name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Algebra.Group.Pointwise.Set.Basic.0.Set.add_univ.match_1_1 | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Membership.mem",
"Set.Nonempty",
"Exists.casesOn",
"Exists.intro",
"Set.instMembership",
"Set"
] | false |
_private.Mathlib.RingTheory.Ideal.Colon.0.Submodule.mem_colon_iff_le._simp_1_1 | Mathlib.RingTheory.Ideal.Colon | [
"SetLike",
"HasSubset.Subset",
"LE.le",
"LE",
"SetLike.coe_subset_coe",
"IsConcreteLE",
"SetLike.coe",
"propext",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
Matrix.transpose_eq_intCast | Mathlib.Data.Matrix.Diagonal | [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Matrix.instIntCastOfZero",
"AddGroupWithOne.toAddGroup",
"Matrix",
"Matrix.transpose_eq_diagonal",
"SubtractionMonoid.toSubNegZeroMonoid",
"Int",
"AddGroupWithOne.toIntCast",
"SubNegZeroMonoid.toNegZeroClass",
"Iff",
"Matrix.transpose",
"AddGroupW... | true |
analyticAt_cexp | Mathlib.Analysis.SpecialFunctions.ExpDeriv | [
"Complex.instNormedAddCommGroup",
"Complex.instDenselyNormedField",
"analyticOnNhd_cexp",
"AnalyticAt",
"Set.mem_univ",
"Complex.exp",
"NontriviallyNormedField.toNormedField",
"DenselyNormedField.toNontriviallyNormedField",
"NormedField.toNormedSpace",
"Complex"
] | true |
IntermediateField.adjoin_insert_adjoin | Mathlib.FieldTheory.IntermediateField.Adjoin.Defs | [
"Iff.mpr",
"IntermediateField.instPartialOrder",
"le_refl",
"IntermediateField.adjoin.mono",
"IntermediateField",
"IntermediateField.adjoin_le_iff",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"Membership.mem",
"Insert.insert",
"HasSubset.Subset",
"LE.le",
"IntermediateField.sub... | true |
AddConjClasses.mk_eq_mk_iff_isAddConj | Mathlib.Algebra.Group.Conj | [
"Quot.sound",
"AddConjClasses.mk",
"IsAddConj",
"AddConjClasses",
"Iff",
"Iff.intro",
"AddMonoid",
"Quotient.exact",
"Eq",
"IsAddConj.setoid"
] | true |
Finset.nsmul_subset_nsmul_right | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"instHSMul",
"Finset",
"AddMonoid.toAddZeroClass",
"Finset.nsmul_right_monotone",
"Membership.mem",
"AddZeroClass.toAddZero",
"HasSubset.Subset",
"LE.le",
"instLENat",
"AddZero.toZero",
"Finset.instSetLike",
"Nat",
"AddMonoid",
"Finset.instHasSubset",
"AddZero.toAdd",
"Zero.toOfNat0",
... | true |
CategoryTheory.PrelaxFunctor.mapFunctor_map | Mathlib.CategoryTheory.Bicategory.Functor.Prelax | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.PrelaxFunctorStruct.map₂",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelaxFunctorStruct",
"CategoryTheory.Functor.map",
"CategoryTheory.Bicategory",
"Prefunctor.map",
"CategoryTheory.PrelaxFu... | true |
_private.Mathlib.Algebra.Order.Floor.Extended.0.ENat.le_ceil._proof_1_4 | Mathlib.Algebra.Order.Floor.Extended | [
"False",
"of_decide_eq_true",
"eq_false",
"Classical.byContradiction",
"HSub.hSub",
"Nat.not_le_eq",
"Eq.mp",
"id",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat.Simproc.add_le_le",
"Bool.true",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat.le_zero_eq",
"Nat",
"True",
... | false |
Module.Invertible.linearEquiv.congr_simp | Mathlib.RingTheory.PicardGroup | [
"Algebra.to_smulCommClass",
"Semiring.toModule",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"Algebra.id",
"LinearMap.module",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"RingHomInvPair.ids",
"Line... | true |
CategoryTheory.Functor.Elements.shrinkYoneda_map_app_coconeπOpCompShrinkYonedaObj_ι_app | Mathlib.CategoryTheory.Limits.Presheaf | [
"CategoryTheory.Functor.op",
"CategoryTheory.categoryOfElements",
"CategoryTheory.Functor.Elements",
"CategoryTheory.Functor",
"Equiv.apply_symm_apply",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
... | true |
Set.powersetCard.mulActionHom_of_embedding_surjective | Mathlib.GroupTheory.GroupAction.SubMulAction.Combination | [
"Eq.mpr",
"Fintype.card_fin",
