name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.SimplicialObject.augmentOfIsTerminal._proof_2 | Mathlib.AlgebraicTopology.SimplicialObject.Basic | [
"CategoryTheory.Limits.IsTerminal.from",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.SimplicialObject.const",
"CategoryTheory.Limits.IsTerminal",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.id",
"CategoryTheory.Category.comp_id",
... | false |
_private.Init.Data.List.Sublist.0.List.cons_subset_cons._simp_1_1 | Init.Data.List.Sublist | [
"Membership.mem",
"List.cons",
"List",
"List.instMembership",
"propext",
"Or",
"List.mem_cons",
"Eq"
] | false |
FirstOrder.Language.DefinableSet.coe_compl | Mathlib.ModelTheory.Definability | [
"Compl.compl",
"Set.instCompl",
"FirstOrder.Language.DefinableSet",
"FirstOrder.Language.Structure",
"SetLike.coe",
"FirstOrder.Language",
"FirstOrder.Language.DefinableSet.instCompl",
"FirstOrder.Language.DefinableSet.instSetLike",
"Eq",
"rfl",
"Set"
] | true |
Std.Time.Month.instTransOrdOffset | Std.Time.Date.Unit.Month | [
"Std.TransOrd",
"Std.Time.Month.instOrdOffset",
"_private.Std.Time.Date.Unit.Month.0.Std.Time.Month.instTransOrdOffset._proof_1",
"Std.Time.Month.Offset"
] | true |
Lean.Server.Test.Runner.Client.instFromJsonInteractiveGoal.fromJson | Lean.Server.Test.Runner | [
"Pure.pure",
"Lean.Server.Test.Runner.Client.instFromJsonRpcRef",
"Lean.Json",
"Lean.instFromJsonString",
"Monad.toApplicative",
"String",
"Lean.instFromJsonOption",
"Lean.Server.Test.Runner.Client.SubexprInfo",
"Lean.Server.Test.Runner.Client.InteractiveGoal",
"Lean.Server.Test.Runner.Client.Inte... | true |
not_isLeftRegular_zero | Mathlib.Algebra.GroupWithZero.Regular | [
"Nontrivial",
"Iff.mpr",
"MulZeroClass.toMul",
"MulZeroClass",
"IsLeftRegular",
"not_isLeftRegular_zero_iff",
"Zero.toOfNat0",
"OfNat.ofNat",
"Not",
"MulZeroClass.toZero"
] | true |
MeasureTheory.VectorMeasure.«_aux_Mathlib_MeasureTheory_VectorMeasure_Integral___delab_app_MeasureTheory_VectorMeasure_term∫ᵛ_,_∂[_;_]_1» | Mathlib.MeasureTheory.VectorMeasure.Integral | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Mathlib.Notation3.MatchState.empty",
"Mathlib.Notation3.withHeadRefIfTagAppFns",
"Mathlib.Notation3.matchApp",
"Lean.PrettyPrinter.Delaborator.instMonadReaderOfSubExprDelabM",
"Lean.SourceInfo",
"Lean.PrettyPrinter... | false |
FreeAlgebra.cardinalMk_le_max_lift | Mathlib.Algebra.FreeAlgebra.Cardinality | [
"Nontrivial",
"Lattice.toSemilatticeSup",
"Cardinal.instOne",
"Cardinal",
"PartialOrder.toPreorder",
"Cardinal.lift",
"FreeAlgebra.cardinalMk_eq_lift",
"Cardinal.mk",
"SemilatticeSup.toMax",
"isEmpty_or_nonempty",
"subsingleton_or_nontrivial",
"Eq.le",
"Eq.trans_le",
"Cardinal.aleph0",
"... | true |
CommMonoid.mul_comm | Mathlib.Algebra.Group.Defs | [
"Semigroup.toMul",
"HMul.hMul",
"CommMonoid.toMonoid",
"Monoid.toSemigroup",
"Eq",
"CommMonoid",
"instHMul"
] | true |
Real.antitone_rpow_of_base_le_one | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"Real.instPow",
"Real.partialOrder",
"Real.instLE",
"Real",
"Preorder.toLT",
"lt_or_eq_of_le",
"Real.instZero",
"instReflLe",
"congrArg",
"PartialOrder.toPreorder",
"Real.instLT",
"Preorder.toLE",
"Std.le_refl._simp_1",
"Real.one_rpow",
"LE.le",
"Or.casesOn",
"Real.instOne",
"Antit... | true |
_private.Mathlib.Probability.Process.Stopping.0.MeasureTheory.measurable_stoppedValue._simp_1_4 | Mathlib.Probability.Process.Stopping | [
"Set.mem_inter_iff",
"Membership.mem",
"Set.instInter",
"Inter.inter",
"And",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
Function.comp_def._simp_2 | Mathlib.Order.OmegaCompletePartialOrder | [
"Function.comp",
"Function.comp_def",
"Eq.symm",
"Eq"
] | false |
TangentBundle.mem_chart_target_iff._simp_1 | Mathlib.Geometry.Manifold.VectorBundle.Tangent | [
"TangentBundle",
"instAddMonoidWithOneENat",
"TangentSpace.fiberBundle",
"NormedSpace",
"chartAt",
"PartialEquiv.target",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"IsManifold",
