name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.Artinian.mk._flat_ctor | Mathlib.CategoryTheory.Noetherian | [
"CategoryTheory.IsArtinianObject",
"CategoryTheory.EssentiallySmall.mk",
"CategoryTheory.Equivalence",
"Exists",
"CategoryTheory.SmallCategory",
"CategoryTheory.Artinian",
"CategoryTheory.Artinian.mk",
"Nonempty",
"CategoryTheory.Category"
] | false |
CategoryTheory.ShortComplex.RightHomologyData.unop._proof_4 | Mathlib.Algebra.Homology.ShortComplex.RightHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.RightHomologyData.wp",
"Opposite",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.Limits.CokernelCofork.IsColimit.ofπUnop",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.RightHomology... | false |
CategoryTheory.Functor.Initial.extendCone._proof_4 | Mathlib.CategoryTheory.Limits.Final | [
"CategoryTheory.Limits.ConeMorphism.mk",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Functor.Initial.lift",
"Quiver.Hom",
"CategoryTheory.Functor.Initial",
"CategoryTheory.Functor.category",
"Cate... | false |
CategoryTheory.Limits.CoconeMorphism.map_w_assoc | Mathlib.CategoryTheory.Limits.Cones | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.CoconeMorphism.hom",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"Ca... | true |
AddCircle.ergodic_nsmul | Mathlib.Dynamics.Ergodic.AddCircle | [
"Ergodic",
"Int.instIsStrictOrderedRing",
"Real",
"instHSMul",
"instConditionallyCompleteLinearOrder",
"Real.instZero",
"Nat.abs_cast",
"abs",
"congrArg",
"AddCommMagma.to_isCommutative",
"MeasureTheory.MeasureSpace.toMeasurableSpace",
"AddGroupWithOne.toAddMonoidWithOne",
"AddMonoid.toNSMul... | true |
String.Pos.next._proof_2 | Init.Data.String.Basic | [
"String.toSlice",
"String",
"String.Pos.toSlice",
"Ne",
"ne_of_apply_ne",
"String.Slice.endPos",
"String.Pos.next._proof_1",
"String.Pos.ofToSlice",
"String.endPos",
"String.Pos",
"String.Slice.Pos"
] | false |
WithLp.prod_norm_sq_eq_of_L2 | Mathlib.Analysis.Normed.Lp.ProdLp | [
"WithLp",
"Norm.norm",
"Eq.mpr",
"Real",
"SeminormedAddCommGroup",
"fact_one_le_two_ennreal",
"congrArg",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"PartialOrder.toPreorder",
"Nat.instAtLeastTwoHAddOfNat",
"Preorder.toLE",
"WithLp.prod_nnnorm_eq_of_L2",
"id",
"Distrib.toAdd",
"Or... | true |
FirstOrder.Language.LHom.comp_onBoundedFormula | Mathlib.ModelTheory.Syntax | [
"FirstOrder.Language.BoundedFormula.imp",
"Eq.mpr",
"FirstOrder.Language.LHom.onRelation",
"FirstOrder.Language.LHom.comp",
"congrArg",
"FirstOrder.Language.Relations.boundedFormula",
"FirstOrder.Language.LHom.onTerm",
"Function.comp",
"FirstOrder.Language.Term",
"Sum",
"id",
"FirstOrder.Langu... | true |
_private.Mathlib.LinearAlgebra.Matrix.Notation.0.Matrix.delabMatrixNotation._sparseCasesOn_7 | Mathlib.LinearAlgebra.Matrix.Notation | [
"Lean.Name.rec",
"Nat.ne_of_beq_eq_false",
"String",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Name.num",
"Lean.Name.ctorIdx",
"Lean.Name.str",
"Lean.Name.anonymous",
"Nat.land",
"Nat",
"Bool",
"Lean.Name",
"Eq.refl",
"OfNat.ofNat",
"Bool.false"
] | false |
SimpleGraph.Walk.isSubwalk_iff_darts_isInfix | Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks | [
"Eq.mpr",
"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix._proof_1_31",
"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Subwalks.0.SimpleGraph.Walk.isSubwalk_iff_darts_isInfix.match_1_3",
"GetElem?.toGetElem",
"congrArg",
"_private.Mathlib.Combinat... | true |
_private.Mathlib.Topology.DiscreteSubset.0.IsDiscrete.biUnion._simp_1_1 | Mathlib.Topology.DiscreteSubset | [
"Subtype",
"propext",
"Subtype.forall'",
"Subtype.val",
"Eq",
"Subtype.property"
] | false |
IntermediateField.map._proof_1 | Mathlib.FieldTheory.IntermediateField.Basic | [
"Subsemiring.instSetLike",
"AlgHom.algHomClass",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"IntermediateField",
"AlgHom",
"AlgHom.funLike",
"Submonoid.toSubsemigroup",
"Algebra",
