name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.MorphismProperty.pushout_inl | Mathlib.CategoryTheory.MorphismProperty.Limits | [
"CategoryTheory.IsPushout.of_hasPushout",
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlong.of_isPushout",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlong",
"CategoryTheory.Limits.pus... | true |
ContinuousSemilinearEquivClass.map_continuous | Mathlib.Topology.Algebra.Module.Equiv | [
"Continuous",
"outParam",
"RingHom",
"AddCommMonoid",
"RingHomInvPair",
"TopologicalSpace",
"EquivLike",
"Semiring",
"Module",
"ContinuousSemilinearEquivClass",
"Semiring.toNonAssocSemiring",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
CategoryTheory.ShortComplex.FunctorEquivalence.inverse_map_τ₂ | Mathlib.Algebra.Homology.ShortComplex.FunctorEquivalence | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.mk",
"CategoryTheory.Functor.category",
"CategoryTheory.ShortComplex",
"CategoryTheory.Functor.comp",
"CategoryTheory.ShortComplex.π₁",
"Category... | true |
Polynomial.cyclotomic_irreducible_pow_of_irreducible_pow | Mathlib.RingTheory.Polynomial.Cyclotomic.Expand | [
"Eq.mpr",
"Polynomial.C",
"RingHom.instRingHomClass",
"IsDomain",
"Nat.zero_le",
"MulOne.toOne",
"Polynomial.instOne",
"CommRing",
"Nat.recAux",
"Nat.Prime",
"Nat.instIsOrderedAddMonoid",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"Nat.instM... | true |
_private.Mathlib.Data.Seq.Computation.0.Stream'.cons.match_1.eq_2 | Mathlib.Data.Seq.Computation | [
"Stream'.cons.match_1",
"instOfNatNat",
"Unit",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
Lean.Name.componentsRev._sunfold | Lean.Data.Name | [
"Lean.Name.mkNum",
"String",
"Lean.Name.mkStr",
"List.cons",
"Lean.Name.anonymous",
"Lean.Name.componentsRev",
"List",
"Unit",
"Nat",
"Lean.Name",
"_private.Lean.Data.Name.0.Lean.Name.getPrefix.match_1",
"List.nil"
] | false |
PartialEquiv.image_symm_image_of_subset_target | Mathlib.Logic.Equiv.PartialEquiv | [
"PartialEquiv.target",
"PartialEquiv",
"PartialEquiv.symm",
"HasSubset.Subset",
"Set.image",
"PartialEquiv.symm_image_image_of_subset_source",
"PartialEquiv.toFun",
"Eq",
"Set.instHasSubset",
"Set"
] | true |
DistLat.Iso.mk._proof_2 | Mathlib.Order.Category.DistLat | [
"Lattice.toSemilatticeSup",
"LatticeHom.ext",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"DistLat.instConcreteCategoryLatticeHomCarrier",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"CategoryTheory.CategoryStruct.id",
"SemilatticeSup.toMa... | false |
instCoeTCAddEquivOfAddEquivClass | Mathlib.Algebra.Group.Equiv.Defs | [
"AddEquivClass",
"CoeTC",
"AddEquivClass.toAddEquiv",
"EquivLike",
"AddEquiv",
"Add",
"CoeTC.mk"
] | true |
DistribLattice.ofInfSupLe._proof_2 | Mathlib.Order.Lattice | [
"Lattice",
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderDual.instDistribLattice",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"inferInstance",
"DistribLattice.toLattice",
"SemilatticeInf.toMin",
"LE.le",
"OrderDual.instLattice",
"Max.max",
"Lat... | false |
_private.Std.Data.DTreeMap.Internal.Model.0.Std.DTreeMap.Internal.Impl.maxView.match_1.splitter | Std.Data.DTreeMap.Internal.Model | [
"Std.DTreeMap.Internal.Impl.Balanced",
"Std.DTreeMap.Internal.Impl.maxView.match_1",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.inner",
"Std.DTreeMap.Internal.Impl.BalancedAtRoot",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Std.DTreeMap.Internal.Impl"
] | true |
