name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
ContinuousAffineEquiv.symm_apply_eq | Mathlib.Topology.Algebra.ContinuousAffineEquiv | [
"AddCommGroup.toAddCommMonoid",
"ContinuousAffineEquiv.instFunLike",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Equiv.symm_apply_eq",
"ContinuousAffineEquiv",
"TopologicalSpace",
"Iff",
"ContinuousAffineEquiv.symm",
"AddTorsor",
"AffineEquiv.toEquiv",
"ContinuousAffineEquiv.toAffineEquiv",
... | true |
_private.Std.Data.HashSet.RawLemmas.0.Std.HashSet.Raw.Equiv.symm.match_1_1 | Std.Data.HashSet.RawLemmas | [
"Std.HashSet.Raw.inner",
"Std.HashSet.Raw.Equiv.casesOn",
"Std.HashSet.Raw.Equiv",
"Unit",
"Std.HashSet.Raw.Equiv.mk",
"Std.HashMap.Raw.Equiv",
"Std.HashSet.Raw"
] | false |
_private.Init.Data.List.MinMaxIdx.0.List.maxIdxOn_eq_zero_iff._simp_1_1 | Init.Data.List.MinMaxIdx | [
"LE.le_opposite_iff",
"LE.le",
"LE",
"propext",
"Eq",
"LE.opposite"
] | false |
Quiver.Path.vertices_comp_get_length_eq._auto_1 | Mathlib.Combinatorics.Quiver.Path.Vertices | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Std.HashSet.Equiv.inter_right | Std.Data.HashSet.Lemmas | [
"Std.HashSet",
"Std.HashSet.Equiv.inner",
"LawfulHashable",
"Inter.inter",
"Std.HashSet.Equiv.mk",
"Std.HashMap.Equiv.inter_right",
"Unit",
"Std.HashSet.instInter",
"EquivBEq",
"Std.HashSet.inner",
"Std.HashSet.Equiv",
"Hashable",
"BEq"
] | true |
DirectLimit.instAddGroup._proof_12 | Mathlib.Algebra.Colimit.DirectLimit | [
"AddGroup.toSubtractionMonoid",
"instHSMul",
"AddMonoid.toAddZeroClass",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"Int",
"SubtractionMonoid.toSubNegMonoid",
"LE.le",
"Nat.cast",
"AddGroup",
"AddGroup.toSubNegMonoid",
"Nat",
"HSMul.hSMul",
"instNatCastInt",
"SubNe... | false |
Ordinal.type_pUnit | Mathlib.SetTheory.Ordinal.Basic | [
"instIsWellOrderEmptyRelationOfSubsingleton",
"emptyRelation",
"Ordinal.type",
"instSubsingletonPUnit",
"Ordinal.one",
"PUnit",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"rfl",
"Ordinal"
] | true |
_private.Lean.Compiler.LCNF.CompatibleTypes.0.Lean.Compiler.LCNF.InferType.Pure.compatibleTypesFull._sparseCasesOn_6 | Lean.Compiler.LCNF.CompatibleTypes | [
"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 |
Equicontinuous | Mathlib.Topology.UniformSpace.Equicontinuity | [
"UniformSpace",
"TopologicalSpace",
"EquicontinuousAt"
] | true |
SimpleGraph.binomialRandom_one | Mathlib.Probability.Combinatorics.BinomialRandomGraph.Defs | [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"MeasureTheory.Measure",
"congrArg",
"SimpleGraph.fromEdgeSet",
"Compl.compl",
"ProbabilityTheory.setBernoulli_one",
"ProbabilityTheory.setBernoulli",
"Measurable",
"Set.instMeasurableSpace",
"Real.semiring",
"SimpleGraph.fromEdgeSet_not... | true |
CommRing.directSumGCommRing | Mathlib.Algebra.DirectSum.Ring | [
"CommRing",
"Ring.directSumGRing",
"AddCommMonoid",
"CommRing.directSumGCommRing._proof_1",
"Ring.toAddCommGroup",
"AddCommMonoid.toAddMonoid",
"CommRing.toRing",
"DirectSum.GCommRing",
"DirectSum.GCommRing.mk"
] | true |
Std.Packages.LinearOrderOfOrdArgs.min_eq | Init.Data.Order.PackageFactories | [
"Std.LawfulOrderOrd",
"Std.Packages.LinearOrderOfOrdArgs",
"Ord",
"Std.TransOrd",
"instDecidableEqBool",
"Std.Packages.LinearOrderOfOrdArgs.min",
"Ord.compare",
"LE",
"Min",
"Bool.true",
"Std.Packages.LinearPreorderOfOrdArgs.ord",
"Bool",
"Std.Packages.LinearPreorderOfOrdArgs.transOrd",
"S... | true |
CategoryTheory.MorphismProperty.Comma.mapRightEq_hom_app_right | Mathlib.CategoryTheory.MorphismProperty.Comma | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.Comma.mapRightEq._proof_1",
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.Comma.instCategory",
"CategoryTheory.Functor.category",
"Ca... | true |
CochainComplex.HomComplex.Cocycle.coe_sub | Mathlib.Algebra.Homology.HomotopyCategory.HomComplex | [
