.RingTheory.HahnSeries.Addition | [
"Monoid",
"instHSMul",
"smul_assoc",
"congrArg",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"SMul",
"AddMonoid.toAddZeroClass",
"HahnSeries.ext",
"AddZeroClass.toAddZero",
"PartialOrder",
"DistribSMul.toSMulZeroClass",
"AddZero.toZero",
"funext",
"HahnSeries.instSMul",
"True",
... | true |
Computation.liftRel_pure_right._simp_1 | Mathlib.Data.Seq.Computation | [
"Membership.mem",
"Exists",
"Computation",
"And",
"Computation.pure",
"Computation.liftRel_pure_right",
"propext",
"Computation.instMembership",
"Eq",
"Computation.LiftRel"
] | false |
Lean.Parser.testParseFile | Lean.Parser.Module | [
"Lean.TSyntax",
"String",
"IO",
"instMonadEIO",
"List.cons",
"IO.FS.readFile",
"Monad.toBind",
"Bind.bind",
"IO.Error",
"Lean.SyntaxNodeKind",
"Lean.Name.mkStr4",
"Lean.Environment",
"System.FilePath",
"System.FilePath.toString",
"Lean.Parser.testParseModule",
"List.nil"
] | true |
Set.Finite.eq_insert_of_subset_of_encard_eq_succ | Mathlib.Data.Set.Card | [
"Eq.mpr",
"Set.encard",
"instAddMonoidWithOneENat",
"instTopENat",
"congrArg",
"CommSemiring.toSemiring",
"instIsLeftCancelAddOfAddLeftReflectLE",
"Set.Finite.encard_lt_top",
"Set.Finite",
"Set.singleton_union",
"Exists",
"Set.instUnion",
"Set.encard_diff_add_encard_of_subset",
"Eq.mp",
... | true |
Lean.Expr.getRevArg!._sunfold | Lean.Expr | [
"panicWithPosWithDecl",
"Lean.Expr",
"Lean.Expr.getRevArg!",
"instOfNatNat",
"Lean.instInhabitedExpr",
"Nat",
"OfNat.ofNat",
"_private.Lean.Expr.0.Lean.Expr.getRevArg!.match_1"
] | false |
HomologicalComplex.homologyι_singleObjOpcyclesSelfIso_inv | Mathlib.Algebra.Homology.SingleHomology | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.CategoryStruct.toQuiver",
"HomologicalComplex.singleObjHomologySelfIso",
"Quiver.Hom",
"congrArg",
"HomologicalComplex.opcycles",
"HomologicalComplex",
"Homolog... | true |
Array.countP_push_of_neg | Init.Data.Array.Count | [
"List.countP",
"False",
"Array.push",
"congrArg",
"List.countP_toArray",
"Bool.false_eq_true",
"Eq.mp",
"Array.casesOn",
"id",
"instOfNatNat",
"List.toArray",
"List.cons",
"Array",
"Bool.true",
"instHAppendOfAppend",
"List",
"instHAdd",
"List.countP_append",
"HAdd.hAdd",
"Array... | true |
Submodule.moduleSubmodule._proof_1 | Mathlib.RingTheory.Ideal.Operations | [
"Submodule",
"MulOne.toOne",
"Ideal.one_eq_top",
"instHSMul",
"Semiring.toModule",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"Algebra.id",
"Submodule.instTop",
"Ideal",
"IsScalarTower.left",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid"... | false |
_private.Init.Data.BitVec.Bitblast.0.BitVec.msb_srem._simp_1_2 | Init.Data.BitVec.Bitblast | [
"GT.gt",
"LT.lt",
"gt_iff_lt",
"propext",
"Eq",
"LT"
] | false |
_private.Lean.Elab.MacroArgUtil.0.Lean.Elab.Command.expandMacroArg.mkSyntaxAndPat | Lean.Elab.MacroArgUtil | [
"Lean.TSyntax",
"Inhabited.default",
"Lean.Syntax.Ident",
"Lean.Syntax.Term",
"List.cons",
"Lean.Elab.Command.instInhabitedCommandElabM",
"Lean.SyntaxNodeKind",
"Prod",
"Lean.Elab.Command.CommandElabM",
"Lean.Name.mkStr1",
"List.nil",
"Option"
] | true |