"Function.Embedding.exists_of_card_eq_finset",
"Finset.univ",
"congrArg",
"Finset",
"Group",
"Finset.map",
"Membership.mem",
"Exists",
"Set.powersetCard.instMulActionElemFinset",
"Set.Elem",
"Fintype.card",
"Set.powersetCard.mulActionHom_of_embedding",
"id",... | true |
Quiver.Path.decidableEqBddPathsOfDecidableEq.match_5 | Mathlib.Combinatorics.Quiver.Path | [
"Subtype.casesOn",
"Quiver.Path.BoundedPaths",
"instOfNatNat",
"LE.le",
"instLENat",
"Quiver.Path",
"Subtype.mk",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Quiver.Path.length",
"Quiver",
"instAddNat",
"OfNat.ofNat"
] | false |
Manifold.pathELength_eq_lintegral_mfderivWithin_Icc | Mathlib.Geometry.Manifold.Riemannian.PathELength | [
"instOneTangentSpaceRealModelWithCornersSelf",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Real.partialOrder",
"Real",
"MeasureTheory.Measure",
"Preorder.toLT",
"mfderiv",
"chartedSpaceSelf",
"Real.lattice",
"NormedSpace",
"Real.denselyNormedField",
"Real.instRCLike",
"congrArg",
"inst... | true |
_private.Batteries.Data.RBMap.Depth.0.Batteries.RBNode.depthUB_le_two_depthLB.match_1_1 | Batteries.Data.RBMap.Depth | [
"Batteries.RBColor.casesOn",
"Batteries.RBColor.red",
"Batteries.RBColor",
"Nat",
"Batteries.RBColor.black"
] | false |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.deleteOne_preserves_strongAssignmentsInvariant._proof_1_22 | Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas | [
"Lean.Grind.Nat.lt_eq",
"Eq.mp",
"instOfNatNat",
"LE.le",
"instLENat",
"Array.toList",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.Lemmas.0.Std.Tactic.BVDecide.LRAT.Internal.Def... | false |
Mathlib.Tactic.Monoidal.mor₁OfExpr | Mathlib.Tactic.CategoryTheory.Monoidal.Datatypes | [
"Inhabited.default",
"instInhabitedOfMonad",
"Lean.Expr",
"Lean.Meta.MetaM",
"Mathlib.Tactic.BicategoryLike.Mor₁",
"Mathlib.Tactic.BicategoryLike.State",
"Lean.Meta.instMonadMetaM",
"Mathlib.Tactic.Monoidal.MonoidalM",
"Mathlib.Tactic.Monoidal.Context",
"StateT.instMonad",
"StateT",
"instInhab... | true |
Batteries.RBNode.any.eq_1 | Batteries.Data.RBMap.Basic | [
"Batteries.RBNode.any",
"Batteries.RBNode.nil",
"Bool",
"Eq.refl",
"Bool.false",
"Eq"
] | true |
Int.negOfNat_mul_negSucc | Init.Data.Int.Lemmas | [
"Eq.mpr",
"Int.negSucc_mul_negOfNat",
"HMul.hMul",
"congrArg",
"id",
"Int.ofNat",
"instMulNat",
"Nat.mul_comm",
"Int",
"Int.instMul",
"Nat",
"Eq.refl",
"Int.mul_comm",
"Int.negSucc",
"Nat.succ",
"Eq",
"Int.negOfNat",
"instHMul"
] | true |
instBooleanAlgebraAsBoolAlg._proof_12 | Mathlib.Algebra.Ring.BooleanRing | [
"instBooleanAlgebraAsBoolAlg._proof_11",
"SemilatticeSup.mk",
"LT.mk",
"Lattice.toSemilatticeSup",
"HMul.hMul",
"Zero.zero",
"CommSemiring.toSemiring",
"Compl.compl",
"BooleanRing.sup",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"instBooleanAlgebraAsBoolAlg._proof_5",
"... | false |
List.IsSuffix.eq_of_length | Init.Data.List.Sublist | [
"List.Sublist.eq_of_length",
"List",
"Nat",
"List.IsSuffix",
"Eq",
"List.length",
"List.IsSuffix.sublist"
] | true |
CategoryTheory.Square.fromArrowArrowFunctor_obj_f₁₃ | Mathlib.CategoryTheory.Square | [
"CategoryTheory.Square.category",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Arrow.left",
"CategoryTheory.Square",
"CategoryTheory.Square.f₁₃",
"CategoryTheory.Arrow.hom",
"CategoryTheory.instCategoryArrow",
"CategoryTheory.Square.fromArrowArrowFunctor",
"Eq.refl",
"... | true |
Lean.PrettyPrinter.Delaborator.appFieldNotationCandidate? | Lean.PrettyPrinter.Delaborator.Builtins | [
"Pure.pure",
"Lean.PrettyPrinter.Delaborator.getPPOption",
"Lean.Expr.isAppOfArity",
"Lean.Expr.isRawNatLit",
"Lean.Expr.isApp",
"ReaderT",
"Lean.PrettyPrinter.Delaborator.instMonadReaderOfSubExprDelabM",
"Lean.PrettyPrinter.Delaborator.Context",
"Lean.Meta.State",
"instMonadLiftT",
"Option.some... | true |