"DivisionSemiring.toGroupWithZero",
"RingHom",
"Membership.mem",
"DivisionMonoid.to... | false |
Lean.SMap.forM | Lean.Data.SMap | [
"Lean.SMap.map₂",
"Lean.PersistentHashMap.forM",
"Lean.SMap.map₁",
"PUnit",
"Lean.SMap",
"Std.HashMap.forM",
"Monad.toBind",
"Bind.bind",
"Hashable",
"Monad",
"BEq"
] | true |
ISize.toInt_toBitVec | Init.Data.SInt.Lemmas | [
"Int",
"System.Platform.numBits",
"ISize.toBitVec",
"BitVec.toInt",
"ISize",
"Eq",
"rfl",
"ISize.toInt"
] | true |
CategoryTheory.ShortComplex.FunctorEquivalence.inverse._proof_2 | Mathlib.Algebra.Homology.ShortComplex.FunctorEquivalence | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.Fu... | false |
HasFDerivWithinAt.of_comp_of_isEmbedding | Mathlib.Analysis.Calculus.FDeriv.OfCompLeft | [
"ContinuousLinearMap.comp",
"Pure.pure",
"Filter.Eventually.self_of_nhdsWithin",
"NormedSpace",
"SProd.sprod",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"nhdsWithin",
"Filter.Eventually",
"NormedSpace.toModule",
"Filter.tendsto_pure._simp_1",
"PseudoMetricSpace.toUniformSp... | true |
Lean.Doc.Data.instReprSyntaxCat.repr | Lean.Elab.DocString.Builtin | [
"Std.Format.nil",
"Lean.Name.instRepr",
"Std.Format.instAppend",
"Std.Format.group",
"Lean.Doc.Data.SyntaxCat.name",
"Int",
"instHAppendOfAppend",
"instOfNat",
"Nat",
"Std.Format.bracket",
"Std.Format",
"Lean.Name",
"OfNat.ofNat",
"Lean.Doc.Data.SyntaxCat",
"HAppend.hAppend",
"Std.Form... | true |
Sum.Lex.noMinOrder | Mathlib.Data.Sum.Order | [
"Iff.mpr",
"Equiv.instEquivLike",
"NoMinOrder",
"Lex",
"Exists",
"Sum",
"Equiv",
"Sum.inl",
"NoMinOrder.mk",
"Sum.Lex.inl_lt_inl_iff",
"Sum.inr",
"_private.Mathlib.Data.Sum.Order.0.Sum.noMinOrder.match_1",
"LT.lt",
"Exists.intro",
"NoMinOrder.exists_lt",
"_private.Mathlib.Data.Sum.Orde... | true |
CategoryTheory.Coverage.Saturate.top | Mathlib.CategoryTheory.Sites.Coverage | [
"CategoryTheory.Coverage",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CategoryTheory.Coverage.Saturate.top",
"CompleteLattice.toBoundedOrder",
"CategoryTheory.Sieve",
"OrderTop.toTop",
"BoundedOrder.toOrderTop",
"CategoryTheory.Sieve.ins... | true |
Std.ExtDTreeMap.maxKey!_erase_eq_of_not_compare_maxKey!_eq | Std.Data.ExtDTreeMap.Lemmas | [
"Iff.mpr",
"Std.ExtDTreeMap.mk",
"Std.ExtDTreeMap.isEmpty_eq_false_iff",
"Std.DTreeMap",
"Std.ExtDTreeMap.erase",
"Ordering",
"Ordering.eq",
"Ne",
"Std.ExtDTreeMap.instEmptyCollection",
"Std.TransCmp",
"Std.ExtDTreeMap.isEmpty",
"Std.ExtDTreeMap.inductionOn",
"Std.ExtDTreeMap",
"Bool",
"... | true |
CauchyFilter.monotone_gen | Mathlib.Topology.UniformSpace.Completion | [
"Filter.instMembership",
"UniformSpace",
"Cauchy",
"SetRel",
"SProd.sprod",
"PartialOrder.toPreorder",
"Monotone",
"Membership.mem",
"Filter.monotone_mem",
"CompleteLattice.toConditionallyCompleteLattice",
"Prod.fst",
"Set.monotone_setOf",
"CompleteBooleanAlgebra.toCompleteLattice",
"Cauch... | true |
_private.Mathlib.Analysis.Hofer.0.hofer._simp_1_4 | Mathlib.Analysis.Hofer | [
"False",
"HMul.hMul",
"eq_false",
"Mul",
"Ne",
"NoZeroDivisors",
"Zero.toOfNat0",
"mul_ne_zero",
"OfNat.ofNat",
"Eq",
"instHMul",
"Zero"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Triangle.Basic.0.SimpleGraph.edgeDisjointTriangles_iff_mem_sym2_subsingleton._simp_1_20 | Mathlib.Combinatorics.SimpleGraph.Triangle.Basic | [
"Exists",
"forall_exists_index",
"propext",
"Exists.intro",
"Eq"
] | false |
RootPairing.Equiv.instSMulCommClassMulOppositeAut | Mathlib.LinearAlgebra.RootSystem.Hom | [
"CommRing",
"instHSMul",
"MonoidHom.instFunLike",
"SemilinearMapClass.toMulActionSemiHomClass",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"MulOpposite",
"LinearMap.... | true |
MvPolynomial.support_X | Mathlib.Algebra.MvPolynomial.Basic | [
"Nontrivial",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"MvPolynomial.support_monomial",
"NeZero.one",
"Semiring.toModule",
"AddMonoidAlgebra.addAddCommMonoid",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"MvPolynomial.X.eq_1",