Aesop.UnorderedArraySet.partition | Aesop.Util.UnorderedArraySet | [
"_private.Aesop.Util.UnorderedArraySet.0.Aesop.UnorderedArraySet.rep",
"_private.Aesop.Util.UnorderedArraySet.0.Aesop.UnorderedArraySet.partition.match_1",
"Prod.mk",
"_private.Aesop.Util.UnorderedArraySet.0.Aesop.UnorderedArraySet.mk",
"Array",
"Array.partition",
"Aesop.UnorderedArraySet",
"Bool",
... | true |
CategoryTheory.Limits.Trident.ofι._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers | [
"CategoryTheory.Limits.WalkingParallelFamily.one",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.WalkingParallelFamily",
"HEq.refl",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingParallelFamily.Hom.line",
"Ca... | false |
analyticOrderAt_mul_eq_top_of_right | Mathlib.Analysis.Analytic.Order | [
"HMul.hMul",
"instTopENat",
"NormedField.toField",
"NormedCommRing.toNonUnitalNormedCommRing",
"Field.toSemifield",
"instDistribOfSemiring",
"NonUnitalNormedRing.toNormedAddCommGroup",
"Semifield.toDivisionSemiring",
"Distrib.toMul",
"ENat",
"analyticOrderAt",
"NonUnitalNormedCommRing.toNonUni... | true |
_private.Lean.Elab.Quotation.0.Lean.Elab.Term.Quotation.getSepFromSplice._sparseCasesOn_1 | Lean.Elab.Quotation | [
"Lean.Syntax.node",
"Lean.Syntax.ident",
"Lean.Syntax.missing",
"Nat.ne_of_beq_eq_false",
"Lean.Syntax.ctorIdx",
"String",
"Lean.SourceInfo",
"Nat.shiftRight",
"Lean.Syntax.atom",
"Lean.Syntax",
"Nat.hasNotBit",
"instOfNatNat",
"Substring.Raw",
"Array",
"Nat.land",
"List",
"Lean.Synt... | false |
Lean.Lsp.CompletionParams._sizeOf_inst | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.CompletionParams._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Lean.Lsp.CompletionParams"
] | false |
_private.Mathlib.MeasureTheory.PiSystem.0.piiUnionInter_singleton._simp_1_6 | Mathlib.MeasureTheory.PiSystem | [
"Finset.mem_singleton",
"Finset",
"Membership.mem",
"Finset.instSetLike",
"propext",
"Finset.instSingleton",
"Singleton.singleton",
"Eq",
"SetLike.instMembership"
] | false |
Finite.ciInf_inf | Mathlib.Data.Fintype.Order | [
"iInf",
"Finite",
"Finite.ciSup_sup",
"ConditionallyCompleteLattice",
"SemilatticeInf.toMin",
"OrderDual.instConditionallyCompleteLattice",
"Nonempty",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder",
"ConditionallyCompleteLattice.toLattice",
"OrderDual",
"ConditionallyComplet... | true |
Int.Linear.Poly.norm._f | Init.Data.Int.Linear | [
"Int.Linear.Poly.insert",
"Int",
"Int.Linear.Var",
"Int.Linear.Poly.num",
"Int.Linear.Poly.add",
"Int.Linear.Poly.denote.match_1",
"Int.Linear.Poly.below",
"Int.Linear.Poly"
] | false |
CliffordAlgebra.ofBaseChange_tmul_one | Mathlib.LinearAlgebra.CliffordAlgebra.BaseChange | [
"Eq.mpr",
"MulOne.toOne",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"AlgHom.algHomClass",
"HMul.hMul",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"congrArg",
"CommSe... | true |
WithVal | Mathlib.Topology.Algebra.Valued.WithVal | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"LinearOrderedCommGroupWithZero",
"Ring",
"Valuation",
"WithVal.toVal"
] | true |
Int.add_shiftLeft | Init.Data.Int.Bitwise.Lemmas | [
"instPowNat",
"HMul.hMul",
"congrArg",
"Int.instHShiftLeftNat",
"HShiftLeft.hShiftLeft",
"Int",
"Int.instNatPow",
"Int.instMul",
"instHAdd",
"HPow.hPow",
"instOfNat",
"HAdd.hAdd",
"Int.shiftLeft_eq",
"Nat",
"congr",
"True",
"eq_self",
"of_eq_true",
"Int.instAdd",
"instHPow",
... | true |
_private.Mathlib.Order.InitialSeg.0.collapseF | Mathlib.Order.InitialSeg | [