AlgebraicGeometry.basicOpenIsoSpecAway_inv_homOfLE | Mathlib.AlgebraicGeometry.Restrict | [
"Eq.mpr",
"AlgebraicGeometry.basicOpenIsoSpecAway",
"CategoryTheory.Category.assoc",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme.homOfLE",
"CommRing",
"AlgebraicGeometry.Scheme",
"HMul.hMul",
"CommRingCat.carrier",
"PrimeSpectrum.basicOpen",
"Algebra.algebraMap",
"CategoryTheory.Catego... | true |
LinearEquiv.restrictScalars._proof_2 | Mathlib.Algebra.Module.Equiv.Basic | [
"LinearEquiv.right_inv",
"LinearMap.toAddHom",
"AddCommMonoid",
"LinearEquiv.invFun",
"LinearEquiv.toLinearMap",
"RingHomInvPair.ids",
"LinearEquiv",
"Function.RightInverse",
"Semiring",
"AddCommSemigroup.toAddCommMagma",
"Module",
"AddCommMonoid.toAddCommSemigroup",
"RingHom.id",
"Semirin... | false |
LinearMap.IsSymmetric.directSumDecomposition._proof_4 | Mathlib.Analysis.InnerProductSpace.Spectrum | [
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"Submodule",
"NormedRing.toRing",
"instAddMonoidWithOneENat",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Submodule.innerProductSpace",
"NormedSpace.toModule",
"Module.End.eigenspace",
"Membership.mem",
"NormedFi... | false |
AffineEquiv.ofEq._proof_3 | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Basic | [
"Submodule",
"Equiv.instEquivLike",
"AddMonoid.toAddSemigroup",
"AddCommGroup.toAddCommMonoid",
"Equiv.setCongr",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddCommGroup",
"AffineSubspace.inclusion.match_1",
"Equiv",
"Subtype",
"Submodule.module",
"AffineSubspace.toAddTorsor",
"LinearEq... | false |
IsLUB.mul_right | Mathlib.Algebra.Order.Field.Basic | [
"Eq.mpr",
"HMul.hMul",
"IsLUB.mul_left",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"Membership.mem",
"PartialOrder",
"Semifield",
"id",
"CommMagma.toMul",
"NonUnitalCommSemiring.toNonUnitalNonAssocCommSemiring",
... | true |
AffineSubspace.mk.inj | Mathlib.LinearAlgebra.AffineSpace.AffineSubspace.Defs | [
"instHSMul",
"AddMonoid.toAddSemigroup",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AffineSubspace.mk",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul.toSMulZeroClass",
"AddTorsor.toVSub",
... | true |
Subtype.coe_inj | Mathlib.Data.Subtype | [
"Function.Injective.eq_iff",
"Subtype",
"Subtype.coe_injective",
"Iff",
"Subtype.val",
"Eq"
] | true |
CFC.eq_one_of_spectrum_subset_one._auto_1 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CategoryTheory.SplitEpiCategory | Mathlib.CategoryTheory.EpiMono | [
"CategoryTheory.Category",
"CategoryTheory.SplitEpiCategory.mk"
] | true |
Subalgebra.LinearDisjoint.basisOfBasisRight.congr_simp | Mathlib.RingTheory.LinearDisjoint | [
"Subalgebra.instSetLike",
"Lattice.toSemilatticeSup",
"Semiring.toModule",
"CompleteLattice.toLattice",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"Algebra.instCompleteLatticeSubalgebra",
"Algebra",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
... | true |
Lean.Meta.Grind.Arith.Linear.Struct.lowers | Lean.Meta.Tactic.Grind.Arith.Linear.Types | [
"Lean.PArray",
"Lean.Meta.Grind.Arith.Linear.Struct",
"Lean.Meta.Grind.Arith.Linear.IneqCnstr"
] | true |
Finset.Ioi_disjUnion_Iio | Mathlib.Order.Interval.Finset.Basic | [
"Preorder.toLT",
"LocallyFiniteOrderTop",
"LinearOrder.toDecidableEq",
"Finset.instUnion",
"Finset.Ioi",
"congrArg",
"Compl.compl",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"Finset.mem_compl._simp_1",
"Finset.Iio",
"Finset.ext",
"lt_or_lt_iff_ne._simp_2",
"Membership.mem",
"... | true |
CategoryTheory.Functor.final_of_exists_of_isFiltered_of_fullyFaithful | Mathlib.CategoryTheory.Filtered.Final | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor.preimage",
"CategoryTheory.Functor",
"CategoryTheory.IsFiltered.coeqHom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsFilteredOrEmpty.of_exists_of_isFiltered_of_fullyFaithful",
"congrArg",
"Exists",
"Eq.mp",
"... | true |