"CochainComplex.HomComplex.instAddCommGroupCochain",
"AddGroupWithOne.toAddMonoidWithOne",
"CochainComplex.HomComplex.instAddCommGroupCocycle",
"HSub.hSub",
"AddCancelMonoid.toAddRightCancelMonoid",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Int",
"CategoryTheory.Preadditive",
"AddSubgroup",
... | true |
Perfection.quotientMulEquiv._proof_5 | Mathlib.RingTheory.Teichmuller | [
"Ideal.Quotient.commSemiring",
"RingHom.instRingHomClass",
"CommRing",
"MulEquiv.instEquivLike",
"Nat.Prime",
"MonoidHom.instFunLike",
"Semiring.toModule",
"Perfection",
"Perfection.coeffMonoidHom",
"Perfection.instCommMonoid",
"Perfection.teichmuller₀",
"MonoidHom",
"Monoid.toMulOneClass",
... | false |
toPrev.eq_1 | Mathlib.Algebra.Homology.BifunctorHomotopy | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"HomologicalComplex",
"AddZeroClass.toAddZero",
"ComplexShape.prev",
"ComplexShape",
"CategoryTheory.Preadditive",
"HomologicalComplex.xPrev",
"AddGroup.toSubNegMonoid",
"Pi.addZeroCl... | true |
CategoryTheory.instCategoryObjOppositeSimplexCategoryNerve._aux_5 | Mathlib.AlgebraicTopology.SimplicialSet.Nerve | [
"CategoryTheory.NatTrans.vcomp",
"Quiver.mk",
"CategoryTheory.Functor",
"Opposite",
"Quiver.Hom",
"PartialOrder.toPreorder",
"Preorder.smallCategory",
"instOfNatNat",
"instHAdd",
"Fin.instPartialOrder",
"HAdd.hAdd",
"Nat",
"CategoryTheory.types",
"SimplexCategory",
"instAddNat",
"Categ... | false |
cauchy_davenport_of_isMulTorsionFree | Mathlib.Combinatorics.Additive.CauchyDavenport | [
"instCompleteLinearOrderENat",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"HMul.hMul",
"ChainCompletePartialOrder.instOfCompleteLattice",
"IsMulTorsionFree",
"ENat.instNatCast",
"instTopENat",
"Monoid.toMulOneClass",
"instLinearOrderENat",
"congrArg",
"CommSemiring.toSemiring",
"Monoid.... | true |
Std.HashMap.Raw.beq | Std.Data.HashMap.Raw | [
"Std.DHashMap.Raw.Const.beq",
"Std.HashMap.Raw",
"Bool",
"Std.HashMap.Raw.inner",
"Hashable",
"BEq"
] | true |
HEq.ndrecOn | Init.Core | [
"HEq.rec",
"HEq"
] | true |
Finset.Nontrivial.ne_singleton | Mathlib.Data.Finset.Insert | [
"False",
"Finset",
"Finset.not_nontrivial_singleton",
"Ne",
"Finset.Nontrivial",
"Eq.ndrec",
"Finset.instSingleton",
"Singleton.singleton",
"Eq.symm",
"Eq"
] | true |
CategoryTheory.Bicategory.associatorNatIsoRightCat_inv_toNatTrans_app | Mathlib.CategoryTheory.Bicategory.Yoneda | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.toCatHom",
"CategoryTheory.Functor.comp",
"CategoryTheory.Cat.str",
"CategoryTheory.Cat.of",
"CategoryTheory.Bicategory.associatorNatIsoRightCat",
"CategoryTheory.Cat.instQuiver",
"CategoryTheory.Bicategory.toCategoryStr... | true |
conjneg_ne_one | Mathlib.Algebra.Star.Conjneg | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommSemiring.toSemiring",
"conjneg",
"Iff.not",
"Ne",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"CommSemiring",
"AddMonoidWithOne.toOne",
"conjneg_eq_one",
"AddGroup",
"Iff",
"Pi.instOne",
"StarRing",
"NonAssocSemiring.toNonUnitalNonAssocSemirin... | true |
lTensor.inverse_of_rightInverse_apply | Mathlib.LinearAlgebra.TensorProduct.RightExactness | [
"Function.Exact",
"Submodule.Quotient.eq",
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"Submodule.Quotient.addCommMonoid",
"CommRing",
"map_sub",
"SemilinearMapClass.distribMulActionSemiHomClass",
"le_comap_range_lTensor",
"congrArg",
"CommSemiring.toSemir... | true |
CategoryTheory.cartesianClosedOfReflective'._proof_3 | Mathlib.CategoryTheory.Monoidal.Closed.Ideal | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.PreservesLimitsOfShape.preservesLimit",
"CategoryTheory.Functor.comp",
"CategoryTheory.monadicOfReflective",
"Category... | false |
Lean.Widget.InfoPopup.rec | Lean.Server.FileWorker.WidgetRequests | [
"String",
"Lean.Widget.InfoPopup",
"Lean.Widget.CodeWithInfos",