"instTopologicalSpaceModelProd",
"FiberBundle.chartedSpace",
"instTopologicalSpaceTangentSpace",
"Prod... | false |
CategoryTheory.MorphismProperty.under | Mathlib.CategoryTheory.MorphismProperty.Comma | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.instCategoryUnder",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Under.right",
"CategoryTheory.Under",
"CategoryTheory.Under.Hom.right",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
AddGrpCat.hasLimits | Mathlib.Algebra.Category.Grp.Limits | [
"AddGrpCat.hasLimitsOfSize",
"AddGrpCat.instCategory",
"CategoryTheory.Limits.HasLimits",
"AddGrpCat",
"UnivLE.self"
] | true |
CategoryTheory.ObjectProperty.full_ι | Mathlib.CategoryTheory.ObjectProperty.FullSubcategory | [
"CategoryTheory.ObjectProperty.ι",
"CategoryTheory.ObjectProperty.fullyFaithfulι",
"CategoryTheory.Functor.FullyFaithful.full",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ObjectProperty.FullSubcategory",
"CategoryTheory.ObjectProperty.FullSubcategory.category",
"CategoryTheory.ObjectPro... | true |
imageToKernel_arrow_apply | Mathlib.Algebra.Homology.ImageToKernel | [
"CategoryTheory.Subobject.arrow",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Subobject.underlying",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Limits.imageSubobject",
"PartialOrder.toPreorder",
"imageToK... | true |
QuadraticForm.isometryEquivWeightedSumSquaresWeightedSumSquares._proof_4 | Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv | [
"Monoid",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Units.instMulAction",
"instHSMul",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Units.instSMul",
"Pi.instInv",
"Units",
"AddZeroClass.toAddZero",
"Pi.mulAction'",
"DistribSMul.toS... | false |
MulEquiv.instMulEquivClass | Mathlib.Algebra.Group.Equiv.Defs | [
"MulEquiv.instEquivLike",
"MulEquiv.map_mul'",
"Mul",
"MulEquivClass",
"MulEquiv",
"MulEquivClass.mk"
] | true |
_private.Init.Data.Vector.Lemmas.0.Array.eraseIdx!.eq_1 | Init.Data.Vector.Lemmas | [
"panicWithPosWithDecl",
"instOfNatNat",
"dite",
"Array",
"Array.eraseIdx!",
"Array.instInhabited",
"Nat",
"LT.lt",
"Nat.decLt",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
"Eq",
"Array.size",
"Not",
"Array.eraseIdx"
] | true |
_private.Mathlib.Geometry.Convex.ConvexSpace.Defs.0.Convexity.StdSimplex.support_weights_restrict._simp_1_3 | Mathlib.Geometry.Convex.ConvexSpace.Defs | [
"Finsupp.instFunLike",
"Exists",
"Ne",
"propext",
"Eq",
"Finsupp.ne_iff",
"DFunLike.coe",
"Finsupp",
"Zero"
] | false |
Finset.mem_filter_univ | Mathlib.Data.Fintype.Defs | [
"Finset.mem_filter._simp_1",
"Finset.univ",
"congrArg",
"Finset",
"Membership.mem",
"iff_self",
"And",
"Iff",
"Fintype",
"Finset.instSetLike",
"DecidablePred",
"True",
"of_eq_true",
"Finset.mem_univ._simp_1",
"congrFun'",
"implies_true",
"Finset.filter",
"SetLike.instMembership",
... | true |
_private.Mathlib.Data.Bool.Count.0.List.IsChain.count_not_le_count_add_one._proof_1_27 | Mathlib.Data.Bool.Count | [
"Bool.not",
"Lean.Grind.nestedProof",
"Lean.Grind.Nat.lt_eq",
"instDecidableEqBool",
"instOfNatNat",
"LE.le",
"instLENat",
"instBEqOfDecidableEq",
"List.cons",
"List.findIdx_le_length",
"GetElem.getElem",
"List.findIdxs",
"List",
"instHAdd",
"List.count",
"HAdd.hAdd",
"Nat.le_trans",... | false |
ContMDiffOn.iterate | Mathlib.Geometry.Manifold.ContMDiff.Basic | [
"Nat.recAux",
"NormedSpace",
"id",
"instOfNatNat",
"Nat.iterate",
"TopologicalSpace",
"ModelWithCorners",
"instHAdd",
"HAdd.hAdd",
"Set.MapsTo",
"Nat",
"ENat",
"NontriviallyNormedField",
"instAddNat",
"NontriviallyNormedField.toNormedField",
"OfNat.ofNat",
"NormedAddCommGroup.toSemin... | true |
CategoryTheory.Bicategory.OplaxTrans.ComonadBicat | Mathlib.CategoryTheory.Bicategory.Monad.Basic | [
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.LocallyDiscrete",
"CategoryTheory.Bicategory",
"Unit",
"CategoryTheory.discreteCategory",
"CategoryTheory.OplaxFunctor",