Odd.pow_injective | Mathlib.Algebra.Order.Ring.Basic | [
"LinearOrder",
"PartialOrder.toPreorder",
"Odd",
"IsStrictOrderedRing",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Distrib.toAdd",
"Odd.strictMono_pow",
"Monoid.toPow",
"ExistsAddOfLE",
"StrictMono.injective",
"HPow.hPow",
"NonAssocSemiring.toNonUnitalNo... | true |
_private.Init.Data.UInt.Bitwise.0.UInt32.and_eq_neg_one_iff._simp_1_2 | Init.Data.UInt.Bitwise | [
"BitVec.and_eq_allOnes_iff",
"BitVec.instAndOp",
"BitVec.allOnes",
"BitVec",
"And",
"Nat",
"propext",
"HAnd.hAnd",
"Eq",
"instHAndOfAndOp"
] | false |
Set.isUnit_iff | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Units.val",
"Eq.mpr",
"MulOne.toOne",
"InvOneClass.toOne",
"HMul.hMul",
"Set.singleton_injective",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"Set.one",
"Units.inv_mul",
"IsUnit",
"DivisionMonoid.toDivInvOneMonoid",
"Exists",
"Units",
"DivisionMonoid",
"Set... | true |
_private.Lean.Compiler.LCNF.InferBorrow.0.Lean.Compiler.LCNF.State.mk.inj | Lean.Compiler.LCNF.InferBorrow | [
"_private.Lean.Compiler.LCNF.InferBorrow.0.Lean.Compiler.LCNF.State.mk",
"_private.Lean.Compiler.LCNF.InferBorrow.0.Lean.Compiler.LCNF.ParamMap",
"_private.Lean.Compiler.LCNF.InferBorrow.0.Lean.Compiler.LCNF.State.mk.noConfusion",
"And",
"And.intro",
"Bool",
"Eq",
"Lean.FVarIdHashSet",
"_private.Lea... | true |
_private.Lean.Meta.IndPredBelow.0.Lean.Meta.IndPredBelow.isIH._sparseCasesOn_1 | Lean.Meta.IndPredBelow | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
_private.Lean.Util.Diff.0.Lean.Diff.lcs.match_8 | Lean.Util.Diff | [
"Subarray",
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"Prod.mk",
"Std.Slice.Internal.SubarrayData",
"Nat",
"Std.Slice.size",
"Subarray.instSliceSizeSubarrayData",
"Prod",
"Prod.casesOn",
"Fin",
"_private.Lean.Util.Diff.0.Lean.Diff.lcs._sparseCasesOn_3",
"Option"
] | false |
AddSubgroup.Normal.hcongr_3 | Mathlib.GroupTheory.IsSubnormal | [
"HEq.refl",
"AddSubgroup",
"AddSubgroup.Normal",
"AddGroup",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Eq"
] | true |
CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse._proof_5 | Mathlib.CategoryTheory.Triangulated.Opposite.Triangle | [
"CategoryTheory.Pretriangulated.TriangleMorphism.hom₂",
"CategoryTheory.Functor",
"CategoryTheory.Equivalence.unitIso",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"Quiver.Hom.op_inj",
"CategoryTheory.Pretriangulated.Triangle.ob... | false |
_private.Mathlib.RingTheory.Ideal.Operations.0.Ideal.finset_inf_span_singleton._simp_1_2 | Mathlib.RingTheory.Ideal.Operations | [
"Dvd.dvd",
"Semiring.toModule",
"CommSemiring.toNonUnitalCommSemiring",
"CommSemiring.toSemiring",
"semigroupDvd",
"Membership.mem",
"SemigroupWithZero.toSemigroup",
"Set.instSingletonSet",
"NonUnitalSemiring.toSemigroupWithZero",
"Ideal",
"NonUnitalCommSemiring.toNonUnitalSemiring",
"CommSemi... | false |
_private.Init.Data.SInt.Bitwise.0.Int16.shiftRight_or._simp_1_1 | Init.Data.SInt.Bitwise | [
"Int16",
"BitVec",
"instOfNatNat",
"Nat",
"Int16.toBitVec",
"propext",
"OfNat.ofNat",
"Eq.symm",
"Int16.toBitVec_inj",
"Eq"
] | false |