"_private.Mathlib.Order.InitialSeg.0.collapseF._proof_3",
"setOf",
"Membership.mem",
"_private.Mathlib.Order.InitialSeg.0.collapseF._proof_1",
"Subtype",
"IsWellOrder",
"_private.Mathlib.Order.InitialSeg.0.collapseF._proof_4",
"_private.Mathlib.Order.InitialSeg.0.collapseF._proof_5",
"Subtype.mk",
... | true |
_private.Mathlib.MeasureTheory.Constructions.SimpleGraph.0.SimpleGraph.measurable_edgeSet._simp_1_1 | Mathlib.MeasureTheory.Constructions.SimpleGraph | [
"Sym2.mk",
"SimpleGraph.Adj",
"Membership.mem",
"SimpleGraph.edgeSet",
"SimpleGraph",
"propext",
"Eq",
"Set.instMembership",
"SimpleGraph.mem_edgeSet",
"Sym2",
"Set"
] | false |
_private.Mathlib.Analysis.Meromorphic.FactorizedRational.0.MeromorphicOn.extract_zeros_poles_log._simp_1_3 | Mathlib.Analysis.Meromorphic.FactorizedRational | [
"HMul.hMul",
"MulZeroClass.toMul",
"MulZeroClass",
"mul_eq_zero",
"NoZeroDivisors",
"propext",
"Zero.toOfNat0",
"Or",
"OfNat.ofNat",
"Eq",
"MulZeroClass.toZero",
"instHMul"
] | false |
Quiver.FreeGroupoid.quotInv | Mathlib.CategoryTheory.Groupoid.FreeGroupoid | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Paths.categoryPaths",
"CategoryTheory.Paths",
"Quiver.symmetrifyQuiver",
"Quot.liftOn",
"CategoryTheory.HomRel.CompClosure",
"Quiver.Symmetrify",
"Quiver.FreeGroupoid",
"Quiver.FreeGroupoid.redStep",
"Quiver.FreeGroupoid.quo... | true |
_private.Mathlib.RingTheory.Spectrum.Prime.FreeLocus.0.Module.rankAtStalk_eq_zero_iff_subsingleton._simp_1_1 | Mathlib.RingTheory.Spectrum.Prime.FreeLocus | [
"Membership.mem",
"Set.eq_empty_iff_forall_notMem",
"propext",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Set.instMembership",
"Not",
"Set"
] | false |
List.getElem_pmap | Init.Data.List.Attach | [
"Nat.zero_le",
"Nat.not_lt_of_le",
"congrArg",
"Membership.mem",
"Eq.rec",
"id",
"instOfNatNat",
"List.rec",
"List.cons",
"Nat.casesAuxOn",
"GetElem.getElem",
"List.pmap",
"List",
"instHAdd",
"And",
"absurd",
"List.instMembership",
"And.right",
"And.left",
"HAdd.hAdd",
"Nat",... | true |
_private.Std.Data.DTreeMap.Internal.Zipper.0.Std.DTreeMap.Internal.Impl.pruneLE.match_1.eq_1 | Std.Data.DTreeMap.Internal.Zipper | [
"Ordering.gt",
"Unit.unit",
"Ordering",
"Ordering.eq",
"_private.Std.Data.DTreeMap.Internal.Zipper.0.Std.DTreeMap.Internal.Impl.pruneLE.match_1",
"Unit",
"Ordering.lt",
"Eq.refl",
"Eq"
] | true |
CategoryTheory.Limits.Fork.IsLimit.homIso._proof_4 | Mathlib.CategoryTheory.Limits.Shapes.Equalizers | [
"CategoryTheory.Limits.Fork.IsLimit.lift'",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Limits.Fork.IsLimit.homIso._proof_3",
"CategoryTheory.Limits.Fork.IsLimit.hom_ext",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"... | false |
instMonoidUniformOnFun._aux_4 | Mathlib.Topology.Algebra.UniformConvergence | [
"Monoid",
"Monoid.toPow",
"HPow.hPow",
"Nat",
"UniformOnFun",
"instHPow",
"Set"
] | false |
CategoryTheory.Limits.cospanCompIso_inv_app_left | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.WalkingPair",
"CategoryTheory.Functor.map... | true |
EuclideanGeometry.Sphere.ext_iff | Mathlib.Geometry.Euclidean.Sphere.Basic | [
"Real",
"HEq.refl",
"EuclideanGeometry.Sphere.ext",
"EuclideanGeometry.Sphere",
"Eq.casesOn",
"And.casesOn",
"EuclideanGeometry.Sphere.center",
"And",
"Iff",
"MetricSpace",
"And.intro",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Eq.symm",
"Eq",
"EuclideanGeometry.Sphere.radius"
] | true |
Fin.image_castSucc_Ioi | Mathlib.Order.Interval.Set.Fin | [
"Set.Ioi",