"CategoryTheory.Discrete"
] | true |
CategoryTheory.MorphismProperty.overObj | Mathlib.CategoryTheory.MorphismProperty.Comma | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Over",
"CategoryTheory.instCategoryOver",
"CategoryTheory.Over.left",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Over.hom",
"CategoryTheory.ObjectProperty",
"CategoryTheory.Category"
] | true |
PiNat.cylinder_eq_pi | Mathlib.Topology.MetricSpace.PiNat | [
"Set.ext",
"Preorder.toLT",
"Finset.coe_range",
"congrArg",
"Finset",
"PiNat.cylinder",
"Membership.mem",
"Set.instSingletonSet",
"iff_self",
"Finset.range",
"Set.mem_pi._simp_1",
"Iff",
"SetLike.coe",
"Finset.instSetLike",
"Nat.instPreorder",
"implies_congr",
"Nat",
"LT.lt",
"Tr... | true |
Lean.Server.Test.Runner.Client.MsgEmbed.ctorElim | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.MsgEmbed.trace",
"Lean.Server.Test.Runner.Client.MsgEmbed.ctorIdx",
"Lean.Server.Test.Runner.Client.SubexprInfo",
"Lean.Server.Test.Runner.Client.InteractiveGoal",
"Lean.Server.Test.Runner.Client.MsgEmbed.expr",
"Lean.Server.Test.Runner.Client.MsgEmbed.widget",
"Lean.Serv... | false |
Pi.nnnorm_def | Mathlib.Analysis.Normed.Group.Constructions | [
"Real.instLE",
"Real",
"Finset.univ",
"Real.instZero",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"SeminormedAddGroup",
"NNReal.instSemilatticeSup",
"NNReal",
"LE.le",
"Fintype",
"Zero.toOfNat0",
"Finset.sup",
"Pi.seminormedAddGroup",
"Subtype.eta",
"OfNat.ofNat",
"Eq",
"norm_... | true |
_private.Mathlib.Order.Filter.Map.0.Filter.comap_comap._simp_1_1 | Mathlib.Order.Filter.Map | [
"Filter.instMembership",
"Compl.compl",
"Membership.mem",
"Set.instCompl",
"propext",
"Filter.compl_mem_comap",
"Set.image",
"Eq",
"Filter",
"Filter.comap",
"Set"
] | false |
SimpleGraph.chromaticNumber_le_sum_right | Mathlib.Combinatorics.SimpleGraph.Sum | [
"SimpleGraph.Colorable.of_sum_right",
"SimpleGraph.chromaticNumber_le_of_forall_imp",
"Sum",
"LE.le",
"instLEENat",
"SimpleGraph",
"Nat",
"ENat",
"SimpleGraph.sum",
"SimpleGraph.Colorable",
"SimpleGraph.chromaticNumber"
] | true |
MulAction.fixedBy | Mathlib.GroupTheory.GroupAction.Defs | [
"Monoid",
"instHSMul",
"setOf",
"MulAction",
"Monoid.toSemigroup",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"MulAction.toSemigroupAction",
"Eq",
"Set"
] | true |
WithTop.top_ne_natCast._simp_1 | Mathlib.Algebra.Order.Monoid.Unbundled.WithTop | [
"False",
"eq_false",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"WithTop.top",
"Nat",
"WithTop.natCast",
"WithTop.top_ne_natCast",
"Top.top",
"Eq",
"AddMonoidWithOne",
"WithTop"
] | false |
DerivedCategory.triangleOfSESδ_naturality | Mathlib.Algebra.Homology.DerivedCategory.ShortExact | [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"instCategoryDerivedCategory",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"CochainComplex.mappingCone.descShortComplex",
"DerivedCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory... | true |
NonUnitalStarAlgebra.elemental.isClosed | Mathlib.Topology.Algebra.NonUnitalStarAlgebra | [
"NonUnitalStarAlgebra.adjoin",
"instSMulOfMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"ContinuousStar",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"Set.instSingletonSet",
"DistribSMul.toSMulZeroClass",
"NonUnitalSemiring.toNonUnitalNonAssocSemir... | true |
Std.TreeMap.compare_maxKey?_modify_eq | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.inner",
"Option.some",
"Ordering",
"Eq.rec",
"Ordering.eq",
"Std.TransCmp",
"Std.TreeMap.maxKey?",
"Bool.true",
"Option.get",
"Option.isSome_some",
"Std.DTreeMap.Const.compare_maxKey?_modify_eq",
"Bool",
"Std.TreeMap.modify",
"Option.isSome",
"Eq.symm",
"Eq",
"Std.TreeMa... | true |
MultilinearMap.domCoprod_apply | Mathlib.LinearAlgebra.Multilinear.TensorProduct | [
"CommSemiring.toSemiring",
"MultilinearMap.domCoprod",
"TensorProduct.addCommMonoid",
"Sum",
"Sum.inl",
"MultilinearMap",
"AddCommMonoid",
"CommSemiring",
"Sum.inr",