fromModuleCatToModuleCatLinearEquivtoModuleCatObj.eq_1 | Mathlib.RingTheory.Morita.Matrix | [
"Pi.Function.module",
"Submodule",
"LinearEquiv.mk",
"Ring.toNonAssocRing",
"ModuleCat",
"instDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Matrix",
"Submodule.addCommMonoid",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"MatrixModCat.toModuleCatObj",
"CategoryTheory.Fu... | true |
Pi.counit_comp_finsuppLcoeFun | Mathlib.RingTheory.Coalgebra.Basic | [
"Finsupp.lcoeFun._proof_2",
"CoalgebraStruct",
"Finsupp.instFunLike",
"Eq.mpr",
"Pi.Function.module",
"Semiring.toModule",
"Pi.addCommMonoid",
"Finsupp.module",
"Finset.univ",
"SemilinearMapClass.distribMulActionSemiHomClass",
"LinearMap.ext",
"congrArg",
"CommSemiring.toSemiring",
"Finset... | true |
CategoryTheory.Endofunctor.Algebra.Hom.mk.congr_simp | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Functor",
"CategoryTheory.Endofunctor.Algebra",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Endofunctor.Algebra.Hom",
"CategoryTheory.Endofunctor.Algebra.Hom.mk",
"CategoryTheory.Endofunctor.Algebra.str",
"Eq.rec",
"CategoryTheory.Endofunctor.Algebra.a",
... | true |
MultilinearMap.mk._flat_ctor | Mathlib.LinearAlgebra.Multilinear.Basic | [
"MultilinearMap.mk",
"instHSMul",
"Function.update",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"MultilinearMap",
"AddCommMonoid",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"Semiring",
"HSMul.hSMul",
"Module.toD... | false |
HomologicalComplex.singleMapHomologicalComplex_inv_app_ne | Mathlib.Algebra.Homology.Additive | [
"HomologicalComplex.singleMapHomologicalComplex._proof_4",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"dite_congr",
"eq_false",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex.single... | true |
CategoryTheory.MonoidalCategoryStruct.recOn | Mathlib.CategoryTheory.Monoidal.Category | [
"CategoryTheory.MonoidalCategoryStruct",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategoryStruct.rec",
"CategoryTheory.Iso",
"CategoryTheory.MonoidalCategoryStruct.mk",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | false |
MvPolynomial.monomial_one_mul_cancel_right_iff | Mathlib.Algebra.MvPolynomial.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"Semiring.toModule",
"HMul.hMul",
"AddMonoidAlgebra.addAddCommMonoid",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"MvPolynomial.monomial",
"LinearMap.instFunLike",
"Function.Injective.eq_iff",
"IsRegular.right",
"Na... | true |
Encodable.decodeSum.eq_1 | Mathlib.Logic.Encodable.Basic | [
"Encodable.decodeSum.match_1",
"Encodable.decodeSum",
"Sum",
"Sum.inl",
"Option.map",
"Sum.inr",
"Nat",
"Bool",
"Eq.refl",
"Nat.boddDiv2",
"Encodable.decode",
"Prod",
"Eq",
"Encodable",
"Option"
] | true |
_private.Mathlib.Topology.ContinuousMap.StoneWeierstrass.0.ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id._simp_1_5 | Mathlib.Topology.ContinuousMap.StoneWeierstrass | [
"Set.mem_inter_iff",
"Membership.mem",
"Set.instInter",
"Inter.inter",
"And",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
ZFSet.Hereditarily.eq_1 | Mathlib.SetTheory.ZFC.Basic | [
"ZFSet",