"MvPolynomial.monomial",... | true |
Class.coe_sUnion._simp_1 | Mathlib.SetTheory.ZFC.Class | [
"Class.ofSet",
"ZFSet",
"Class.coe_sUnion",
"ZFSet.sUnion",
"Class.sUnion",
"Class",
"Eq.symm",
"Eq"
] | false |
_private.Mathlib.Order.Filter.Basic.0.Filter.mem_iInf_of_directed._simp_1_2 | Mathlib.Order.Filter.Basic | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
Affine.Simplex.excenterWeightsUnnorm | Mathlib.Geometry.Euclidean.Incenter | [
"InnerProductSpace.toNormedSpace",
"Affine.Simplex.height",
"Nat.instMulZeroClass",
"Real",
"HMul.hMul",
"Real.instRCLike",
"Real.instInv",
"Finset",
"NormedSpace.toModule",
"instDecidableEqFin",
"Membership.mem",
"Affine.Simplex",
"Real.instRing",
"instOfNatNat",
"Real.instOne",
"inst... | true |
Submodule.smithNormalFormOfLE._proof_5 | Mathlib.LinearAlgebra.FreeModule.PID | [
"Submodule",
"CommRing",
"instHSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Fin.castLE",
"Submodule.addCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"AddCommG... | false |
Lean.Grind.imp_eq_of_eq_false_left | Init.Grind.Lemmas | [
"False",
"congrArg",
"false_implies",
"implies_congr",
"True",
"eq_self",
"of_eq_true",
"Eq.refl",
"congrFun'",
"Eq",
"Eq.trans"
] | true |
instLEBitVec | Init.Prelude | [
"BitVec",
"BitVec.toNat",
"LE.le",
"instLENat",
"LE",
"Nat",
"LE.mk"
] | true |
tangentMapWithin_eq_tangentMap | Mathlib.Geometry.Manifold.MFDeriv.Basic | [
"Eq.mpr",
"TangentBundle",
"tangentMapWithin_subset",
"NormedSpace",
"mdifferentiableWithinAt_univ",
"congrArg",
"Set.subset_univ",
"Set.univ",
"MDifferentiableAt",
"UniqueMDiffWithinAt",
"Eq.mp",
"id",
"TopologicalSpace",
"Bundle.TotalSpace.proj",
"ModelWithCorners",
"tangentMapWithin... | true |
Std.DTreeMap.Internal.Impl.getKey?._f | Std.Data.DTreeMap.Internal.Queries | [
"Ord",
"Std.DTreeMap.Internal.Impl.contains.match_3",
"Option.some",
"Ordering",
"Std.DTreeMap.Internal.Impl.inner",
"Ord.compare",
"Option.none",
"Unit",
"Std.DTreeMap.Internal.Impl.below",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Std.DTreeMap.Internal.Impl.contains.match_1",
"Std.DTreeMa... | false |
CategoryTheory.GrothendieckTopology.pointBot_fiber | Mathlib.CategoryTheory.Sites.Point.Presheaf | [
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"Lattice.toSemilatticeSup",
"Opposite",
"CompleteLattice.toLattice",
"CategoryTheory.LocallySmall",
"CategoryTheory.shrinkYoneda",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"Preorder.toLE",
"Complete... | true |
DirectLimit.NonUnitalStarRing.lift_apply | Mathlib.Algebra.Colimit.DirectLimit | [
"NonUnitalStarRingHom.instFunLike",
"Preorder.toLE",
"NonUnitalStarRingHom",
"StarHomClass",
"DirectLimit.lift",
"LE.le",
"StarAddMonoid.toInvolutiveStar",
"DirectLimit",
"DirectLimit.NonUnitalStarRing.lift._proof_1",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"StarRing.toStarAddMonoid",
"Di... | true |
_private.Mathlib.GroupTheory.FreeGroup.Basic.0.FreeGroup.Red.red_iff_irreducible._simp_1_4 | Mathlib.GroupTheory.FreeGroup.Basic | [
"False",
"eq_false",
"List.cons",
"List",
"List.cons_ne_nil",
"Eq",
"List.nil"
] | false |
ContDiffMapSupportedIn.compact_supp | Mathlib.Analysis.Distribution.ContDiffMapSupportedIn | [
"HasCompactSupport.intro",
"Real",
"NormedSpace",
"NormedAddCommGroup.toMetricSpace",
"PseudoMetricSpace.toUniformSpace",
"PseudoEMetricSpace.pseudoMetrizableSpace",
"EMetricSpace.toPseudoEMetricSpace",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"ContDiffMapSupporte... | true |
CategoryTheory.instRepresentablyCoflatIndYoneda | Mathlib.CategoryTheory.Limits.Indization.Category | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.RepresentablyCoflat.mk",
"CategoryTheory.Ind.yonedaCompInclusion",
"CategoryTheory.Functor.category",
"CategoryTheory.Ind",
"CategoryTheory.Functor.comp",
"CategoryTheory.yoneda",
"CategoryTheory.Ind.inclusion",
"CategoryTheory.Ind.isIndObject_... | true |