"MultilinearMap.instFunLikeForall",
"TensorProduct",
"Eq.refl",
"TensorProduct.tmul",
"Module",
"Eq",
"DFunLike.coe",
... | true |
CategoryTheory.Triangulated.TStructure.truncGELTToLTGE_app_pentagon | Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE | [
"_private.Mathlib.CategoryTheory.Triangulated.TStructure.TruncLTGE.0.CategoryTheory.Triangulated.TStructure.TruncAux.triangle._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Triangulated.TStructure.truncGE",
"CategoryTheory.Functor.Additive",
"HSub.hSub",
... | true |
_private.Mathlib.Order.Category.BddOrd.0.BddOrd.Hom.mk._flat_ctor | Mathlib.Order.Category.BddOrd | [
"BoundedOrderHom",
"BddOrd.Hom",
"PartOrd.str",
"PartialOrder.toPreorder",
"BddOrd.toPartOrd",
"BddOrd",
"BddOrd.isBoundedOrder",
"PartOrd.carrier",
"_private.Mathlib.Order.Category.BddOrd.0.BddOrd.Hom.mk"
] | false |
_private.Mathlib.CategoryTheory.Monoidal.Mod.0.CategoryTheory.AddMod.Hom.ext.match_1 | Mathlib.CategoryTheory.Monoidal.Mod | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.AddMod.addMod",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.AddMod",
"CategoryTheory.AddMod.Hom.casesOn",
"CategoryTheory.IsAddModHom",
"CategoryTheory.MonoidalCategory.MonoidalLeftAction",
"CategoryTheory.AddMonObj",
"... | false |
DerivedCategory.isLE_Q_obj_iff | Mathlib.Algebra.Homology.DerivedCategory.TStructure | [
"HomologicalComplex.homologyFunctor",
"CategoryTheory.Abelian.toPreadditive",
"_private.Mathlib.Algebra.Homology.DerivedCategory.TStructure.0.DerivedCategory.isLE_Q_obj_iff._simp_1_3",
"instCategoryDerivedCategory",
"HomologicalComplex.instCategory",
"DerivedCategory",
"HomologicalComplex.ExactAt",
"c... | true |
Lean.instBEqExtraModUse.beq | Lean.ExtraModUses | [
"Bool.and",
"instDecidableEqBool",
"instBEqOfDecidableEq",
"BEq.beq",
"_private.Lean.ExtraModUses.0.Lean.instBEqExtraModUse.beq.match_1",
"Bool",
"Lean.Name",
"Bool.false",
"Lean.Name.instBEq",
"Lean.ExtraModUse"
] | true |
Ideal.comap_le_comap_iff_of_surjective | Mathlib.RingTheory.Ideal.Maps | [
"Ideal.le_comap_of_map_le",
"Semiring.toModule",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Ideal.map",
"Eq.le",
"Submodule.instPartialOrder",
"LE.le",
"Ideal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Iff",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Iff.intro",
"Ideal.comap",... | true |
Std.TreeSet.toList_roo | Std.Data.TreeSet.Slice | [
"Pure.pure",
"Std.Slice.toList",
"Std.TreeSet",
"Std.DTreeMap.Internal.Unit.RooSliceData",
"Std.TreeSet.toList",
"Std.DTreeMap.Internal.Unit.RooSlice.instToIterator",
"Monad.toApplicative",
"Std.Iterators.Types.Map.instIterator",
"Std.DTreeMap.Internal.Unit.RooSlice",
"MonadLiftT.monadLift",
"in... | true |
AEMeasurable.iInf | Mathlib.MeasureTheory.Constructions.BorelSpace.Order | [
"OrderTopology",
"MeasureTheory.Measure",
"iInf",
"AEMeasurable",
"OrderDual.borelSpace",
"SecondCountableTopology",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"BorelSpace",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"instMeasurableSpaceOrderDual",
"Mea... | true |
_private.Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction.0.UpperHalfPlane.denom_cocycle._simp_1_2 | Mathlib.Analysis.Complex.UpperHalfPlane.MoebiusAction | [
"False",
"eq_false",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"three_ne_zero",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
_private.Init.Data.Range.Polymorphic.PRange.0.Std.instDecidableEqRoc.decEq._proof_1 | Init.Data.Range.Polymorphic.PRange | [
"Eq",
"Std.Roc.mk",
"Std.Roc",
"rfl"
] | false |
Mathlib.Tactic.Ring.Common.evalPow._sunfold | Mathlib.Tactic.Ring.Common | [
"Pure.pure",
"Mathlib.Tactic.Ring.Common.evalPow",
"Mathlib.Tactic.Ring.Common.Result.mk",
"Mathlib.Tactic.Ring.Common.ExSumNat",
"Lean.Meta.State",
"Lean.Expr.const",
"Lean.Name.mkStr5",
"Mathlib.Tactic.Ring.Common.Result",
"Mathlib.Tactic.Ring.Common.ExSum",
"Lean.Meta.MetaM",
"Mathlib.Tactic.... | false |