"Membership.mem",
"ZFSet.Hereditarily",
"And",
"ZFSet.Hereditarily.eq_def",
"Eq.refl",
"Eq",
"ZFSet.instSetLike",
"SetLike.instMembership",
"Eq.trans"
] | true |
scalarSMulCLE._proof_1 | Mathlib.Analysis.InnerProductSpace.StandardSubspace | [
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace.toModule",
"IsBoundedSMul.toUniformContinuousConstSMul",
"Complex.instNormedField",
"PseudoMetricSpace.toUniformSpace",
"Units.in... | false |
IsUniformInducing.isUltraUniformity | Mathlib.Topology.UniformSpace.Ultra.Completion | [
"UniformSpace",
"IsUniformInducing.comap_uniformSpace",
"Eq.rec",
"inferInstance",
"IsUniformInducing",
"IsUltraUniformity",
"UniformSpace.comap",
"Eq",
"IsUltraUniformity.comap"
] | true |
CategoryTheory.Bicategory.OplaxTrans.ComonadBicat.inst._proof_28 | Mathlib.CategoryTheory.Bicategory.Monad.Basic | [
"CategoryTheory.Bicategory.OplaxTrans.ComonadBicat",
"Quiver.mk",
"CategoryTheory.CategoryStruct.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.Bicategory.whisker_exchange._autoParam",
"CategoryTheory.Bicategory.OplaxTrans.Comon... | false |
Submodule.instIsModularLattice | Mathlib.LinearAlgebra.Span.Basic | [
"Iff.mpr",
"Eq.mpr",
"Submodule",
"Lattice.toSemilatticeSup",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"HSub.hSub",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Exists",
"SemilatticeI... | true |
BoundedOrderHom.toOrderHom | Mathlib.Order.Hom.Bounded | [
"BoundedOrderHom",
"Preorder.toLE",
"BoundedOrder",
"OrderHom",
"Preorder"
] | true |
HomologicalComplex₂.totalFlipIso_hom_f_D₁ | Mathlib.Algebra.Homology.TotalComplexSymmetry | [
"HomologicalComplex₂.totalFlipIso",
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex₂.toGradedObject",
"HomologicalComplex₂.HasTotal",
"HomologicalComplex",
"HomologicalComplex₂.flip",
"HomologicalComplex₂.in... | true |
CategoryTheory.Limits.HasImage.exists_image | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.ImageFactorisation",
"Nonempty",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Limits.HasImage",
"CategoryTheory.Category"
] | true |
CategoryTheory.ShortComplex.homologyFunctorIso._proof_1 | Mathlib.Algebra.Homology.ShortComplex.PreservesHomology | [
"CategoryTheory.Functor.PreservesHomology.preservesRightHomologyOf",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.ShortComplex.hasHomology_of_preserves",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.HasHomology",
"CategoryTheory.Functor.PreservesHomo... | false |
ComputeAsymptotics.MultiseriesExpansion.Multiseries.tail_nil | Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | [
"ComputeAsymptotics.Basis",
"Real",
"ComputeAsymptotics.MultiseriesExpansion.Multiseries.nil",
"Stream'.Seq.nil",
"eq_self",
"of_eq_true",
"Prod",
"Eq",
"ComputeAsymptotics.MultiseriesExpansion.Multiseries.tail",
"ComputeAsymptotics.MultiseriesExpansion",
"ComputeAsymptotics.MultiseriesExpansion... | true |
Turing.ToPartrec.Code.fix.sizeOf_spec | Mathlib.Computability.TuringMachine.Config | [
"Turing.ToPartrec.Code._sizeOf_inst",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Turing.ToPartrec.Code.fix",