_private.Mathlib.Tactic.Linter.DeprecatedSyntaxLinter.0.Mathlib.Linter.Style.isDecideNative | Mathlib.Tactic.Linter.DeprecatedSyntaxLinter | [
"Option.instBEq",
"Lean.Syntax.matchesIdent",
"Lean.SourceInfo",
"Lean.Syntax.isOfKind",
"Option.some",
"Lean.Syntax",
"instDecidableEqBool",
"instOfNatNat",
"instBEqOfDecidableEq",
"Array",
"GetElem.getElem",
"_private.Mathlib.Tactic.Linter.DeprecatedSyntaxLinter.0.Mathlib.Linter.Style.isDeci... | true |
_private.Mathlib.Order.WellFounded.0.exists_not_acc_lt_of_not_acc._simp_1_1 | Mathlib.Order.WellFounded | [
"and_comm",
"And",
"propext",
"Eq"
] | false |
lt_of_mul_lt_mul_left | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Defs | [
"Preorder.toLT",
"HMul.hMul",
"PosMulReflectLT.toContravariantClass",
"Preorder.toLE",
"Mul",
"Subtype",
"LE.le",
"Subtype.mk",
"PosMulReflectLT",
"LT.lt",
"ContravariantClass.elim",
"Zero.toOfNat0",
"OfNat.ofNat",
"Subtype.val",
"Preorder",
"instHMul",
"Zero"
] | true |
_private.Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic.0.Nat.isSemilinearSet_diff | Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic | [
"_private.Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic.0.Nat.isSemilinearSet_compl",
"False",
"Pi.addCommMonoid",
"Finite",
"_private.Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic.0.Nat.isSemilinearSet_inter",
"Membership.mem",
"SDiff.sdiff",
"IsSemilinearSet",
"Nat",
"N... | true |
CompleteLattice.MulticoequalizerDiagram.multicofork._proof_1 | Mathlib.Order.CompleteLattice.MulticoequalizerDiagram | [
"CategoryTheory.Limits.MultispanShape.prod",
"CompleteLattice.MulticoequalizerDiagram.multispanIndex",
"CategoryTheory.Limits.MultispanShape.L",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CategoryTheory.Limits.MultispanIndex.right",
"Preorder.smallCategory",
"CategoryTheory.Limits.MultispanShape.fst... | false |
Sym2.instDecidableRel._proof_1 | Mathlib.Data.Sym.Sym2 | [
"Sym2.Rel",
"Prod.mk",
"Prod.fst",
"And",
"Iff",
"Sym2.rel_iff",
"Or",
"Prod",
"Eq",
"Prod.snd"
] | false |
Algebra.adjoin_mono | Mathlib.Algebra.Algebra.Subalgebra.Lattice | [
"Subalgebra.instSetLike",
"ChainCompletePartialOrder.instOfCompleteLattice",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"Algebra.adjoin",
"HasSubset.Subset",
"LE.le",
"ChainCompletePartialOrder.toPartialOrder",
"CommSemiring",
"SetLike.coe",
"Subalgebra.instPartialOrder",
"Comple... | true |
Lean.Meta.Sym.ProofInstInfo.noConfusionType | Lean.Meta.Sym.SymM | [
"Lean.Meta.Sym.ProofInstInfo",
"Lean.Meta.Sym.ProofInstInfo.casesOn",
"Lean.Meta.Sym.ProofInstArgInfo",
"Array",
"Eq"
] | false |
ValuationSubring.instIsScalarTowerSubtypeMemValuationSubringWithZeroMultiplicativeInt | Mathlib.RingTheory.Valuation.AlgebraInstances | [
"Int.instAddCommGroup",
"Int.instAddCommMonoid",
"Multiplicative.linearOrder",
"Int.instIsStrictOrderedRing",
"CommSemiring.toSemiring",
"Int.instLinearOrder",
"IsScalarTower",
"PartialOrder.toPreorder",
"Algebra",
"Algebra.toSMul",
"Membership.mem",
"Field.toDivisionRing",
"SemilatticeInf.t... | true |
Array.swap_perm | Init.Data.Array.Perm | [
"Eq.mpr",
"Array.swap",
"_private.Init.Data.Array.Perm.0.Array.swap_perm._simp_1_1",
"Array.set",
"id",
"List.set",
"List.Perm",
"Array.toList",
"Array",
"GetElem.getElem",
"Array.swap._proof_1",
"Array.Perm",
"Array.instGetElemNatLtSize",
"Nat",
"LT.lt",
"List.set_set_perm",
"instLT... | true |
HomologicalComplex.HomologySequence.snakeInput._proof_1 | Mathlib.Algebra.Homology.HomologySequence | [
"HomologicalComplex.homologyFunctor",
"CategoryTheory.Abelian.toPreadditive",
"HomologicalComplex.instCategory",
"CategoryTheory.Abelian",
"HomologicalComplex",
"ComplexShape",
"HomologicalComplex.instPreservesZeroMorphismsHomologyFunctor",
"CategoryTheory.Preadditive.preadditiveHasZeroMorphisms",
"... | false |
Std.TreeMap.Raw.getElem!_filter | Std.Data.TreeMap.Raw.Lemmas | [
"Iff.mpr",
"Option.pfilter",
"Std.TreeMap.Raw.WF.out",
"Option.some",
"Membership.mem",
"Ordering",