_private.Mathlib.Probability.Kernel.Disintegration.Density.0.ProbabilityTheory.Kernel.tendsto_densityProcess_fst_atTop_univ_of_monotone._simp_1_6 | Mathlib.Probability.Kernel.Disintegration.Density | [
"Filter.NeBot",
"nhds",
"TopologicalSpace",
"Filter.Tendsto",
"propext",
"T1Space",
"Eq",
"tendsto_const_nhds_iff",
"Filter"
] | false |
Order.coheight | Mathlib.Order.KrullDimension | [
"ENat",
"OrderDual",
"Order.height",
"OrderDual.instPreorder",
"Preorder"
] | true |
Std.TreeMap.maxKey!_modify_eq_maxKey! | Std.Data.TreeMap.Lemmas | [
"Std.TreeMap.inner",
"Ordering",
"Std.TransCmp",
"Std.LawfulEqCmp",
"Std.TreeMap.maxKey!",
"Std.DTreeMap.Const.maxKey!_modify_eq_maxKey!",
"Inhabited",
"Std.TreeMap.modify",
"Eq",
"Std.TreeMap"
] | true |
SimpleGraph.EdgeLabeling.labelGraph | Mathlib.Combinatorics.SimpleGraph.Coloring.EdgeLabeling | [
"SimpleGraph.fromEdgeSet",
"setOf",
"Membership.mem",
"Exists",
"SimpleGraph.EdgeLabeling",
"SimpleGraph.edgeSet",
"Subtype.mk",
"SimpleGraph",
"Eq",
"Set.instMembership",
"Sym2",
"Set"
] | true |
Array.mk._flat_ctor | Init.Prelude | [
"Array",
"List",
"Array.mk"
] | false |
CategoryTheory.Abelian.SpectralObject.homologyDataIdId_left_H | Mathlib.Algebra.Homology.SpectralObject.Page | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Abelian.SpectralObject.H",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.Abelian",
"CategoryTheory.ComposableArrows",
"CategoryTheory.CategoryStruct.id",
... | true |
Pi.nonAssocRing._proof_2 | Mathlib.Algebra.Ring.Pi | [
"HMul.hMul",
"NonAssocSemiring.toOne",
"NonUnitalNonAssocSemiring.toMul",
"NonAssocRing",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"NonAssocSemiring.mul_one",
"Pi.nonAssocSemiring",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"NonAssocRing.toNonAssocSemiring",
"instHMul"
] | false |
ContinuousWithinAt.sub | Mathlib.Topology.Algebra.Group.Defs | [
"ContinuousWithinAt",
"nhdsWithin",
"HSub.hSub",
"ContinuousSub",
"TopologicalSpace",
"instHSub",
"Filter.Tendsto.sub",
"Sub",
"Set"
] | true |
MeasureTheory.Measure.sub_self | Mathlib.MeasureTheory.Measure.Sub | [
"MeasureTheory.Measure",
"le_rfl",
"PartialOrder.toPreorder",
"HSub.hSub",
"MeasureTheory.Measure.instSub",
"MeasureTheory.Measure.instZero",
"MeasurableSpace",
"instHSub",
"MeasureTheory.Measure.sub_eq_zero_of_le",
"MeasureTheory.Measure.instPartialOrder",
"Zero.toOfNat0",
"OfNat.ofNat",
"E... | true |
LieModule.chainBotCoeff | Mathlib.Algebra.Lie.Weights.Chain | [
"NegZeroClass.toNeg",
"IsDomain",
"CommRing",
"Pi.instNeg",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieRing.IsNilpotent",
"Module.IsTorsionFree",
"AddGroupWithOne.toAddMonoidWithOne",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"IsAdd... | true |
AddCommGrpCat.image.lift._proof_2 | Mathlib.Algebra.Category.Grp.Images | [
"CategoryTheory.Limits.MonoFactorisation.fac",
"CategoryTheory.Limits.MonoFactorisation.I",
"Eq.mpr",
"AddMonoidHom.instAddMonoidHomClass",
"CategoryTheory.Limits.MonoFactorisation.m_mono",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"Classical.indefiniteDes... | false |
forall_isClosed_iff | Mathlib.Topology.Closure | [
"IsClosed.closure_eq",
"Eq.rec",
"IsClosed",
"TopologicalSpace",
"Iff",
"closure",
"Iff.intro",
"isClosed_closure",
"Eq",
"Set"
] | true |
_private.Mathlib.Topology.Algebra.Valued.LocallyCompact.0.Valued.integer.compactSpace_iff_completeSpace_and_isDiscreteValuationRing_and_finite_residueField.match_1_1 | Mathlib.Topology.Algebra.Valued.LocallyCompact | [
"CompleteSpace",
"Subring.instSetLike",
"Valued.integer",
"Valued.ResidueField",
"IsDiscreteValuationRing",
"Finite",
"instUniformSpaceSubtype",
"Membership.mem",
"Field.toDivisionRing",
"Subtype",
"DivisionRing.toRing",
"LinearOrderedCommGroupWithZero",
"CommRing.toNonAssocCommRing",
"Fie... | false |
spectralAlgNorm_extends | Mathlib.Analysis.Normed.Unbundled.SpectralNorm | [