"PartialOrder.toPreorder",
"instOfNatNat",
"instHAdd",
"Fin.instPartialOrder",
"Fin.image_castAdd_Ioi",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"Fin.last",
"instAddNat",
"Set.image",
"Fin.castSucc",
"OfNat.ofNat",
"Fin",
"Eq",
"Set.Ioo",
"Set"
] | true |
Mathlib.Meta.Positivity.div_nonneg_of_pos_of_nonneg | Mathlib.Algebra.Order.Field.Basic | [
"GroupWithZero.toMonoidWithZero",
"Preorder.toLT",
"instHDiv",
"GroupWithZero.toDivInvMonoid",
"MulZeroClass.toMul",
"PartialOrder.toPreorder",
"GroupWithZero",
"Preorder.toLE",
"PartialOrder",
"HDiv.hDiv",
"LT.lt.le",
"LE.le",
"MonoidWithZero.toMulZeroOneClass",
"PosMulReflectLT",
"LT.l... | true |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital.0.wrapped._proof_1._@.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital.1784184353._hygCtx._hyg.8 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital | [
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"IsTopologicalSemiring",
"ContinuousStar",
"PseudoMetricSpace.toUniformSpace",
"Algebra",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"StarAddMonoid.toInvolutiveStar",
"NonAssocRing.toNonUnitalNonAssocRing",
"CommSemiring",
"NonUnitalNon... | false |
CategoryTheory.ComposableArrows.fourδ₁Toδ₀._auto_1 | Mathlib.CategoryTheory.ComposableArrows.Four | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Lean.PrettyPrinter.OneLine.State.mk._flat_ctor | Lean.PrettyPrinter.Formatter | [
"Lean.PrettyPrinter.OneLine.State",
"List",
"Nat",
"Std.Format",
"Prod",
"Lean.PrettyPrinter.OneLine.State.mk"
] | false |
_private.Mathlib.Algebra.Polynomial.Splits.0.Polynomial.Splits.comp_of_natDegree_le_one_of_invertible._simp_1_1 | Mathlib.Algebra.Polynomial.Splits | [
"Multiset.map",
"Multiset.mem_map",
"Membership.mem",
"Exists",
"Multiset",
"Multiset.instMembership",
"And",
"propext",
"Eq"
] | false |
lt_sSup_iff | Mathlib.Order.CompleteLattice.Defs | [
"CompleteLinearOrder.toLinearOrder",
"Preorder.toLT",
"lt_isLUB_iff",
"PartialOrder.toPreorder",
"Membership.mem",
"Exists",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"And",
"Iff",
"LT.lt",
"CompleteSemilatticeSup.toSupSet",
"CompleteLinearOrder",
... | true |
_private.Init.Data.List.SplitOn.Basic.0.List.splitOnPTR.go.eq_def | Init.Data.List.SplitOn.Basic | [
"cond",
"_private.Init.Data.List.SplitOn.Basic.0.List.splitOnPTR.go",
"List.brecOn",
"Eq.mpr",
"List.brecOn.go",
"List.brecOn.eq",
"Array.push",
"congrArg",
"_private.Init.Data.List.SplitOn.Basic.0.List.splitOnPTR.go.match_1.splitter",
"id",
"List.rec",
"Array.toList",
"List.toArray",
"Lis... | true |
Lean.Compiler.LCNF.Simp.CtorInfo.ctor.inj | Lean.Compiler.LCNF.Simp.DiscrM | [
"Lean.Compiler.LCNF.Arg",
"Lean.ConstructorVal",
"Lean.Compiler.LCNF.Purity.pure",
"Array",
"And",
"Lean.Compiler.LCNF.Simp.CtorInfo",
"Lean.Compiler.LCNF.Simp.CtorInfo.ctor.noConfusion",
"And.intro",
"Lean.Compiler.LCNF.Simp.CtorInfo.ctor",
"Eq"
] | true |
Std.ExtDTreeMap.getKey_insert_self | Std.Data.ExtDTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.ExtDTreeMap.insert",
"Ordering",
"Std.TransCmp",
"Std.ExtDTreeMap.mem_insert_self",
"Std.ExtDTreeMap.inductionOn",
"Std.ExtDTreeMap",
"Std.DTreeMap.getKey_insert_self",
"Eq",
"Std.ExtDTreeMap.getKey"
] | true |
CategoryTheory.Functor.LaxMonoidal.tensorHom_ε_comp_μ_assoc | Mathlib.CategoryTheory.Monoidal.Functor | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategoryStruct.rightUnitor",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.LaxMonoidal.ε",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq... | true |