"Std.TreeMap.Raw.instMembership",
"Option.get!",
"Std.TreeMap.Raw.filter",
"Std.TransCmp",
"Std.TreeMap.Raw.WF",
"Std.TreeMap.Raw.inner",
"Std.DTreeMap.Raw.Const.get!_filter",
"Std.TreeMap.R... | true |
ConvexCone.closure_eq | Mathlib.Analysis.Convex.Cone.Closure | [
"ConvexCone.closure",
"SMul",
"ConvexCone.instSetLike",
"PartialOrder",
"ContinuousConstSMul",
"AddCommMonoid",
"TopologicalSpace",
"Iff",
"SetLike.coe",
"closure",
"ConvexCone",
"SetLike.ext'_iff",
"Semiring",
"AddCommSemigroup.toAddCommMagma",
"ContinuousAdd",
"AddCommMonoid.toAddCom... | true |
SSet.Subcomplex.liftPath._proof_2 | Mathlib.AlgebraicTopology.SimplicialSet.Path | [
"SSet.Path",
"Opposite",
"Membership.mem",
"CategoryTheory.Subfunctor.obj",
"instOfNatNat",
"SSet",
"instHAdd",
"HAdd.hAdd",
"SimplexCategory.mk",
"Opposite.op",
"Nat",
"CategoryTheory.types",
"SimplexCategory",
"instAddNat",
"CategoryTheory.Category.opposite",
"SSet.Subcomplex",
"Si... | false |
SummationFilter.mk.sizeOf_spec | Mathlib.Topology.Algebra.InfiniteSum.SummationFilter | [
"SummationFilter.mk",
"Finset",
"SummationFilter",
"SummationFilter._sizeOf_inst",
"instOfNatNat",
"instHAdd",
"Filter._sizeOf_inst",
"HAdd.hAdd",
"Finset._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"SizeOf",
"OfNat.ofNat",
"Eq",
"Filter"
] | true |
_private.Init.Data.Range.Polymorphic.Instances.0.Std.instLawfulUpwardEnumerableLTOfLawfulUpwardEnumerableOfLawfulUpwardEnumerableLEOfLawfulOrderLT._simp_1 | Init.Data.Range.Polymorphic.Instances | [
"Std.LawfulOrderLT.lt_iff",
"LE.le",
"Std.LawfulOrderLT",
"LE",
"And",
"LT.lt",
"propext",
"Eq",
"Not",
"LT"
] | false |
Matrix.IsSymm.transpose | Mathlib.LinearAlgebra.Matrix.Symmetric | [
"Matrix",
"congr_arg",
"Matrix.transpose",
"Matrix.IsSymm"
] | true |
ENNReal.add_div | Mathlib.Data.ENNReal.Inv | [
"ENNReal.instAdd",
"instHDiv",
"CommSemiring.toSemiring",
"Distrib.rightDistribClass",
"HDiv.hDiv",
"ENNReal.instCommSemiring",
"instDistribOfSemiring",
"instHAdd",
"Inv.inv",
"Distrib.toMul",
"HAdd.hAdd",
"ENNReal",
"ENNReal.instDivInvMonoid",
"DivInvMonoid.toDiv",
"ENNReal.instInv",
... | true |
instAddMonoidLex.eq_1 | Mathlib.Algebra.Order.Group.Synonym | [
"Lex",
"AddMonoid",
"Eq.refl",
"instAddMonoidLex",
"Eq"
] | true |
Lean.Elab.Tactic.evalInhabit | Mathlib.Tactic.Inhabit | [
"Pure.pure",
"Lean.MVarId.withContext",
"Lean.TSyntax.getId",
"Lean.Meta.isProp",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"instMonadControlTOfPure",
"Lean.Meta.State",
"instMonadLiftT",
"Lean.MVarId.intro1P",
"Lean.Syntax.Ident",
"Lean.Elab.Tactic.Context",
"Lean.Syntax",
"Lean.MVa... | true |
Equiv.distribLattice._proof_2 | Mathlib.Order.Lattice | [
"Preorder.toLT",
"Equiv.instEquivLike",
"Iff.rfl",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Equiv",
"DistribLattice",
"Iff",
"LT.lt",
"DFunLike.coe",
"Lattice.toSemilatticeInf",
"EquivLike.toFunLike"
] | false |
Lean.Meta.SolveByElim.SolveByElimConfig.maxDepth._default | Lean.Meta.Tactic.SolveByElim | [
"id",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | false |
List.prev._unsafe_rec | Mathlib.Data.List.Cycle | [
"List.getLast",
"False",
"False.elim",
"Membership.mem",
"Eq.mp",
"List.not_mem_nil._simp_1",
"dite",
"List.cons",
"List",
"List.prev._proof_3",
"List.instMembership",
"List.prev.match_1",
"List.cons_ne_nil",
"List.prev._unsafe_rec",
"Eq",
"Not",
"List.nil",
"DecidableEq",
"ite"
... | false |
Nucleus.instCompleteLattice._proof_1 | Mathlib.Order.Nucleus | [
"SemilatticeSup.le_sup_left",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"Nucleus",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"Nucleus.instCompleteSemilatticeInf",
"SemilatticeSup.toPartialOrder",
"CompleteLattice",
"Lattice.toSemilatticeInf",
"SemilatticeSup.sup",
"... | false |
Lean.Elab.Do.ControlLifter.rec | Lean.Elab.Do.Control | [
"Lean.Elab.Do.CodeLiveness",
"Lean.Elab.Do.ControlLifter",
"Lean.Elab.Do.ControlLifter.mk",
"Lean.Elab.Do.ControlStack",
"Lean.Expr",