"AlgebraNorm.instFunLikeReal",
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"NormedField.toField",
"Field.toDivisionRing",
"NormedField.toNorm",
"DivisionRing.toRing",
"Algebra.IsAlgebraic",
"Field.toSemi... | true |
FundamentalGroupoid.eqToHom_eq | Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.eqToHom",
"Eq.rec",
"Quotient.mk",
"Path.Homotopic.setoid",
"congr_arg",
"Path.cast",
"TopologicalSpace",
"FundamentalGroupoid",
"FundamentalGroupoid.mk",
"FundamentalGroupoid.as",
"Path",
"Eq.refl",
"FundamentalGrou... | true |
Semiquot.blur'._proof_1 | Mathlib.Data.Semiquot | [
"Membership.mem",
"Set.Elem",
"Semiquot.s",
"HasSubset.Subset",
"Semiquot",
"Subtype.val",
"Set.instMembership",
"Subtype.property",
"Set.instHasSubset",
"Set"
] | false |
_private.Lean.Meta.CongrTheorems.0.Lean.Meta.EqInfo.noConfusion | Lean.Meta.CongrTheorems | [
"_private.Lean.Meta.CongrTheorems.0.Lean.Meta.EqInfo.noConfusionType",
"_private.Lean.Meta.CongrTheorems.0.Lean.Meta.EqInfo",
"Lean.FVarId",
"Eq.ndrec",
"Eq.refl",
"Eq",
"_private.Lean.Meta.CongrTheorems.0.Lean.Meta.EqInfo.casesOn"
] | false |
List.max?_toArray | Init.Data.Array.MinMax | [
"Eq.mpr",
"instDecidableNot",
"Decidable.casesOn",
"Array.max",
"congrArg",
"List.instDecidableEqNil",
"List.min_toArray._proof_2",
"Decidable",
"Option.some",
"Max",
"Eq.mp",
"dif_pos",
"id",
"Ne",
"Array.max?",
"Decidable.not_not._simp_1",
"Array.instDecidableEqEmp",
"List.max?",... | true |
Cardinal.lift_le_aleph1 | Mathlib.SetTheory.Cardinal.Aleph | [
"Cardinal.aleph",
"Ordinal.partialOrder",
"Cardinal",
"PartialOrder.toPreorder",
"Cardinal.lift",
"Preorder.toLE",
"LE.le",
"Cardinal.instLE",
"Ordinal.one",
"Iff",
"Cardinal.lift_le_aleph_one",
"One.toOfNat1",
"OrderEmbedding",
"OfNat.ofNat",
"DFunLike.coe",
"instFunLikeOrderEmbedding... | true |
_private.Mathlib.Data.Fintype.Pi.0.Set.iUnion_snoc._simp_1_2 | Mathlib.Data.Fintype.Pi | [
"propext",
"Or",
"or_comm",
"Eq"
] | false |
Std.ExtDTreeMap.diff.congr_simp | Std.Data.ExtDTreeMap.Lemmas | [
"Ordering",
"Eq.rec",
"Std.TransCmp",
"Std.ExtDTreeMap",
"Eq.refl",
"Std.ExtDTreeMap.diff",
"Eq"
] | true |
Concept.instSupSet | Mathlib.Order.Concept | [
"Concept.instSupSet._proof_1",
"Set.iInter",
"Membership.mem",
"Concept.intent",
"SupSet.mk",
"Concept.ofIsIntent",
"SupSet",
"Concept",
"Set.instMembership",
"Set"
] | true |
CategoryTheory.ConcreteCategory.homEquiv | Mathlib.CategoryTheory.ConcreteCategory.Basic | [
"CategoryTheory.ConcreteCategory.homEquiv._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"Equiv.mk",
"CategoryTheory.ToHom",
"Equiv",
"CategoryTheory.ConcreteCategory",
"CategoryTheory.ConcreteCategory.ofHom_hom",
"CategoryTheory.ConcreteC... | true |
CategoryTheory.Limits.image.map | Mathlib.CategoryTheory.Limits.Shapes.Images | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasImageMap.imageMap",
"CategoryTheory.Arrow.left",
"CategoryTheory.Arrow.hom",
"CategoryTheory.Limits.image",
"CategoryTheory.Limits.HasImageMap",
"CategoryTheory.Limits.ImageMap.map",
"CategoryTheory.Category.toCategory... | true |
groupCohomology.coboundaries₁ | Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | [
"Pi.Function.module",
"Submodule",
"Rep.V",
"CommRing",
"Pi.addCommMonoid",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Group",
"Rep.hV1",
"LinearMap.range",
"DivInvMonoid.toMonoid",
"groupCohomology.coboundaries₁._proof_1",
"Group.toDivInvMonoid",
"ModuleCat.o... | true |
hasFDerivAt_pi_polarCoord_symm | Mathlib.Analysis.SpecialFunctions.PolarCoord | [
"ContinuousLinearMap.comp",
"HasFDerivAt",
"Eq.mpr",
"Pi.Function.module",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Fintype.ofFinite",
"Prod.normedSpace",
"Semiring.toModule",
"Pi.addCommMonoid",
"Prod.normedAddCommGroup",
"fderivPiPolarCoordSymm",
... | true |
Std.DTreeMap.size_emptyc | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap.Internal.Impl.size_empty",