"Lean.Widget.InfoPopup.mk",
"Option"
] | false |
Lean.Lsp.DiagnosticSeverity.error.sizeOf_spec | Lean.Data.Lsp.Diagnostics | [
"Lean.Lsp.DiagnosticSeverity",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Lean.Lsp.DiagnosticSeverity.error",
"Eq.refl",
"Lean.Lsp.DiagnosticSeverity._sizeOf_inst",
"OfNat.ofNat",
"Eq"
] | true |
LTSeries.last_map | Mathlib.Order.RelSeries | [
"Preorder.toLT",
"StrictMono",
"RelSeries.last",
"setOf",
"FiniteDimensionalOrder.match_1",
"LTSeries",
"LT.lt",
"LTSeries.map",
"Prod",
"Eq",
"rfl",
"Preorder"
] | true |
Lean.Meta.Match.Extension.Entry.mk | Lean.Meta.Match.MatcherInfo | [
"Lean.Meta.Match.MatcherInfo",
"Lean.Meta.Match.Extension.Entry.mk",
"Lean.Name",
"Lean.Meta.Match.Extension.Entry"
] | true |
NonUnitalStarSubalgebra.prod | Mathlib.Algebra.Star.NonUnitalSubalgebra | [
"Set.instSProd",
"NonUnitalSubalgebra",
"SProd.sprod",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"NonUnitalStarSubalgebra.prod._proof_4",
"Prod.instNonUnitalNonAssocSemiring",
"AddZeroClass.toAddZero",
"NonUnitalStarSubalgebra.prod._proof_2",
"NonUnitalSubsemiring.mk",
"NonUnitalSta... | true |
NonUnitalCommCStarAlgebra.toIsScalarTower | Mathlib.Analysis.CStarAlgebra.Classes | [
"instSMulOfMul",
"NonUnitalNonAssocRing.toMul",
"NonUnitalCommCStarAlgebra",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"NormedSpace.toModule",
"Complex.instNormedField",
"NormedField.toField",
"NonUnitalRing.toNonUnitalNonAssocRing",
"Field.toSemifield",
"NonUnitalNormedRing.toNonUnitalRi... | true |
SimpleGraph.maximumIndepSet_exists | Mathlib.Combinatorics.SimpleGraph.Clique | [
"SimpleGraph.IsMaximumIndepSet",
"congrArg",
"Compl.compl",
"Finset",
"Finite",
"Exists",
"_private.Mathlib.Combinatorics.SimpleGraph.Clique.0.SimpleGraph.maximumIndepSet_exists._simp_1_2",
"SimpleGraph",
"funext",
"SimpleGraph.instCompl",
"True",
"SimpleGraph.IsMaximumClique",
"of_eq_true",... | true |
CategoryTheory.Functor.instAdditiveObjPostcompose₂ | Mathlib.CategoryTheory.Preadditive.AdditiveFunctor | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.instAdditiveObjWhiskeringRight",
"CategoryTheory.Functor.postcompose₂",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.category",
"CategoryTheory.functorCategoryPreadditive",
"CategoryTheory.Functor.comp",
"inferInstance",
"id",
"Catego... | true |
VitaliFamily.ae_eventually_measure_zero_of_singular | Mathlib.MeasureTheory.Covering.Differentiation | [
"NNReal.instTopologicalSpace",
"MeasureTheory.ae",
"Iff.mpr",
"Eq.mpr",
"ENNReal.instAdd",
"_private.Mathlib.MeasureTheory.Covering.Differentiation.0.VitaliFamily.ae_eventually_measure_zero_of_singular._simp_1_4",
"MulOne.toOne",
"le_refl",
"Semigroup.toMul",
"ENNReal.ofNNReal",
"instHSMul",
"... | true |
PosMulReflectLE.toPosMulStrictMono | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs | [
"not_le",
"Preorder.toLT",
"HMul.hMul",
"LinearOrder",
"PartialOrder.toPreorder",
"PosMulReflectLE",
"Preorder.toLE",
"Mul",
"PosMulStrictMono.mk",
"LE.le",
"le_of_mul_le_mul_left",
"LT.lt",
"Iff.mp",
"PosMulStrictMono",
"Zero.toOfNat0",
"LT.lt.not_ge",
"OfNat.ofNat",
"LinearOrder.... | true |
Lean.Parser.Term.unsafe._regBuiltin.Lean.Parser.Term.unsafe_1 | Lean.Parser.Term | [
"IO",
"Unit",
"Lean.Parser.addBuiltinLeadingParser",
"Lean.Parser.Term.unsafe",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | false |
Int16.or_self | Init.Data.SInt.Bitwise | [
"instHOrOfOrOp",
"Int16",
"BitVec",
"BitVec.or_self",
"instOfNatNat",
"HOr.hOr",
"Nat",
"instOrOpInt16",
"Int16.toBitVec",
"Iff.mp",
"OfNat.ofNat",
"Int16.toBitVec_inj",
"Eq"
] | true |
List.zip_eq_nil_iff._simp_1 | Init.Data.List.Zip | [
"List.zip",
"List.zip_eq_nil_iff",
"List",
"propext",
"Or",
"Prod",
"Eq",
"List.nil"
] | false |
_private.Lean.Compiler.NameDemangling.0.Lean.Name.Demangle.skipWhile.eq_def | Lean.Compiler.NameDemangling | [