CategoryTheory.Lax.OplaxTrans.vCompNaturality | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Lax | [
"CategoryTheory.Lax.OplaxTrans.naturality",
"CategoryTheory.Lax.OplaxTrans",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.whiskerRight",
"CategoryTheory.Lax.OplaxTrans.app",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.PrelaxFunctor.toPrelaxFuncto... | true |
Ordering.isEq | Init.Data.Ord.Basic | [
"Ordering",
"Ordering.then.match_1",
"Bool.true",
"Unit",
"Bool",
"Bool.false"
] | true |
List.Vector.set._proof_1 | Mathlib.Data.Vector.Basic | [
"List.Vector.length_val",
"congrArg",
"List.Vector",
"List.set",
"Fin.val",
"List",
"Nat",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Fin",
"Subtype.val",
"Eq",
"List.length",
"Eq.trans",
"List.length_set"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Subgraph.0.SimpleGraph.Subgraph.map_mono._simp_1_1 | Mathlib.Combinatorics.SimpleGraph.Subgraph | [
"Set.mem_image",
"Membership.mem",
"Exists",
"And",
"propext",
"Set.image",
"Eq",
"Set.instMembership",
"Set"
] | false |
List.ofFn_congr | Mathlib.Data.List.OfFn | [
"Eq.mpr",
"congrArg",
"List.ofFn",
"Eq.rec",
"id",
"funext",
"List",
"Fin.cast",
"congrFun",
"Nat",
"eq_self",
"of_eq_true",
"Eq.refl",
"Eq.symm",
"Fin",
"Eq",
"Fin.cast_refl"
] | true |
Std.DTreeMap.Raw.self_le_maxKey?_insert | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.maxKey?",
"Std.DTreeMap.Internal.Impl.self_le_maxKey?_insert!",
"Ord.mk",
"Ordering",
"Std.TransCmp",
"Bool.true",
"Std.DTreeMap.Raw.isSome_maxKey?_insert",
"Std.DTreeMap.Raw.WF.out",
"Option.get",
"Std.DTreeMap.Raw.inner",
"Bool",
"Std.DTreeMap.Raw.insert",
"Ordering.isLE"... | true |
_private.Mathlib.SetTheory.Ordinal.Exponential.0.Ordinal.lt_omega0_omega0_opow._simp_1_6 | Mathlib.SetTheory.Ordinal.Exponential | [
"Preorder.toLT",
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"HPow.hPow",
"LT.lt",
"True",
"Ordinal.zero",
"eq_true",
"Zero.toOfNat0",
"instHPow",
"OfNat.ofNat",
"Ordinal.instPow",
"Eq",
"Ordinal.opow_pos",
"Ordinal"
] | false |
_private.Mathlib.Probability.Martingale.Upcrossing.0.MeasureTheory.upcrossingStrat_le_one._simp_1_2 | Mathlib.Probability.Martingale.Upcrossing | [
"Lattice.toSemilatticeSup",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"SemilatticeInf.toMin",
"LE.le",
"Set.Ico",
"CompleteLatt... | false |
AlgHom.toEnd._proof_1 | Mathlib.Algebra.Algebra.Hom | [
"AlgHom.toLinearMap",
"MulOne.toOne",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AlgHom",
"Algebra",
"Algebra.toModule",
"AlgHom.End",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"MulOneClass.toMulOne",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semiring",
"... | false |
Lean.NameHashSet.insert | Lean.Data.NameMap.Basic | [
"Lean.NameHashSet",
"Std.HashSet",
"Std.HashSet.insert",
"Lean.Name",
"Lean.Name.instBEq",
"Lean.instHashableName"
] | true |
CategoryTheory.PreOneHypercover.congrIndexOneOfEqIso_inv_p₁ | Mathlib.CategoryTheory.Sites.Hypercover.One | [
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.PreOneHypercover",
"CategoryTheory.PreOneHypercover.I₁",
"CategoryTheory.eqToHom",
"CategoryTheory.PreOneHypercover.toPreZeroHypercover",
"Eq.rec",
"Equiv",
"CategoryTheory.PreZeroHypercove... | true |
BooleanSubalgebra | Mathlib.Order.BooleanSubalgebra | [
"BooleanAlgebra",
"BooleanSubalgebra.mk"
] | true |