"Std.DTreeMap",
"Ordering",
"instOfNatNat",
"Std.DTreeMap.size",
"Nat",
"Std.DTreeMap.instEmptyCollection",
"EmptyCollection.emptyCollection",
"OfNat.ofNat",
"Eq"
] | true |
WithZero.coe_mul | Mathlib.Algebra.GroupWithZero.WithZero | [
"HMul.hMul",
"MulZeroClass.toMul",
"Mul",
"WithZero.instMulZeroClass",
"WithZero",
"WithZero.coe",
"Eq",
"rfl",
"instHMul"
] | true |
Lean.Elab.Tactic.Conv.evalNestedTacticCore | Lean.Elab.Tactic.Conv.Basic | [
"Lean.Syntax",
"instOfNatNat",
"Lean.Elab.Tactic.instMonadTacticM",
"GetElem.getElem",
"Unit",
"Lean.Elab.Tactic.Tactic",
"Nat",
"True",
"Monad.toBind",
"Bind.bind",
"Lean.Elab.Tactic.TacticM",
"OfNat.ofNat",
"Lean.Elab.Tactic.evalTactic",
"Lean.Syntax.instGetElemNatTrue",
"True.intro",
... | true |
IsDiscrete.recOn | Mathlib.Topology.Constructions | [
"IsDiscrete.rec",
"DiscreteTopology",
"Membership.mem",
"Set.Elem",
"TopologicalSpace",
"IsDiscrete.mk",
"IsDiscrete",
"instTopologicalSpaceSubtype",
"Set.instMembership",
"Set"
] | false |
MultilinearMap.ofSubsingleton_apply_apply | Mathlib.LinearAlgebra.Multilinear.Basic | [
"Equiv.instEquivLike",
"LinearMap.instFunLike",
"Equiv",
"LinearMap",
"MultilinearMap",
"AddCommMonoid",
"MultilinearMap.instFunLikeForall",
"Semiring",
"Subsingleton",
"Eq.refl",
"MultilinearMap.ofSubsingleton",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.co... | true |
Multiset.prod_hom_rel | Mathlib.Algebra.BigOperators.Group.Multiset.Defs | [
"MulOne.toOne",
"HMul.hMul",
"Multiset.map",
"Monoid.toMulOneClass",
"Multiset.prod",
"Multiset",
"MulOne.toMul",
"Quotient.inductionOn",
"List",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"One.toOfNat1",
"List.isSetoid",
"OfNat.ofNat",
"CommMonoid",
"List.prod_hom_rel",
"instHMu... | true |
RestrictedProduct.nhds_zero_eq_map_ofPre | Mathlib.Topology.Algebra.RestrictedProduct.TopologicalSpace | [
"SetLike",
"Filter.map",
"RestrictedProduct.inclusion",
"RestrictedProduct.instZeroCoeOfZeroMemClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"nhds",
"RestrictedProduct.topologicalSpace",
"ZeroMemClass",
"LE.le",
"RestrictedProduct",
"TopologicalSpace",
"SetLike.coe",
"Filter.principa... | true |
UInt64.add_eq_right | Init.Data.UInt.Lemmas | [
"UInt64.instOfNat",
"UInt64.toBitVec_add",
"instAddUInt64",
"congrArg",
"UInt64",
"BitVec.instAdd",
"BitVec",
"UInt64.eq_iff_toBitVec_eq._simp_1",
"UInt64.toBitVec_ofNat",
"instOfNatNat",
"BitVec.ofNat",
"BitVec.add_left_eq_self._simp_1",
"iff_self",
"instHAdd",
"Iff",
"HAdd.hAdd",
"... | true |
FreeAbelianGroup.ofMulHom_coe | Mathlib.GroupTheory.FreeAbelianGroup | [
"Monoid",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"MulOneClass.toMulOne",
"FreeAbelianGroup.ring",
"FreeAbelianGroup.ofMulHom",
"FreeAbelianGroup.of",
"FreeAbelianGroup",
"Ring.toSemiring",
"Eq",
"DFunL... | true |
NumberField.InfinitePlace.Completion.WithAbs.ratCast_equiv | Mathlib.NumberTheory.NumberField.Completion.InfinitePlace | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"UniformSpace.Completion.coe'",
"RingHom.instRingHomClass",
"Real.partialOrder",
"Real",
"UniformSpace.Completion.coeRingHom",
"NormedRing.toRing",
"WithAbs",
"DivisionRing.toRatCast",
"WithAbs.instRing",
"RingEquiv.instEqui... | true |
Std.Internal.IO.Async.System.OSInfo.name | Std.Internal.Async.System | [
"Std.Internal.IO.Async.System.OSInfo",
"String"
] | true |
Lean.Elab.Tactic.BVDecide.Frontend.State.mk.injEq | Lean.Elab.Tactic.BVDecide.Frontend.BVDecide.Reflect | [
"Eq.propIntro",
"Lean.Expr.instBEq",
"Lean.Elab.Tactic.BVDecide.Frontend.State.mk.inj",
"Lean.injEq_helper",
"Lean.Elab.Tactic.BVDecide.Frontend.State",
"Lean.Expr",
"Std.HashMap",
"And",
"Lean.Elab.Tactic.BVDecide.Frontend.State.mk",
"Eq.ndrec",
"Eq.refl",
"Lean.Expr.instHashable",
"Eq",
... | true |
ShiftLeft.recOn | Init.Prelude | [
"ShiftLeft",
"ShiftLeft.mk",