"Lean.Elab.Do.DoElemCont",
"Option"
] | false |
Nat.castEmbedding | Mathlib.Algebra.Ring.CharZero | [
"Function.Embedding.mk",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"Function.Embedding",
"CharZero",
"Nat",
"Nat.cast_injective",
"AddMonoidWithOne"
] | true |
_private.Init.Data.Range.Polymorphic.BitVec.0.BitVec.succ?_eq_some._simp_1_4 | Init.Data.Range.Polymorphic.BitVec | [
"Option.ite_none_left_eq_some",
"Decidable",
"Option.some",
"Option.none",
"And",
"propext",
"Eq",
"Not",
"Option",
"ite"
] | false |
isLeftRegular_iff_isRegular | Mathlib.Algebra.Group.Defs | [
"HMul.hMul",
"congrArg",
"and_self",
"IsRegular",
"CommMagma.toMul",
"CommMagma",
"_private.Mathlib.Algebra.Group.Defs.0.isLeftRegular_iff_isRegular._simp_1_1",
"iff_self",
"IsLeftRegular",
"funext",
"IsRightRegular",
"And",
"Iff",
"True",
"mul_comm",
"of_eq_true",
"Function.Injectiv... | true |
_private.Init.Data.String.Substring.0.Substring.Raw.get.match_1.eq_1 | Init.Data.String.Substring | [
"Substring.Raw.mk",
"String",
"_private.Init.Data.String.Substring.0.Substring.Raw.get.match_1",
"String.Pos.Raw",
"Substring.Raw",
"Eq.refl",
"Eq"
] | true |
_private.Mathlib.Algebra.Star.SelfAdjoint.0.isSelfAdjoint_ringInverse_iff._proof_1_1 | Mathlib.Algebra.Star.SelfAdjoint | [
"False",
"IsSelfAdjoint",
"eq_false",
"congrArg",
"Classical.byContradiction",
"IsUnit",
"Eq.mp",
"id",
"Ring.inverse",
"StarAddMonoid.toInvolutiveStar",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"StarRing.toStarAddMonoid",
"StarRing",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"... | false |
Std.TreeMap.Raw.Equiv.of_toArray_perm | Std.Data.TreeMap.Raw.Lemmas | [
"Ordering",
"Std.TreeMap.Raw.Equiv",
"Std.TreeMap.Raw.inner",
"Std.DTreeMap.Raw.Equiv.of_constToArray_perm",
"Array.Perm",
"Std.TreeMap.Raw",
"Std.TreeMap.Raw.toArray",
"Std.TreeMap.Raw.Equiv.mk",
"Prod"
] | true |
MeasureTheory.AddContent.isCaratheodory_inducedOuterMeasure_of_mem | Mathlib.MeasureTheory.OuterMeasure.OfAddContent | [
"MeasureTheory.AddContent.isCaratheodory_ofFunction_of_mem",
"ENNReal.instAddCommMonoid",
"MeasureTheory.OuterMeasure.IsCaratheodory",
"MeasureTheory.inducedOuterMeasure",
"Membership.mem",
"MeasureTheory.AddContent.extend",
"MeasureTheory.IsSetSemiring",
"MeasureTheory.AddContent",
"ENNReal",
"Me... | true |
FiniteMulArchimedeanClass.mk._proof_1 | Mathlib.Algebra.Order.Archimedean.Class | [
"Iff.mpr",
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"IsOrderedMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"DivisionMonoid.toDivInvOneMonoid",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Iff.not",
"M... | false |
List.decidableLE._proof_1 | Init.Data.List.Basic | [
"False",
"List.instLT",
"List",
"absurd",
"LT.lt",
"Not",
"LT"
] | false |
FreeAddMonoid.length_eq_zero | Mathlib.Algebra.FreeMonoid.Basic | [
"FreeAddMonoid.toList",
"Equiv.instEquivLike",
"AddMonoid.toAddZeroClass",
"FreeAddMonoid.instAddCancelMonoid",
"AddCancelMonoid.toAddRightCancelMonoid",
"FreeAddMonoid.length",
"AddZeroClass.toAddZero",
"Equiv",
"instOfNatNat",
"AddZero.toZero",
"List",
"Iff",
"Nat",
"AddRightCancelMonoid... | true |
Lean.Meta.SolveByElim.ApplyRulesConfig.ctorIdx | Lean.Meta.Tactic.SolveByElim | [
"Lean.Meta.SolveByElim.ApplyRulesConfig",
"Nat"
] | false |
eq_one_of_mul_le_one_left | Mathlib.Algebra.Order.Monoid.Unbundled.Basic | [
"MulOne.toOne",
"Preorder.toLT",
"HMul.hMul",
"PartialOrder.toPreorder",
"LE.le.eq_of_not_lt'",
"Preorder.toLE",
"PartialOrder",
"MulLeftMono",
"MulOne.toMul",
"LE.le",
"MulOneClass.toMulOne",
"LE.le.not_gt",
"LT.lt",
"One.toOfNat1",
"one_lt_mul_of_lt_of_le'",
"MulOneClass",
"OfNat.o... | true |
LinearMap.lift_rank_comap_le | Mathlib.LinearAlgebra.Dimension.RankNullity | [
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"le_refl",
"Submodule.mem_comap._simp_1",
"Cardinal",
"Iff.of_eq",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"AddMonoid.toAddZeroClass",
"add_le_add",