CategoryTheory.Pseudofunctor.StrongTrans.naturality_comp._autoParam | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Pseudo | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
instBooleanAlgebraSubtypeIsIdempotentElem._proof_15 | Mathlib.Algebra.Order.Ring.Idempotent | [
"IsIdempotentElem.one_sub",
"CommRing",
"Lattice.toSemilatticeSup",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"instBooleanAlgebraSubtypeIsIdempotentElem._proof_7",
"instBooleanAlgebraSubtypeIsIdempotentElem._proof_9",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
... | false |
Geometry.SimplicialComplex.facets | Mathlib.Analysis.Convex.SimplicialComplex.Basic | [
"AddCommGroup.toAddCommMonoid",
"PreAbstractSimplicialComplex.faces",
"Finset",
"setOf",
"Membership.mem",
"PartialOrder",
"AddCommGroup",
"HasSubset.Subset",
"Geometry.SimplicialComplex.toPreAbstractSimplicialComplex",
"And",
"Finset.instHasSubset",
"Geometry.SimplicialComplex",
"Module",
... | true |
_private.Mathlib.Combinatorics.Matroid.Basic.0.Matroid.singleton_subset_ground | Mathlib.Combinatorics.Matroid.Basic | [
"Iff.mpr",
"Set.singleton_subset_iff",
"Matroid.E",
"Membership.mem",
"Set.instSingletonSet",
"HasSubset.Subset",
"Singleton.singleton",
"Set.instMembership",
"Matroid",
"Set.instHasSubset",
"Set"
] | true |
Lean.Meta.NormCast.Label.ofNat_ctorIdx | Lean.Meta.Tactic.NormCast | [
"Lean.Meta.NormCast.Label.elim",
"Lean.Meta.NormCast.Label.ofNat",
"Lean.Meta.NormCast.Label.casesOn",
"Lean.Meta.NormCast.Label",
"Eq.refl",
"Lean.Meta.NormCast.Label.squash",
"Eq",
"Lean.Meta.NormCast.Label.ctorIdx",
"Lean.Meta.NormCast.Label.move"
] | true |
TopPair.incl._proof_2 | Mathlib.Topology.Category.TopPair | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.MorphismProperty.IsMultiplicative.instTop",
"TopCat.instCategory",
"CategoryTheory.MorphismProperty.Comma.instCategory",
"CategoryThe... | false |
HomologicalComplex₂.ιTotal_totalFlipIso_f_hom_assoc | Mathlib.Algebra.Homology.TotalComplexSymmetry | [
"HomologicalComplex₂.totalFlipIso",
"CategoryTheory.Category.assoc",
"HomologicalComplex.instCategory",
"instHSMul",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"HomologicalComplex₂.ιTotal",
"Units.instSMul",
"HomologicalComplex₂.HasTotal",
"... | true |
CategoryTheory.MonoidalCategory.MonoidalLeftAction.monoidalOppositeLeftAction._proof_6 | Mathlib.CategoryTheory.Monoidal.Action.Opposites | [
"CategoryTheory.MonoidalOpposite.unmop",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.MonoidalOpposite",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalRightAction.actionHom_comp",
"CategoryTheory.MonoidalCategory.MonoidalRightActionS... | false |
Nat.coprime_two_right._simp_1 | Mathlib.Data.Nat.Prime.Basic | [
"Nat.Coprime",
"Odd",
"instOfNatNat",
"Nat.coprime_two_right",
"Nat",
"propext",
"Nat.instSemiring",
"OfNat.ofNat",
"Eq"
] | false |
MvPowerSeries.HasGaussNorm | Mathlib.RingTheory.MvPowerSeries.GaussNorm | [
"Nat.instMulZeroClass",
"Real.instLE",
"Real",
"Semiring.toModule",
"HMul.hMul",
"LinearMap.instFunLike",
"MvPowerSeries",
"MvPowerSeries.instModule",
"LinearMap",
"BddAbove",
"MvPowerSeries.instAddCommMonoid",
"Monoid.toPow",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Real.instMonoid",... | true |
SheafOfModules.QuasicoherentData.IsFinitePresentation.isFinite_presentation | Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent | [
"CategoryTheory.Over",
"AddCommGrpCat.instCategory",
"SheafOfModules.QuasicoherentData.I",
"AddMonoid.toAddZeroClass",
"RingCat.ring",
"CategoryTheory.Sheaf.over",
"AddCommGroup.toAddGroup",
"RingHom",
"AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier",
"AddZeroClass.toAddZero",
"SheafOfMod... | true |
Std.Iter.findSomeM?_eq_match_step.match_1 | Init.Data.Iterators.Lemmas.Consumers.Loop | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Option"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.getD_congr._simp_1_3 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