"String.Pos.next",
"_private.Lean.Compiler.NameDemangling.0.Lean.Name.Demangle.skipWhile._unary.eq_def",
"String",
"id",
"instDecidableEqBool",
"dite",
"Bool.true",
"_private.Lean.Compiler.NameDemangling.0.Lean.Name.Demangle.skipWhile",
"String.endPos",
"String.Pos",
"Bool",
"Char",
"String.... | true |
Set.OrdConnected.predOrder._proof_10 | Mathlib.Order.SuccPred.Basic | [
"Eq.mpr",
"Decidable.casesOn",
"instReflLe",
"congrArg",
"PartialOrder.toPreorder",
"Decidable",
"Classical.propDecidable",
"Preorder.toLE",
"Std.le_refl._simp_1",
"Membership.mem",
"Subtype.instReflLE",
"PartialOrder",
"Set.Elem",
"dif_pos",
"id",
"Subtype",
"LE.le",
"dif_neg",
... | false |
Nat.factorial_coe_dvd_prod | Mathlib.Data.Nat.Factorial.BigOperators | [
"Iff.mpr",
"Int.instCommMonoid",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Dvd.dvd",
"Int.natCast_ne_zero",
"Nat.factorial_dvd_ascFactorial",
"AddMonoid.toAddSemigroup",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"AddGroupWithOne.toAddMonoidWithOne",
"Membership.mem",
"Ex... | true |
Finset.coe_insert | Mathlib.Data.Finset.Insert | [
"_private.Mathlib.Data.Finset.Insert.0.Finset.coe_insert._proof_1_1",
"Finset",
"Insert.insert",
"Finset.instInsert",
"Set.instInsert",
"SetLike.coe",
"Finset.instSetLike",
"Eq",
"DecidableEq",
"Set"
] | true |
_private.Mathlib.Data.List.SplitBy.0.List.getLast?.match_1.eq_2 | Mathlib.Data.List.SplitBy | [
"List.cons",
"List",
"Unit",
"Eq.refl",
"Eq",
"List.getLast?.match_1",
"List.nil"
] | true |
ContinuousMap.notMem_idealOfSet | Mathlib.Topology.ContinuousMap.Ideals | [
"Mathlib.Tactic.Push.not_forall_eq",
"Eq.mpr",
"Semiring.toModule",
"congrArg",
"IsTopologicalSemiring",
"Compl.compl",
"ContinuousMap",
"Iff.rfl",
"Membership.mem",
"Exists",
"id",
"ContinuousMap.instSemiringOfIsTopologicalSemiring",
"Ne",
"Ideal",
"Set.instCompl",
"Classical.not_imp.... | true |
List.dropSlice.eq_1 | Batteries.Data.List.Basic | [
"List.dropSlice.match_1",
"List.dropSlice.eq_def",
"List.cons",
"List",
"List.drop",
"Nat",
"List.dropSlice",
"Eq.refl",
"Eq",
"Eq.trans",
"List.nil"
] | true |
_private.Mathlib.Logic.Equiv.List.0.Encodable.encodeList.match_1.splitter | Mathlib.Logic.Equiv.List | [
"List.cons",
"List",
"Unit",
"Encodable.encodeList.match_1",
"List.nil"
] | true |
Std.Sat.AIG.Decl.relabel.match_1 | Std.Sat.AIG.Relabel | [
"Std.Sat.AIG.Decl.casesOn",
"Unit.unit",
"Std.Sat.AIG.Decl",
"Unit",
"Std.Sat.AIG.Decl.gate",
"Std.Sat.AIG.Decl.atom",
"Std.Sat.AIG.Decl.false",
"Std.Sat.AIG.Fanin"
] | false |
_private.Std.Data.DTreeMap.Internal.Balancing.0.Std.DTreeMap.Internal.Impl.balance!_eq_balanceₘ._proof_1_34 | Std.Data.DTreeMap.Internal.Balancing | [
"Lean.Omega.LinearCombo.coordinate_eval_6",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"HMul.hMul",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.a... | false |
CategoryTheory.enrichedFunctorTypeEquivFunctor._proof_2 | Mathlib.CategoryTheory.Enriched.Basic | [
"CategoryTheory.categoryOfEnrichedCategoryType",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.typesCartesianMonoidalCategory",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"TypeCat.ofHom",
"TypeCat.Fun.toFun",
"CategoryTheory... | false |
_private.Std.Data.DTreeMap.Internal.Balancing.0.Std.DTreeMap.Internal.Impl.balanceLErase.match_3.eq_3 | Std.Data.DTreeMap.Internal.Balancing | [
"Std.DTreeMap.Internal.Impl.balanceLErase.match_3",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.inner",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Eq.refl",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.BalanceLErasePrecon... | true |
Lean.Parser.Tactic.Conv._aux_Init_Conv___macroRules_Lean_Parser_Tactic_Conv_convIntro____1 | Init.Conv | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.Syntax.getArgs",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"Lean.Name.mkStr5",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Array.mkArray0",