"PartialOrder.toPreorder",
"Submodule.rank_le",
"LinearMap.k... | true |
List.Perm.foldl_eq' | Init.Data.List.Perm | [
"Eq.mpr",
"congrArg",
"List.Mem.tail",
"Membership.mem",
"id",
"List.Perm",
"List.foldl",
"List.Perm.subset",
"List.cons",
"List",
"List.instMembership",
"eq_self",
"List.Mem.head",
"of_eq_true",
"List.Perm.symm",
"Eq",
"List.Perm.recOnSwap'",
"Eq.trans",
"List.nil"
] | true |
Affine.Simplex.sign_excenterWeights_singleton_pos | Mathlib.Geometry.Euclidean.Incenter | [
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"InnerProductSpace.toNormedSpace",
"MulOne.toOne",
"False",
"Affine.Simplex.height",
"Nat.instMulZeroClass",
"Real.partialOrder",
"Real",
"instHSMul",
"Preorder.toLT",
"instSMulOfMul",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"Finset.univ... | true |
Std.Internal.Parsec.String.take | Std.Internal.Parsec.String | [
"Std.Internal.Parsec.ParseResult.error",
"bne",
"Std.Internal.Parsec.ParseResult",
"String",
"String.Slice.mk",
"instDecidableEqBool",
"Sigma.fst",
"instBEqOfDecidableEq",
"_private.Std.Internal.Parsec.String.0.Std.Internal.Parsec.String.take._proof_1",
"Bool.true",
"String.Slice.copy",
"Nat",... | true |
ContinuousLinearEquiv.continuousAlternatingMapCongrRightEquiv | Mathlib.Topology.Algebra.Module.Alternating.Basic | [
"ContinuousLinearEquiv.symm",
"ContinuousLinearEquiv.continuousAlternatingMapCongrRightEquiv._proof_1",
"Equiv.mk",
"Equiv",
"ContinuousLinearEquiv.continuousAlternatingMapCongrRightEquiv._proof_2",
"AddCommMonoid",
"TopologicalSpace",
"ContinuousLinearMap.compContinuousAlternatingMap",
"ContinuousL... | true |
Lean.SMap.find? | Lean.Data.SMap | [
"_private.Lean.Data.SMap.0.Lean.SMap.find?.match_1",
"Option.orElse",
"Lean.PHashMap",
"Membership.mem",
"Std.HashMap",
"Unit",
"Lean.SMap",
"Hashable",
"GetElem?.getElem?",
"Std.HashMap.instGetElem?Mem",
"BEq",
"Lean.PersistentHashMap.find?",
"Std.HashMap.instMembership",
"Option"
] | true |
Polynomial.exists_monic_irreducible_factor | Mathlib.RingTheory.Polynomial.UniqueFactorization | [
"Iff.mpr",
"Polynomial.C",
"dvd_zero",
"IsUnit.inv",
"Dvd.dvd",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Ne.isUnit",
"Polynomial.instDecidableEq",
"semigroupDvd",
"IsUnit",
"Cla... | true |
_private.Init.Data.List.Sublist.0.List.Sublist.trans.match_1_1 | Init.Data.List.Sublist | [
"HEq.refl",
"List.Sublist.cons_cons",
"List.cons",
"List",
"List.Sublist.slnil",
"List.Sublist.casesOn",
"eq_of_heq",
"Eq.ndrec",
"List.Sublist",
"Eq.refl",
"HEq",
"Eq.symm",
"List.Sublist.cons",
"Eq",
"List.nil"
] | false |
Std.DTreeMap.Internal.Impl.WF.below.insert | Std.Data.DTreeMap.Internal.WF.Defs | [
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.size",
"instOfNatNat",
"Std.DTreeMap.Internal.Impl.WF.below",
"Std.DTreeMap.Internal.Impl.WF",
"instHAdd",
"Std.DTreeMap.Internal.Impl.WF.below.insert",
"HAdd.hAdd",
"Na... | true |
HomologicalComplex.exactAt_iff_isZero_homology | Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex | [
"Eq.mpr",
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.ExactAt",
"congrArg",
"Iff.rfl",
"HomologicalComplex.HasHomology",
"HomologicalComplex",
"CategoryTheory.ShortComplex.exact_iff_isZero_homology",
"id",
"HomologicalComplex.exactAt_iff",
"ComplexShape",
"HomologicalComplex.... | true |
CochainComplex.mappingCone.lift.congr_simp | Mathlib.Algebra.Homology.HomotopyCategory.MappingCone | [
"HomologicalComplex.instCategory",
"CochainComplex.HomComplex.instAddCommGroupCochain",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CochainComplex.HomComplex.Cochain.comp",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelS... | true |
Lean.Compiler.LCNF.Simp.Config.etaPoly._default | Lean.Compiler.LCNF.Simp.Config | [
"id",
"Bool",
"Bool.false"
] | false |
Pi.eq_bot_iff_irrefl_of_subsingleton._simp_1 | Mathlib.Order.PropInstances | [
"Std.Irrefl",
"OrderBot.toBot",
"Prop.le",
"Prop.instBoundedOrder",
"Pi.instBotForall",
"Pi.eq_bot_iff_irrefl_of_subsingleton",