_private.Init.Data.Int.Cooper.0.Int.Cooper.resolve_left_inv.eq_1 | Init.Data.Int.Cooper | [
"Int.instDiv",
"Int.Cooper.resolve_left_inv",
"instHDiv",
"HDiv.hDiv",
"Int",
"instHAdd",
"HAdd.hAdd",
"Int.instAdd",
"Eq.refl",
"Eq"
] | true |
_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.Goal.getEqcs._sparseCasesOn_1 | Lean.Meta.Tactic.Grind.Types | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"List.rec",
"List.cons",
"Nat.land",
"List",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"List.ctorIdx",
"List.nil"
] | false |
IsManifold.maximalAtlas | Mathlib.Geometry.Manifold.IsManifold.Basic | [
"NormedSpace",
"contDiffGroupoid",
"TopologicalSpace",
"ModelWithCorners",
"ENat",
"NontriviallyNormedField",
"StructureGroupoid.maximalAtlas",
"NontriviallyNormedField.toNormedField",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"OpenPartialHomeomorph",
"NormedAddCommGroup",
"WithTop",
"S... | true |
Aesop.PhaseSpec.unsafe.elim | Aesop.Builder.Basic | [
"PULift.up",
"Aesop.PhaseSpec.ctorElim",
"Aesop.PhaseSpec.unsafe",
"Aesop.UnsafeRuleInfo",
"Aesop.PhaseSpec.ctorIdx",
"Nat",
"Aesop.PhaseSpec",
"Eq.symm",
"Eq"
] | false |
mem_lowerBounds_image2 | Mathlib.Order.Bounds.Image | [
"Iff.mpr",
"Monotone._to_dual_cast_2",
"Set.forall_mem_image2",
"lowerBounds",
"Function.swap",
"Monotone",
"Preorder.toLE",
"Membership.mem",
"Eq.mp",
"LE.le",
"Set.image2",
"Set.instMembership",
"LE.le.trans'",
"Preorder",
"Set"
] | true |
gauge_neg_set_neg | Mathlib.Analysis.Convex.Gauge | [
"AddGroup.toSubtractionMonoid",
"gauge_def'",
"Eq.mpr",
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"Real",
"Set.Ioi",
"instHSMul",
"gauge",
"Real.instZero",
"congrArg",
"Real.instInv",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroC... | true |
MvPowerSeries.coeff_zero_eq_constantCoeff_apply | Mathlib.RingTheory.MvPowerSeries.Basic | [
"Nat.instMulZeroClass",
"Semiring.toModule",
"LinearMap.instFunLike",
"MvPowerSeries",
"RingHom",
"MvPowerSeries.constantCoeff",
"MvPowerSeries.instModule",
"LinearMap",
"MvPowerSeries.instAddCommMonoid",
"MvPowerSeries.instSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"RingHom.instF... | true |
Polynomial.coeff_divByMonic_X_sub_C | Mathlib.Algebra.Polynomial.Div | [
"Nontrivial",
"Iff.mpr",
"Polynomial.monic_X_sub_C",
"WithBot.instPreorder",
"Eq.mpr",
"Polynomial.C",
"Finset.mul_sum",
"MulOne.toOne",
"Semigroup.toMul",
"WithBot",
"Preorder.toLT",
"le_rfl",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"HMul.hMul",
"Nat.instOne",
"Finset.sum_... | true |
MeasureTheory.MemLp.zero | Mathlib.MeasureTheory.Function.LpSeminorm.Basic | [
"Eq.mpr",
"MeasureTheory.Measure",
"Preorder.toLT",
"congrArg",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"ESeminormedAddMonoid",
"MeasureTheory.eLpNorm_zero",
"AddZeroClass.toAddZero",
"id",
"Pi.instZero",
"NNReal",
"MeasureTheory.MemLp",
"ESeminormedAddMonoid.toAddMonoid",
... | true |
Lean.Grind.CommRing.Poly.mulMonC_nc.go | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly",
"Int",
"Lean.Grind.CommRing.Poly.mulMonC_nc.go._f",
"Nat",
"Lean.Grind.CommRing.Poly.brecOn",
"Lean.Grind.CommRing.Mon"
] | true |
Combinatorics.Subspace.reindex | Mathlib.Combinatorics.HalesJewett | [
"Combinatorics.Subspace.idxFun",
"Equiv.instEquivLike",
"Sum.map",
"Equiv",
"Combinatorics.Subspace.reindex._proof_1",
"Combinatorics.Subspace.mk",
"Equiv.symm",
"DFunLike.coe",
"EquivLike.toFunLike",
"Combinatorics.Subspace"
] | true |
_private.Std.Data.Internal.List.Associative.0.List.forIn'_cons.match_1.splitter | Std.Data.Internal.List.Associative | [
"ForInStep.done",
"ForInStep",
"List.forIn'_cons.match_1",
"ForInStep.yield"
] | true |
_private.Lean.Elab.DocString.0.Lean.Doc.fixupBlock._unsafe_rec | Lean.Elab.DocString | [
"Pure.pure",
"Lean.Doc.Context",
"Lean.Doc.Block.blockquote",
"_private.Lean.Elab.DocString.0.Lean.Doc.fixupBlock.match_3",
"Lean.Elab.Term.instMonadTermElabM",
"String",
"Lean.Doc.Block",