"ShiftLeft.rec"
] | false |
ENat.sSup_mul | Mathlib.Data.ENat.Lattice | [
"Eq.mpr",
"instCompleteLinearOrderENat",
"HMul.hMul",
"Iff.of_eq",
"CommSemiring.toNonUnitalCommSemiring",
"congrArg",
"CommSemiring.toSemiring",
"iSup",
"ENat.mul_sSup",
"Membership.mem",
"id",
"CommMagma.toMul",
"NonUnitalCommSemiring.toNonUnitalNonAssocCommSemiring",
"ConditionallyCompl... | true |
List.dropLast_prefix | Init.Data.List.Sublist | [
"List.getLast",
"Eq.mpr",
"List.dropLast.eq_1",
"congrArg",
"List.dropLast_concat_getLast",
"id",
"List.dropLast",
"List.append_nil",
"List.cons",
"instHAppendOfAppend",
"List",
"Unit",
"List.IsPrefix",
"List.cons_ne_nil",
"Exists.intro",
"Eq.refl",
"_private.Init.Data.List.Sublist.0... | true |
_private.Mathlib.AlgebraicTopology.SimplicialObject.DeltaZeroIter.0.CategoryTheory.SimplicialObject.σ₀Iter_δ₀Iter._simp_1_3 | Mathlib.AlgebraicTopology.SimplicialObject.DeltaZeroIter | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.map",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Functor.map_comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq.symm",
"Eq",
"CategoryTheory.Functor.obj",
"CategoryTheory.Cate... | false |
BoxIntegral.Prepartition.distortion_le_of_mem | Mathlib.Analysis.BoxIntegral.Partition.Basic | [
"BoxIntegral.Prepartition",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"BoxIntegral.Box.distortion",
"NNReal.instSemilatticeSup",
"NNReal",
"LE.le",
"BoxIntegral.Prepartition.boxes",
"BoxIntegral.Prepartition.distortion",
"NNReal.instPartialOrder",
"Fintype",
"BoxIntegral.... | true |
BitVec.toInt_eq_toNat_of_lt | Init.Data.BitVec.Lemmas | [
"instPowNat",
"HMul.hMul",
"congrArg",
"HSub.hSub",
"BitVec",
"instMulNat",
"instOfNatNat",
"Int",
"BitVec.toNat",
"ite_cond_eq_true",
"Nat.cast",
"instNatPowNat",
"instHSub",
"HPow.hPow",
"Nat",
"LT.lt",
"True",
"eq_self",
"eq_true",
"of_eq_true",
"Nat.decLt",
"Int.instSub... | true |
preimage_map_fst_pullbackDiagonal | Mathlib.Data.Set.Prod | [
"Set.ext",
"Eq.mpr",
"_private.Mathlib.Data.Set.Prod.0.preimage_map_fst_pullbackDiagonal._simp_1_2",
"congrArg",
"Function.Pullback",
"setOf",
"and_iff_left",
"Subtype.casesOn",
"Membership.mem",
"id",
"_private.Mathlib.Data.Set.Prod.0.preimage_map_fst_pullbackDiagonal._simp_1_4",
"Prod.mk",
... | true |
HomotopicalAlgebra.CofibrantObject.HoCat.adjUnit._proof_2 | Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy | [
"CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteColimits",
"HomotopicalAlgebra.ModelCategory.cm1a",
"HomotopicalAlgebra.ModelCategory.cm1b",
"HomotopicalAlgebra.BifibrantObject.homRel._proof_2",
"CategoryTheory.Limits.hasColimitsOfShape_discrete",
"CategoryTheory.Limits.hasFiniteProducts_of_hasFini... | false |
DomMulAct.mk_pow | Mathlib.GroupTheory.GroupAction.DomAct.Basic | [
"Monoid",
"DomMulAct",
"Equiv.instEquivLike",
"DomMulAct.instMonoidOfMulOpposite",
"Equiv",
"DomMulAct.mk",
"Monoid.toPow",
"HPow.hPow",
"Nat",
"MulOpposite.instMonoid",
"instHPow",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
Lean.Lsp.CodeAction.title | Lean.Data.Lsp.CodeActions | [
"String",
"Lean.Lsp.CodeAction"
] | true |
Matroid.RankFinite | Mathlib.Combinatorics.Matroid.Basic | [
"Matroid.RankFinite.mk",
"Matroid"
] | true |
CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId_hom_app_app | Mathlib.CategoryTheory.Limits.FormalCoproducts.Basic | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Limits.FormalCoproduct",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasProducts",
"CategoryTheory.Limits.FormalCoproduct.evalOpCompInlIsoId._proof_1",
"CategoryTheory.Limits.FormalC... | true |
Set.monoid._proof_1 | Mathlib.Algebra.Group.Pointwise.Set.Basic | [
"Monoid",
"MulOne.toOne",
"Mul.mk",
"Semigroup.toMul",
"Semigroup.mul_assoc",
"One.mk",
"Monoid.toMulOneClass",
"Set.mulOneClass",
"Semigroup.mk",
"npowRecAuto",
"instOfNatNat",
"Set.semigroup",