"Le... | false |
AlgebraicGeometry.Scheme.Cover.RelativeGluingData.glued | Mathlib.AlgebraicGeometry.RelativeGluing | [
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"AlgebraicGeometry.Scheme.OpenCover",
"CategoryTheory.PreZeroHypercover.I₀",
"CategoryTheory.Limits.colimit",
"AlgebraicGeometry.Scheme.Cover.RelativeGluingData",
"Quiver.IsThin",
"AlgebraicGeometry.Scheme.Cover.RelativeGluingData.g... | true |
ArchimedeanClass.liftOrderHom_mk | Mathlib.Algebra.Order.Archimedean.Class | [
"Eq.ge",
"ArchimedeanClass.liftOrderHom",
"AddCommGroup.toAddCommMonoid",
"ArchimedeanClass.lift_mk",
"LinearOrder",
"ArchimedeanClass.instLinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"PartialOrder",
"AddCommGroup",
"DistribLattice.toLattice",
"E... | true |
CategoryTheory.GrothendieckTopology.diagramPullback._proof_1 | Mathlib.CategoryTheory.Sites.Plus | [
"CategoryTheory.Limits.multiequalizer",
"CategoryTheory.Functor.op",
"CategoryTheory.Limits.MulticospanShape.snd",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Limits.Multiequalizer.condition",
"CategoryTheory.GrothendieckTopology.Cover.shape",
"Category... | false |
Subsemiring.closure_singleton_one | Mathlib.Algebra.Ring.Subsemiring.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Subsemiring.closure",
"congrArg",
"Subsemiring.instBot",
"cast",
"Set.instSingletonSet",
"AddMonoidWithOne.toNatCast",
"Subsemiring.closure_singleton_natCast",
"instOfNatNat",
"Bot.bot",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Subsemiring",
"Na... | true |
Std.ExtHashMap.getD_inter | Std.Data.ExtHashMap.Lemmas | [
"Std.ExtHashMap.getD",
"Std.ExtHashMap.inner",
"Membership.mem",
"LawfulHashable",
"Std.ExtHashMap",
"Inter.inter",
"Std.ExtHashMap.instDecidableMem",
"Std.ExtDHashMap.Const.getD_inter",
"EquivBEq",
"Std.ExtHashMap.instInterOfEquivBEqOfLawfulHashable",
"Hashable",
"Std.ExtHashMap.instMembershi... | true |
Submonoid.LocalizationMap.map_surjective_of_surjOn | Mathlib.GroupTheory.MonoidLocalization.Maps | [
"Eq.mpr",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"Submonoid.LocalizationMap.mk'",
"Set.SurjOn",
"Subtype.casesOn",
"Membership.mem",
"Exists",
"Submonoid.LocalizationMap.map_mk'",
"id",
"Subtype",
"Subtype.mk",
"And.casesOn",
"MulOneClass.toMulOne",
... | true |
Lean.Meta.Grind.AC.EqCnstrProof.ctorIdx | Lean.Meta.Tactic.Grind.AC.Types | [
"Lean.Meta.Grind.AC.EqCnstr",
"Lean.Grind.AC.Expr",
"Lean.Expr",
"Lean.Meta.Grind.AC.EqCnstrProof.casesOn",
"Lean.Meta.Grind.AC.EqCnstrProof",
"Nat",
"Bool",
"Lean.Grind.AC.Var",
"Lean.Grind.AC.Seq"
] | false |
Lean.Compiler.LCNF.FloatLetIn.BaseFloatContext.mk | Lean.Compiler.LCNF.FloatLetIn | [
"Lean.Compiler.LCNF.Purity.pure",
"List",
"Lean.Compiler.LCNF.CodeDecl",
"Lean.Compiler.LCNF.FloatLetIn.BaseFloatContext.mk",
"Lean.Compiler.LCNF.FloatLetIn.BaseFloatContext"
] | true |
Subfield.rank_comap | Mathlib.FieldTheory.Relrank | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Subfield.relrank",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Cardinal",
"congrArg",
"Cardinal.lift",
"RingHom",
"Membership.mem",
"Field.toDivisionRing",
"DivisionRing.toDivisionSemiring",
"Eq.mp",
"Subtype",
"NonUnitalNonAssocR... | true |
ContinuousLinearMap.ebound | Mathlib.Analysis.Normed.Operator.Basic | [
"ENNReal.ofNNReal",
"Preorder.toLT",
"SeminormedAddCommGroup",
"HMul.hMul",
"NormedSpace",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"RingHom",
"RingHomIsome... | true |
List.rotate_eq_nil_iff | Mathlib.Data.List.Rotate | [
"False",
"Nat.recAux",
"congrArg",
"List.append_eq_nil_iff._simp_1",
"False.elim",
"List.rotate_cons_succ",
"noConfusion_of_Nat",
"List.cons_ne_self._simp_1",
"List.rotate_nil",
"instOfNatNat",
"List.cons",
"iff_self",
"instHAppendOfAppend",
"List",
"instHAdd",
"And",
"Iff",