"Lean.Doc.Block.concat",
"Lean.Doc.InternalState",
"ReaderT.instMonad",
"IO.RealWorld",
"Lean.Doc.DescIte... | false |
CliffordAlgebra.GradedAlgebra.ι_apply | Mathlib.LinearAlgebra.CliffordAlgebra.Grading | [
"Submodule",
"CliffordAlgebra.ι",
"CommRing",
"ZMod.commRing",
"instAddCommMonoidDirectSum",
"Ring.toNonAssocRing",
"DirectSum.instModule",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"Submodule.addCommMonoid",
"instAlgebraCliffordAlgebra",
"AddMonoid.toAddZ... | true |
Lean.Meta.CheckAssignment.State.mk | Lean.Meta.ExprDefEq | [
"Lean.ExprStructMap",
"Lean.Expr",
"Lean.Meta.CheckAssignment.State.mk",
"Lean.Meta.CheckAssignment.State"
] | true |
GenContFract.abs_sub_convs_le | Mathlib.Algebra.ContinuedFractions.Computation.Approximations | [
"GenContFract.s",
"Iff.mpr",
"_private.Mathlib.Algebra.ContinuedFractions.Computation.Approximations.0.GenContFract.abs_sub_convs_le._proof_1_1",
"GenContFract.contsAux",
"Int.cast",
"Eq.mpr",
"GenContFract.convs",
"GroupWithZero.toMonoidWithZero",
"NegZeroClass.toNeg",
"GenContFract.dens",
"Nat... | true |
SimpleGraph.Walk.isHamiltonian_iff_support_get_bijective | Mathlib.Combinatorics.SimpleGraph.Hamiltonian | [
"List.get_bijective_iff",
"instLawfulBEq",
"List.get",
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"instOfNatNat",
"instBEqOfDecidableEq",
"SimpleGraph",
"List.count",
"Iff",
"Nat",
"Function.Bijective",
"OfNat.ofNat",
"Fin",
"Eq",
"List.length",
"SimpleGraph.Walk.IsHamiltonian",... | true |
Pell.yn_succ | Mathlib.NumberTheory.PellMatiyasevic | [
"HMul.hMul",
"Pell.xn",
"instMulNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Pell.yn",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"Eq",
"rfl",
"instHMul"
] | true |
_private.Lean.LocalContext.0.Lean.LocalContext.findFromUserNames.match_1 | Lean.LocalContext | [
"Prod.mk",
"Std.HashMap",
"Array",
"Lean.Name",
"Lean.LocalDecl",
"Prod",
"Prod.casesOn",
"Lean.Name.instBEq",
"Lean.instHashableName"
] | false |
Aesop.EMap.idx | Aesop.EMap | [
"Nat",
"Lean.Meta.DiscrTree",
"Aesop.EMap"
] | true |
DivInvMonoid.zpow_succ'._autoParam | Mathlib.Algebra.Group.Defs | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Topology.lowerSet._proof_2 | Mathlib.Topology.Order.UpperLowerSetTopology | [
"Preorder.toLE",
"Set.instInter",
"Inter.inter",
"IsLowerSet",
"Preorder",
"IsLowerSet.inter",
"Set"
] | false |
Std.HashMap.Raw.erase | Std.Data.HashMap.Raw | [
"Std.HashMap.Raw",
"Std.HashMap.Raw.mk",
"Std.HashMap.Raw.inner",
"Hashable",
"BEq",
"Std.DHashMap.Raw.erase"
] | true |
CategoryTheory.ComposableArrows.whiskerLeftFunctor_obj_obj | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"CategoryTheory.Functor",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.ComposableArrows",
"Preorder.smallCategory",
"instOfNatNat",
"instHAdd",
"CategoryTheory.ComposableArrows.whiskerLeftFunctor",
"Fin.instPartialOrder",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Eq... | true |
Std.HashMap.ofListWith.match_1 | Batteries.Data.HashMap.Basic | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Option"
] | false |
SSet.Edge.CompStruct.mk._proof_6 | Mathlib.AlgebraicTopology.SimplicialSet.CompStruct | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.ConcreteCategory.hom",
"SSet.Truncated.Edge._proof_2",
"SSet.Truncated.Edge.edge",
"Quiver.Hom.op",
"SimplexCategory.Truncated.δ₂",
"CategoryTheory.Functor.category",
"SSet.Tru... | false |
MvPowerSeries.lexOrder_mul_ge | Mathlib.RingTheory.MvPowerSeries.LexOrder | [
"Nat.instMulZeroClass",
"Preorder.toLT",
"HMul.hMul",
"WithTop.instPreorder",
"Lex",
"LinearOrder",
"MvPowerSeries.lexOrder",
"AddMonoid.toAddZeroClass",
"WellFoundedGT",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Nat.instAddMonoid",
"MvPowerSeries",
"SemilatticeInf.toPartialOrder",
"M... | true |
_private.Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point.0.WeierstrassCurve.Affine.CoordinateRing.smul_basis_mul_Y._simp_1_1 | Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | [
"Monoid",
"HMul.hMul",
"Monoid.toMulOneClass",
"MulOne.toMul",
"instOfNatNat",
"sq",
"Monoid.toPow",
"MulOneClass.toMulOne",
"HPow.hPow",
"Nat",
"instHPow",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"instHMul"
] | false |
_private.Batteries.Data.List.Basic.0.List.rotate'.match_1.eq_1 | Batteries.Data.List.Basic | [
"List.rotate'.match_1",
"instOfNatNat",
"List.cons",
"List",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq",
"List.nil"
] | true |
CategoryTheory.Triangulated.TStructure.essImage_ιHeart | Mathlib.CategoryTheory.Triangulated.TStructure.Heart | [
"CategoryTheory.Functor.Additive",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Triangulated.TStructure.heart",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Functor.essImage",
"CategoryTheory.Preadditive",
"CategoryTheory.Triangulated.TStructure",
"CategoryTheory.Triangulated.TStructure.ιHeart",
... | true |
String.Slice.Pattern.ForwardPattern.skipPrefixOfNonempty?._default | Init.Data.String.Pattern.Basic | [
"String.Slice",
"id",
"String.Slice.isEmpty",
"Bool",
"String.Slice.Pos",
"Bool.false",
"Eq",
"Option"
] | false |
_private.Lean.Compiler.LCNF.AlphaEqv.0.Lean.Compiler.LCNF.AlphaEqv.eqv.match_1 | Lean.Compiler.LCNF.AlphaEqv | [
"_private.Lean.Compiler.LCNF.AlphaEqv.0.Lean.Compiler.LCNF.AlphaEqv.eqv._sparseCasesOn_6",
"Lean.Compiler.LCNF.Arg",
"Lean.Compiler.LCNF.Code.setTag",
"_private.Lean.Compiler.LCNF.AlphaEqv.0.Lean.Compiler.LCNF.AlphaEqv.eqv._sparseCasesOn_8",
"Lean.Compiler.LCNF.Code.unreach",
"_private.Lean.Compiler.LCNF.... | false |
Lean.Syntax.formatStx | Init.Data.Format.Syntax | [
"Lean.Syntax.formatStxAux",
"Lean.Syntax",
"instOfNatNat",
"Option.none",
"Nat",
"Std.Format",
"Bool",
"optParam",
"OfNat.ofNat",
"Bool.false",
"Option"
] | true |
AlgHom.comp | Mathlib.Algebra.Algebra.Hom | [
"AlgHom.comp._proof_1",
"AlgHom.toMonoidHom'._proof_2",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"RingHom",
"CommSemiring",
"RingHom.comp",
"AlgHom.toRingHom",
"RingHomClass.toRingHom",
"AlgHom.mk",
"Semiring",
"Semiring.toNonAssocSemiring"
] | true |
ULift.divisionSemiring._proof_1 | Mathlib.Algebra.Field.ULift | [
"GroupWithZero.div_eq_mul_inv",
"GroupWithZero.toMonoidWithZero",
"Semigroup.toMul",
"instHDiv",
"GroupWithZero.toInv",
"HMul.hMul",
"ULift",
"DivisionSemiring.toGroupWithZero",
"GroupWithZero.toDiv",
"ULift.groupWithZero",
"HDiv.hDiv",
"DivisionSemiring",
"Inv.inv",
"Monoid.toSemigroup",
... | false |
CategoryTheory.Limits.Types.pullbackLimitCone._proof_4 | Mathlib.CategoryTheory.Limits.Types.Pullbacks | [
"CategoryTheory.Limits.PullbackCone.condition",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Limits.PullbackCone.fst",
"TypeCat.ofHom",
"id",
"Prod.mk",
... | false |
PrimeSpectrum.specComap_surjective_of_faithfullyFlat | Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra | [
"CommRing",
"Algebra.algebraMap",
"PrimeSpectrum.comap_surjective_of_faithfullyFlat",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.toModule",
"CommRing.toCommSemiring",
"Ring.toAddCommGroup",
"PrimeSpectrum",
"Module.FaithfullyFlat",
"CommRing.toRing",
"PrimeSpectrum.comap",
"Function.Surj... | true |
ProbabilityTheory.Kernel.condKernelCountable.congr_simp | Mathlib.Probability.Kernel.Disintegration.Basic | [
"Membership.mem",
"Eq.rec",
"MeasurableSpace",
"ProbabilityTheory.Kernel.condKernelCountable",
"measurableAtom",
"Eq.ndrec",
"Countable",
"Eq.refl",
"Prod",
"Eq",
"Set.instMembership",
"ProbabilityTheory.Kernel",
"Prod.instMeasurableSpace",
"Set"
] | true |
uzpow_sub | Mathlib.Data.ZMod.IntUnitsPower | [
"Int.instCommMonoid",
"CommRing",
"instHDiv",
"Equiv.instEquivLike",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"Additive",
"Units.instDiv",
"HSub.hSub",
"sub_smul",
"Units",
"Equiv",
"HDiv.hDiv",
"Additive.ofMul",
"Int",
"Int.instUnitsPow",
"Int.instMonoid",
"SubNegM... | true |
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