"Turing.ToPartrec.Code"
] | true |
ContinuousMap.continuousAt | Mathlib.Topology.ContinuousMap.Basic | [
"ContinuousAt",
"ContinuousMap",
"ContinuousMap.instContinuousMapClass",
"TopologicalSpace",
"map_continuousAt",
"ContinuousMap.instFunLike",
"DFunLike.coe"
] | true |
LinearMap.mapMatrix_neg | Mathlib.Data.Matrix.Basic | [
"Matrix.module",
"AddCommGroup.toAddCommMonoid",
"Matrix",
"Matrix.addCommGroup",
"RingHom",
"AddCommGroup",
"Matrix.addCommMonoid",
"LinearMap",
"AddCommMonoid",
"Semiring",
"LinearMap.mapMatrix",
"Module",
"Semiring.toNonAssocSemiring",
"Eq",
"Neg.neg",
"rfl",
"LinearMap.instNeg"
] | true |
CategoryTheory.Limits.Types.Pushout.Rel'.inr_inl | Mathlib.CategoryTheory.Limits.Types.Pushouts | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Sum.inl",
"CategoryTheory.Limits.Types.Pushout.Rel'",
"Sum.inr",
"CategoryTheory.types",
"CategoryTheory.Limits.Types.Pushout.Rel'.inr_inl",
"CategoryTheory.Category.toCategoryStruct"
] | true |
_private.Mathlib.NumberTheory.FLT.Three.0.FermatLastTheoremForThreeGen.Solution.formula3._simp_1_1 | Mathlib.NumberTheory.FLT.Three | [
"Monoid",
"Units.val",
"Units",
"Monoid.toPow",
"HPow.hPow",
"Nat",
"instHPow",
"Units.val_pow_eq_pow_val",
"Eq.symm",
"Eq",
"Units.instMonoid"
] | false |
RelSeries.last_map | Mathlib.Order.RelSeries | [
"RelSeries.map",
"SetRel",
"RelSeries.last",
"RelHom.instFunLike",
"Membership.mem",
"Prod.mk",
"RelSeries",
"SetRel.Hom",
"Prod",
"Eq",
"Set.instMembership",
"DFunLike.coe",
"rfl"
] | true |
Matroid.IsBase.compl_isBase_of_dual | Mathlib.Combinatorics.Matroid.Dual | [
"Matroid.dual_isBase_iff'",
"Matroid.E",
"Matroid.dual",
"Matroid.IsBase",
"HasSubset.Subset",
"SDiff.sdiff",
"And",
"And.left",
"Iff.mp",
"Matroid",
"Set.instSDiff",
"Set.instHasSubset",
"Set"
] | true |
MeasureTheory.measure_union_lt_top_iff | Mathlib.MeasureTheory.Measure.MeasureSpaceDef | [
"MeasureTheory.measure_union_lt_top",
"MeasureTheory.Measure",
"Preorder.toLT",
"PartialOrder.toPreorder",
"Set.subset_union_right",
"Set.instUnion",
"Set.subset_union_left",
"MeasurableSpace",
"And",
"Iff",
"And.right",
"And.left",
"And.intro",
"LT.lt",
"Iff.intro",
"ENNReal",
"Meas... | true |
Lean.PrettyPrinter.Parenthesizer.Context._sizeOf_1 | Lean.PrettyPrinter.Parenthesizer | [
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.Context",
"instHAdd",
"Lean.PrettyPrinter.Parenthesizer.Context.rec",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"SizeOf.sizeOf",
"Bool",
"instAddNat",
"Lean.Name",
"OfNat.ofNat",
"Bool._sizeOf_inst"
] | false |
Lean.logInfo | Lean.Log | [
"Lean.MessageData",
"Lean.log",
"Lean.MonadLog",
"Lean.AddMessageContext",
"Unit",
"Lean.MessageSeverity.information",
"Monad",
"Bool.false",
"Lean.MonadOptions"
] | true |
ContinuousLinearEquiv.coe_inj | Mathlib.Topology.Algebra.Module.Equiv | [
"Function.Injective.eq_iff",
"RingHom",
"AddCommMonoid",
"RingHomInvPair",
"ContinuousLinearMap",
"ContinuousLinearEquiv.coe_injective",
"TopologicalSpace",
"Iff",
"ContinuousLinearEquiv",
"Semiring",
"Module",
"Semiring.toNonAssocSemiring",
"Eq",
"ContinuousLinearEquiv.toContinuousLinearM... | true |