"HAdd.... | true |
SubMulAction.ofFixingSubgroup_equivariantMap.eq_1 | Mathlib.GroupTheory.GroupAction.SubMulAction.OfFixingSubgroup | [
"SubMulAction.instSetLike",
"MonoidHom.instFunLike",
"instSMulOfMul",
"MonoidHom",
"Monoid.toMulOneClass",
"SubMulAction.ofFixingSubgroup_equivariantMap._proof_1",
"Subgroup.subtype",
"fixingSubgroup",
"Subgroup.mul",
"Group",
"Membership.mem",
"Subgroup.instMulAction",
"Subtype",
"DivInvM... | true |
Ideal.comap._proof_6 | Mathlib.RingTheory.Ideal.Maps | [
"_private.Mathlib.RingTheory.Ideal.Maps.0.Ideal.comap._simp_2",
"Eq.mpr",
"instHSMul",
"Semiring.toModule",
"HMul.hMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Eq.mp",
"id",
"DistribSMul.toSMulZeroClass",
"Idea... | false |
Int64.toInt_maxValue | Init.Data.SInt.Lemmas | [
"instPowNat",
"Int64.toInt",
"HSub.hSub",
"Int64.maxValue",
"instOfNatNat",
"Int",
"Int.instNatPow",
"instHSub",
"HPow.hPow",
"instOfNat",
"Nat",
"Int.instSub",
"instHPow",
"OfNat.ofNat",
"Eq",
"rfl"
] | true |
CategoryTheory.IsFilteredOrEmpty | Mathlib.CategoryTheory.Filtered.Basic | [
"CategoryTheory.IsFilteredOrEmpty.mk",
"CategoryTheory.Category"
] | true |
Std.TreeMap.isEmpty_inter_iff | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.instInter",
"Std.TreeMap.inner",
"Membership.mem",
"Ordering",
"Std.DTreeMap.isEmpty_inter_iff",
"Std.TransCmp",
"Std.TreeMap.isEmpty",
"Inter.inter",
"Bool.true",
"Iff",
"Std.TreeMap.instMembership",
"Bool",
"Eq",
"Not",
"Std.TreeMap"
] | true |
_private.Init.Meta.Defs.0.Lean.Name.hasNum._sunfold | Init.Meta.Defs | [
"_private.Init.Meta.Defs.0.Lean.Name.hasNum",
"String",
"_private.Init.Meta.Defs.0.Lean.Name.hasNum.match_1",
"Bool.true",
"Unit",
"Nat",
"Bool",
"Lean.Name",
"Bool.false"
] | false |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Proof.0.Lean.Meta.Grind.Arith.Cutsat.mkMulEqProof.go | Lean.Meta.Tactic.Grind.Arith.Cutsat.Proof | [
"Inhabited.default",
"ReaderT",
"Lean.Meta.Grind.instInhabitedGoalM",
"Lean.Expr",
"IO.RealWorld",
"Int",
"Array",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Proof.0.Lean.Meta.Grind.Arith.Cutsat.ProofM.Context",
"_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.Proof.0.Lean.Meta.Grind.Arith.Cutsat.Pr... | true |
ZeroHom.zero_comp | Mathlib.Algebra.Group.Hom.Defs | [
"ZeroHom.comp",
"ZeroHom",
"Zero.toOfNat0",
"instZeroZeroHom",
"OfNat.ofNat",
"Eq",
"rfl",
"Zero"
] | true |
_private.Mathlib.CategoryTheory.Functor.TypeValuedFlat.0.CategoryTheory.FunctorToTypes.fromOverFunctorElementsEquivalence._proof_5 | Mathlib.CategoryTheory.Functor.TypeValuedFlat | [
"CategoryTheory.categoryOfElements",
"CategoryTheory.Over",
"CategoryTheory.Functor.Elements",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.elementsMk",
"CategoryTheory.Over.Hom.left",
... | false |
_private.Mathlib.SetTheory.ZFC.Rank.0.PSet.rank_powerset._simp_1_2 | Mathlib.SetTheory.ZFC.Rank | [
"PSet.instHasSubset",
"PSet.instMembership",
"PSet.powerset",
"Membership.mem",
"PSet.mem_powerset",
"HasSubset.Subset",
"PSet",
"propext",
"Eq"
] | false |
Lean.ProjectionFunctionInfo.mk | Lean.ProjFns | [
"Lean.ProjectionFunctionInfo",
"Nat",
"Bool",
"Lean.Name",
"Lean.ProjectionFunctionInfo.mk"
] | true |
CFC.rpow_sqrt_nnreal | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic | [
"Real.instIsOrderedRing",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"IsSelfAdjoint",
"Real.partialOrder",
"Real.instLE",
"Real",
"Algebra.to_smulCommClass",
"DivInvMonoid.toInv",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instStarRingReal",
"InvOneClass.toOne",
"HMul.h... | true |
Real.mk_add | Mathlib.Data.Real.Basic | [
"Real",
"Real.equivCauchy._proof_1",
"abs",
"congrArg",
"IsAbsoluteValue.abs_isAbsoluteValue",
"Rat",
"_private.Mathlib.Data.Real.Basic.0.Real.mk_add._simp_1_2",
"Rat.linearOrder",
"Real.ofCauchy",
"Rat.instLattice",
"Rat.instDivisionRing",