"One.one",
"MulOneClass.toMulOne",
"Mul.mul",
"Nat",
"Monoid.toSemigroup",
"One.toOfNat... | false |
_private.Lean.Meta.CongrTheorems.0.Lean.Meta.EqInfo._sizeOf_inst | Lean.Meta.CongrTheorems | [
"_private.Lean.Meta.CongrTheorems.0.Lean.Meta.EqInfo",
"_private.Lean.Meta.CongrTheorems.0.Lean.Meta.EqInfo._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
DifferentiableWithinAt.continuousMultilinear_apply_const | Mathlib.Analysis.Calculus.FDeriv.CompCLM | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Fintype.ofFinite",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"ContinuousLinearMap.topologicalSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.... | true |
Std.DTreeMap.wf | Std.Data.DTreeMap.Basic | [
"Std.DTreeMap",
"Ord.mk",
"Ordering",
"Std.DTreeMap.inner",
"Std.DTreeMap.Internal.Impl.WF",
"autoParam",
"Std.DTreeMap._auto_1"
] | true |
_private.Mathlib.Logic.Equiv.Set.0.Equiv.preimage_piEquivPiSubtypeProd_symm_pi._simp_1_3 | Mathlib.Logic.Equiv.Set | [
"Subtype.forall",
"Subtype",
"Subtype.mk",
"propext",
"Eq"
] | false |
LinearEquiv.prodProdProdComm_apply | Mathlib.LinearAlgebra.Prod | [
"LinearEquiv.prodProdProdComm",
"Prod.mk",
"Prod.fst",
"AddCommMonoid",
"RingHomInvPair.ids",
"LinearEquiv",
"Semiring",
"LinearEquiv.instEquivLike",
"Eq.refl",
"Module",
"Prod",
"Prod.instModule",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
"Prod.snd",
"DFunLike.coe",
"Equi... | true |
Lean.Parser.registerBuiltinDynamicParserAttribute | Lean.Parser.Extension | [
"Lean.Parser.registerBuiltinDynamicParserAttribute._auto_1",
"IO",
"autoParam",
"Unit",
"Lean.Parser.mkParserAttributeImpl",
"Lean.Name",
"Lean.registerBuiltinAttribute"
] | true |
RCLike.natCast._inherited_default | Mathlib.Analysis.RCLike.Basic | [
"One.mk",
"Add.mk",
"id",
"semiOutParam",
"Nat",
"Zero.mk",
"Nat.unaryCast"
] | false |
Mathlib.Tactic.Linarith.GlobalBranchingPreprocessor._sizeOf_inst | Mathlib.Tactic.Linarith.Datatypes | [
"Mathlib.Tactic.Linarith.GlobalBranchingPreprocessor",
"SizeOf.mk",
"Mathlib.Tactic.Linarith.GlobalBranchingPreprocessor._sizeOf_1",
"SizeOf"
] | false |
_private.Lean.Compiler.Old.0.Lean.Compiler.checkIsDefinition.match_4 | Lean.Compiler.Old | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"_private.Lean.Compiler.Old.0.Lean.Compiler.checkIsDefinition._sparseCasesOn_4",
"Lean.AsyncConstantInfo",
"Option"
] | false |
CategoryTheory.Limits.BinaryCofan.IsColimit.hom_ext | Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | [
"CategoryTheory.Limits.BinaryCofan.inr",
"CategoryTheory.Functor",
"CategoryTheory.Limits.IsColimit.hom_ext",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingPair.right",
"CategoryTheory.Limits.IsColimit",
"CategoryTheory.Limit... | true |
CategoryTheory.Functor.mapMonCompIso._proof_6 | Mathlib.CategoryTheory.Monoidal.Mon | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Mon.Hom.hom",
"CategoryTheory.Mon.mkIso",
"CategoryTheory.Functor.comp",
"CategoryTheory.Iso.refl",
"id",
"CategoryTheory.Iso",
"CategoryTheory.Funct... | false |
VectorBundleCore.vectorBundle | Mathlib.Topology.VectorBundle.Basic | [
"VectorBundleCore.Fiber",
"NormedSpace",
"ContinuousLinearMap.topologicalSpace",
"MemTrivializationAtlas.casesOn",
"FiberBundle.trivializationAtlas",
"AddCommGroup.toAddCommMonoid",
"FiberBundleCore.Fiber",
"VectorBundleCore.toTopologicalSpace",
"NormedSpace.toModule",
"VectorBundle.mk",
"Pseudo... | true |
IsLocalization.algEquivOfAlgEquiv | Mathlib.RingTheory.Localization.Basic | [
"AlgEquiv.instEquivLike",
"RingEquiv.toEquiv",
"IsLocalization",
"CommSemiring.toSemiring",
"IsScalarTower",
"IsLocalization.algEquivOfAlgEquiv._proof_4",
"Algebra",
"Algebra.toSMul",
"Distrib.toAdd",
"AlgEquivClass.toAlgHomClass",
"RingHomClass.toMonoidWithZeroHomClass",
"NonAssocSemiring.toM... | true |
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