Std.DTreeMap.isEmpty_keys | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.isEmpty",
"Ordering",
"Std.DTreeMap.inner",
"List.isEmpty",
"Bool",
"Std.DTreeMap.Internal.Impl.isEmpty_keys",
"Std.DTreeMap.keys",
"Eq"
] | true |
Finset.sdiff_eq_filter | Mathlib.Data.Finset.Basic | [
"instDecidableNot",
"Finset",
"Finset.instSDiff",
"Membership.mem",
"SDiff.sdiff",
"Finset.instSetLike",
"Finset.decidableMem",
"Finset.filter",
"Eq",
"Not",
"SetLike.instMembership",
"DecidableEq",
"_private.Mathlib.Data.Finset.Basic.0.Finset.sdiff_eq_filter._proof_1_1"
] | true |
_private.Std.Data.TreeMap.Raw.Lemmas.0.Std.TreeMap.Raw.Equiv.trans.match_1_1 | Std.Data.TreeMap.Raw.Lemmas | [
"Ordering",
"Std.DTreeMap.Raw.Equiv",
"Std.TreeMap.Raw.Equiv",
"Std.TreeMap.Raw.inner",
"Std.TreeMap.Raw",
"Std.TreeMap.Raw.Equiv.mk",
"Std.TreeMap.Raw.Equiv.casesOn"
] | false |
Nat.twoStepInduction | Mathlib.Data.Nat.Init | [
"Nat.brecOn",
"instOfNatNat",
"Nat.below",
"Nat.twoStepInduction.match_1",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.succ"
] | true |
Fin.coe_divNat | Batteries.Data.Fin.Lemmas | [
"instHDiv",
"HMul.hMul",
"HDiv.hDiv",
"instMulNat",
"Fin.val",
"Nat",
"Nat.instDiv",
"Fin",
"Eq",
"Fin.divNat",
"rfl",
"instHMul"
] | true |
Metric.hausdorffEDist_ne_top_of_nonempty_of_bounded | Mathlib.Topology.MetricSpace.HausdorffDistance | [
"le_max_right",
"Eq.mpr",
"Real.instLE",
"Real",
"Metric.hausdorffEDist_le_of_mem_edist",
"ENNReal.ofReal_le_ofReal_iff",
"PseudoMetricSpace.toBornology",
"Real.instZero",
"ENNReal.ofReal",
"congrArg",
"PartialOrder.toPreorder",
"dist_nonneg",
"Preorder.toLE",
"Membership.mem",
"Exists",... | true |
_private.Mathlib.MeasureTheory.Integral.IntervalIntegral.Slope.0.MonotoneOn.intervalIntegral_slope_le._proof_1_11 | Mathlib.MeasureTheory.Integral.IntervalIntegral.Slope | [
"instLawfulOrderLT_mathlib",
"of_eq_false",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.RArray.leaf",
"Lean.Grind.Field.toCommRing",
"False",
"Lean.Grind.Order.lt_unsat_k",
"Lean.Grind.and_eq_of_eq_true_right",
"Real.partialOrder",
"Real.instLE",
"Real",
"Lattice.toSemilatticeSup",
"Real.latti... | false |
continuousAt_sign_of_neg | Mathlib.Topology.Instances.Sign | [
"Eq.mpr",
"OrderTopology",
"Preorder.toLT",
"SignType.instOne",
"congrArg",
"ContinuousAt",
"Filter.Eventually",
"PartialOrder.toPreorder",
"setOf",
"SignType.instLinearOrder",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"nhds",
"PartialOrder",
"ContinuousAt.congr",
... | true |
_private.Lean.Meta.Tactic.Induction.0.Lean.MVarId.induction.match_1 | Lean.Meta.Tactic.Induction | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Nat",
"Option"
] | false |
PNat.XgcdType | Mathlib.Data.PNat.Xgcd | [
"PNat.XgcdType.mk"
] | true |
Valuation.is_topological_valuation | Mathlib.Topology.Algebra.ValuativeRel.ValuativeTopology | [
"Valuation.mem_nhds_zero_iff",
"Filter.instMembership",
"Units.val",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"CommRing",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"ValuationClass.t... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.