"Bot.bot",
"BoundedOrder.toOrderBot",
"propext",
"Subsingleton",
"Eq"
] | false |
_private.Lean.Elab.Calc.0.Lean.Elab.Term.annotateFirstHoleWithType.go | Lean.Elab.Calc | [
"Inhabited.default",
"instInhabitedOfMonad",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.Syntax",
"Lean.Expr",
"Lean.Elab.Term.TermElabM",
"Bool",
"Inhabited",
"StateT.instMonad",
"StateT",
"Inhabited.mk"
] | true |
HopfAlgCat.Hom.toBialgHom | Mathlib.Algebra.Category.HopfAlgCat.Basic | [
"CommRing",
"Coalgebra.toCoalgebraStruct",
"HopfAlgebraStruct.toBialgebra",
"Ring.toNonAssocRing",
"Bialgebra.toCoalgebra",
"CategoryTheory.ConcreteCategory.hom",
"HopfAlgCat.concreteCategory",
"BialgHom.funLike",
"HopfAlgCat.Hom",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSe... | true |
_private.Init.Data.Range.Polymorphic.UInt.0.UInt8.instLawfulHasSize._simp_2 | Init.Data.Range.Polymorphic.UInt | [
"BitVec",
"instOfNatNat",
"UInt8.toBitVec",
"Nat",
"propext",
"UInt8.toBitVec_inj",
"OfNat.ofNat",
"Eq.symm",
"UInt8",
"Eq"
] | false |
AddGrpCat.FilteredColimits.colimitAddGroup._proof_2 | Mathlib.Algebra.Category.Grp.FilteredColimits | [
"CategoryTheory.Functor",
"AddMonoid.toAddSemigroup",
"Zero.zero",
"AddGrpCat.instCategory",
"Add.mk",
"Neg.mk",
"AddMonoid.toZero",
"CategoryTheory.SmallCategory",
"Add.add",
"Int",
"AddMonCat.str",
"zsmulRec",
"AddGrpCat",
"AddSemigroup.toAdd",
"instOfNat",
"nsmulRec",
"AddGrpCat.F... | false |
_private.Mathlib.Algebra.Polynomial.Bivariate.0.Polynomial.Bivariate.swap_monomial._simp_1_1 | Mathlib.Algebra.Polynomial.Bivariate | [
"Polynomial.C",
"Semiring.toModule",
"HMul.hMul",
"LinearMap.instFunLike",
"Polynomial.C_mul_X_pow_eq_monomial",
"RingHom",
"Polynomial.monomial",
"LinearMap",
"Polynomial",
"Monoid.toPow",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"RingHom.instFunLike",
"HPow.hPow",
"NonAssocSemiring.t... | false |
_private.Mathlib.RingTheory.Extension.Generators.0.Algebra.Generators.map_toComp_ker._simp_1_6 | Mathlib.RingTheory.Extension.Generators | [
"Finset",
"Membership.mem",
"And",
"Finset.instSetLike",
"DecidablePred",
"propext",
"Finset.mem_filter",
"Finset.filter",
"Eq",
"SetLike.instMembership"
] | false |
Mathlib.Tactic.GCongr.Context._sizeOf_1 | Mathlib.Tactic.GCongr.Core | [
"Mathlib.Tactic.GCongr.Context.rec",
"Lean.MVarId",
"Lean.Meta.MetaM",
"instOfNatNat",
"Unit",
"Nat",
"Bool",
"OfNat.ofNat",
"Mathlib.Tactic.GCongr.Context"
] | false |
_private.Std.Data.DTreeMap.Internal.WF.Lemmas.0.Std.DTreeMap.Internal.Impl.applyCell_eq_apply_toListModel._simp_1_5 | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"and_imp",
"And",
"propext",
"Eq"
] | false |
DirectSum.«_aux_Mathlib_Algebra_DirectSum_Basic___macroRules_DirectSum_term⨁_,__1» | Mathlib.Algebra.DirectSum.Basic | [
"Pure.pure",
"Lean.Syntax.node",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax... | false |
Complex.sin_nat_mul_pi | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"Real.pi",
"HMul.hMul",
"Complex.sin",
"Complex.instZero",
"Complex.instMul",
"SubtractionMonoid.toSubNegZeroMonoid",
"Complex.instNatCast",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"Complex.ofReal",
"Nat.cast",
"Complex.sin_antiperiodic",
"Complex.addC... | true |
ConjAct.unitsMulSemiringAction | Mathlib.Algebra.Ring.Action.ConjAct | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"ConjAct.unitsMulSemiringAction._proof_2",
"Units",
"ConjAct.instDivInvMonoid",
"DistribMulAction.mk",
"DivInvMonoid.toMonoid",
"Units.instDivInvMonoid",
"ConjAct.unitsMulSemiringAction._proof_3",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"MulSemiringAct... | true |
Lean.MessageData.kind._unsafe_rec | Lean.Message | [
"Lean.MessageData",
"Lean.Name.anonymous",
"Lean.NamingContext",
"Lean.MessageDataContext",
"Lean.Name",
"_private.Lean.Message.0.Lean.MessageData.kind.match_1",
"Lean.MessageData.kind._unsafe_rec"
] | false |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.