"DivisionRing.toRing",
"CauSeq.Completion.mk",
"C... | true |
LieModule.isLieAbelian_of_ker_traceForm_eq_bot | Mathlib.Algebra.Lie.TraceForm | [
"LieAlgebra.toModule",
"Eq.mpr",
"Submodule",
"IsDomain",
"CommRing",
"Semiring.toModule",
"_private.Mathlib.Algebra.Lie.TraceForm.0.LieModule.isLieAbelian_of_ker_traceForm_eq_bot._simp_1_1",
"LieModule.lowerCentralSeries_one_inf_center_le_ker_traceForm",
"LieRing.toAddCommGroup",
"congrArg",
"C... | true |
SubMulAction.instOne | Mathlib.GroupTheory.GroupAction.SubMulAction.Pointwise | [
"Monoid",
"instHSMul",
"One",
"One.mk",
"SubMulAction.instOne._proof_1",
"SubMulAction.mk",
"MulAction",
"Monoid.toSemigroup",
"One.toOfNat1",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"Set.range",
"MulAction.toSemigroupAction",
"OfNat.ofNat",
"SubMulAction"
] | true |
Function.const_inv | Mathlib.Algebra.Notation.Pi.Defs | [
"Inv",
"Pi.instInv",
"Inv.inv",
"Function.const",
"Eq",
"rfl"
] | true |
instOrderBotSubtypeIsIdempotentElem._proof_1 | Mathlib.Algebra.Order.Ring.Idempotent | [
"IsIdempotentElem.zero",
"MulZeroClass.toMul",
"CommMonoidWithZero.toMonoidWithZero",
"IsIdempotentElem",
"MonoidWithZero.toMulZeroOneClass",
"CommMonoidWithZero",
"Zero.toOfNat0",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"MulZeroClass.toZero"
] | false |
_private.Std.Sat.AIG.RefVecOperator.Map.0.Std.Sat.AIG.RefVec.denote_map._proof_1_1 | Std.Sat.AIG.RefVecOperator.Map | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",... | false |
OpenSubgroup.instOrderTop._proof_1 | Mathlib.Topology.Algebra.OpenSubgroup | [
"OpenSubgroup",
"Set.subset_univ",
"Set.univ",
"Group",
"OpenSubgroup.instSetLike",
"HasSubset.Subset",
"TopologicalSpace",
"SetLike.coe",
"Set.instHasSubset",
"Set"
] | false |
initFn._@.Mathlib.Tactic.Attr.Register.2899626838._hygCtx._hyg.24 | Mathlib.Tactic.Attr.Register | [
"Lean.Name.mkNum",
"IO",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.Meta.Simp.Simprocs",
"Option.none",
"Lean.Meta.Simp.registerSimprocAttr",
"Nat",
"IO.Ref",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.Meta.Simp.SimprocExtension"
] | false |
BddDistLat.Hom.Simps.hom | Mathlib.Order.Category.BddDistLat | [
"BddDistLat.isBoundedOrder",
"BddDistLat.instDistribLatticeCarrier",
"BddDistLat.Hom",
"BddDistLat",
"DistribLattice.toLattice",
"BddDistLat.Hom.hom",
"BoundedLatticeHom",
"BddDistLat.toDistLat",
"DistLat.carrier"
] | true |
Lean.Server.RequestContext | Lean.Server.Requests | [
"Lean.Server.RequestContext.mk"
] | true |
AlgebraicGeometry.Scheme.Modules.Hom | Mathlib.AlgebraicGeometry.Modules.Sheaf | [
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.PresheafedSpace.carrier",
"TopologicalSpace.Opens.instPartialOrder",
"CommRingCat",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"CommRingCat.instCategory",
"Opens.grothendieckTopology",
"Preorder.smallCategory",
"AlgebraicGeometry.LocallyRing... | true |
Quaternion.imJ_coe | Mathlib.Algebra.Quaternion | [
"Quaternion.coe",
"NegZeroClass.toNeg",
"CommRing",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"AddMonoidWithOne.toOne",
"CommRing.toCommSemiring",
"Ring.... | true |
ENNReal.instSemilatticeSup._aux_1 | Mathlib.Data.ENNReal.Basic | [
"WithTop.map₂",
"SemilatticeSup.toMax",
"NNReal.instSemilatticeSup",
"NNReal",
"Max.max",
"ENNReal"
] | false |
Polynomial.instCommRingUniversalFactorizationRing._proof_25 | Mathlib.RingTheory.Polynomial.UniversalFactorizationRing | [
"Polynomial.instCommRingUniversalFactorizationRing._aux_1",
"Mul.mk",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"Semigroup.toMul",
"CommRing",
"Semiring.toModule",
"Equiv.instEquivLike",
"One.mk",
"HMul.hMul",
"Polynomial.MonicDegreeEq",
"Polynomial.instCommRingUniversalFactorizatio... | false |
LinearEquiv.extendScalarsOfSurjective | Mathlib.Algebra.Algebra.Basic | [
"LinearEquiv.mk",
"Algebra.algebraMap",
"LinearEquiv.extendScalarsOfSurjective._proof_3",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Algebra",
"RingHom",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"LinearEquiv.extendScalarsOfSurj... | true |
Localization.AtPrime.mapPiEvalRingHom_comp_algebraMap | Mathlib.RingTheory.Localization.AtPrime.Basic | [
"RingHom.instRingHomClass",
"Algebra.algebraMap",
"OreLocalization.instAlgebra",
"CommSemiring.toSemiring",
"Localization.AtPrime",
"Localization.localRingHom._proof_2",
"Localization.AtPrime.mapPiEvalRingHom",
"RingHom",
"IsLocalization.map_comp",
"Ideal.IsPrime.comap",
"Algebra.id",
"Localiz... | true |
notation_class | Mathlib.Tactic.Simps.NotationClass | [
"Lean.ParserDescr.nonReservedSymbol",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.const",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1"
] | true |
FreeRing.coe_sub | Mathlib.RingTheory.FreeCommRing | [
"Eq.mpr",
"RingHom.instRingHomClass",
"RingHomClass.toAddMonoidHomClass",
"map_sub",
"FreeCommRing",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"HSub.hSub",
"instCommRingFreeCommRing",
"instRingFreeRing",
"RingHom",
"id",
"SubtractionMonoid.toSubNegMonoid",
"Sub... | true |
_private.Lean.Meta.ExprDefEq.0.Lean.Meta.isEtaUnassignedMVar._sparseCasesOn_1 | Lean.Meta.ExprDefEq | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
CategoryTheory.ShortComplex.homologyπ | Mathlib.Algebra.Homology.ShortComplex.Homology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.leftHomologyπ",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.HasHomology",
"CategoryTheory.ShortComplex.leftHomology",
"CategoryTheory.ShortComplex.homology",
... | true |
Topology.IsLowerSet.closure_eq_upperClosure | Mathlib.Topology.Order.UpperLowerSetTopology | [
"UpperSet",
"UpperSet.instSetLike",
"Topology.IsLowerSet",
"upperClosure",
"Preorder.toLE",
"Topology.IsUpperSet.closure_eq_lowerClosure",
"TopologicalSpace",
"SetLike.coe",
"closure",
"OrderDual.instTopologicalSpace",
"OrderDual.instIsUpperSet",
"OrderDual",
"OrderDual.instPreorder",
"Eq"... | true |
CategoryTheory.OplaxFunctor.PseudoCore | Mathlib.CategoryTheory.Bicategory.Functor.Oplax | [
"CategoryTheory.Bicategory",
"CategoryTheory.OplaxFunctor",
"CategoryTheory.OplaxFunctor.PseudoCore.mk"
] | true |
Unitary.spectrum_subset_slitPlane_iff_norm_lt_two | Mathlib.Analysis.CStarAlgebra.Unitary.Connected | [
"Norm.norm",
"Complex.subset_slitPlane_iff_of_subset_sphere",
"Real",
"NormedRing.toRing",
"spectrum",
"Ring.toNonAssocRing",
"Monoid.toMulOneClass",
"AddGroupWithOne.toAddGroup",
"congrArg",
"unitary",
"Nat.instAtLeastTwoHAddOfNat",
"Complex.instNormedField",
"Unitary.norm_sub_one_lt_two_if... | true |
Std.TreeSet.Raw.le_min! | Std.Data.TreeSet.Raw.Lemmas | [
"Std.TreeSet.Raw.WF.out",
"Std.TreeSet.Raw.min!",
"Membership.mem",
"Ordering",
"Std.TreeSet.Raw.instMembership",
"Std.TransCmp",
"Bool.true",
"Std.TreeSet.Raw",
"Unit",
"Iff",
"Std.TreeMap.Raw.le_minKey!",
"Bool",
"Inhabited",
"Std.TreeSet.Raw.isEmpty",
"Ordering.isLE",
"Bool.false",
... | true |
MeasureTheory.isMulLeftInvariant_map | Mathlib.MeasureTheory.Group.Measure | [
"MulHom",
"Eq.mpr",
"MeasureTheory.Measure",
"HMul.hMul",
"MeasureTheory.map_mul_left_eq_self",
"congrArg",
"MeasureTheory.Measure.IsMulLeftInvariant.mk",
"Measurable",
"MeasurableMul.measurable_const_mul",
"Mul",
"Function.comp",
"Exists",
"Eq.rec",
"id",
"MeasurableMul",
"MeasurableS... | true |
CategoryTheory.Limits.binaryBiconeOfIsSplitEpiOfKernel._proof_7 | Mathlib.CategoryTheory.Preadditive.Biproducts | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.IsSplitEpi",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.IsSplitEpi.id",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.section_",
"of_eq_true",
"CategoryTheory.Category.toCate... | false |
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