LocallyConstant.instNonUnitalCommSemiring | Mathlib.Topology.LocallyConstant.Algebra | [
"AddMonoid.toNSMul",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Distrib.toAdd",
"Function.Injective.nonUnitalCommSemiring",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"LocallyConstant",
"LocallyConstant.instMul",
"NonUnitalCommSemiring.toNonUnitalSemiring",
"LocallyConstant.instNonUnitalComm... | true |
_private.Mathlib.Tactic.Linter.Whitespace.0.Mathlib.Linter.FormatError.mk._flat_ctor | Mathlib.Tactic.Linter.Whitespace | [
"_private.Mathlib.Tactic.Linter.Whitespace.0.Mathlib.Linter.FormatError.mk",
"String",
"_private.Mathlib.Tactic.Linter.Whitespace.0.Mathlib.Linter.FormatError",
"String.Pos.Raw",
"Nat"
] | false |
Lean.Elab.Tactic.checkTerminalAsSorry | Lean.Elab.Tactic.Grind.Main | [
"Pure.pure",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"Lean.Meta.debug.terminalTacticsAsSorry",
"Lean.Meta.State",
"instMonadLiftT",
"Lean.Elab.Tactic.Context",
"Lean.Core.instMonadOptionsCoreM",
"Lean.MVarId",
"Lean.instMonadOptionsOfMonadLift",
"Lean.Meta.MetaM",
"IO.RealWorld",
"in... | true |
Lean.Meta.Monotonicity.defaultFailK | Lean.Elab.Tactic.Monotonicity | [
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"String",
"List.map",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.MessageData.instAppend",
"Lean.throwError",
"Array.isEmpty",
"Lean.MonadQuotation.toMonadRef",
"Lean.Exp... | true |
MeasurableSpace.sUnion_countablePartition | Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated | [
"sUnion_memPartition",
"Set.univ",
"Set.sUnion",
"Set.enumerateCountable",
"MeasurableSpace",
"MeasurableSpace.countableGeneratingSet",
"Nat",
"Set.instEmptyCollection",
"MeasurableSpace.CountablyGenerated",
"MeasurableSpace.countable_countableGeneratingSet",
"EmptyCollection.emptyCollection",
... | true |
Delone.DeloneSet.mapIsometry_symm_apply_packingRadius | Mathlib.Analysis.AperiodicOrder.Delone.Basic | [
"Equiv.instEquivLike",
"Delone.DeloneSet.mapIsometry",
"Equiv",
"EMetricSpace.toPseudoEMetricSpace",
"NNReal",
"Delone.DeloneSet",
"MetricSpace",
"Eq.refl",
"MetricSpace.toEMetricSpace",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"IsometryEquiv",
"Delone.DeloneSet.packingRadius",
"EquivLike.toF... | true |
ChartedSpaceCore.noConfusionType | Mathlib.Geometry.Manifold.ChartedSpace | [
"PartialEquiv",
"PartialEquiv.trans",
"Membership.mem",
"PartialEquiv.symm",
"TopologicalSpace",
"ChartedSpaceCore.casesOn",
"PartialEquiv.source",
"ContinuousOn",
"HEq",
"IsOpen",
"PartialEquiv.toFun",
"ChartedSpaceCore",
"Set.instMembership",
"Set"
] | false |
Submodule.lTensorOne'.eq_1 | Mathlib.LinearAlgebra.TensorProduct.Submodule | [
"Subalgebra.instSetLike",
"Submodule.mulMap",
"Submodule",
"Lattice.toSemilatticeSup",
"Submodule.mulMap'._proof_3",
"CompleteLattice.toLattice",
"CommSemiring.toSemiring",
"Submodule.addCommMonoid",
"TensorProduct.addCommMonoid",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Algebra.instCompl... | true |
_private.Lean.Expr.0.Lean.Expr.getAppArgsAux._f | Lean.Expr | [
"HSub.hSub",
"Lean.Expr",
"instSubNat",
"instOfNatNat",
"Array",
"instHSub",
"_private.Lean.Expr.0.Lean.Expr.getAppArgsAux.match_1",
"Nat",
"Lean.Expr.app",
"Array.set!",
"OfNat.ofNat",
"Lean.Expr.below"
] | false |
_private.Mathlib.NumberTheory.JacobiSum.Basic.0.jacobiSum_nontrivial_inv._simp_1_11 | Mathlib.NumberTheory.JacobiSum.Basic | [
"False",
"eq_false",
"AddMonoid.toAddSemigroup",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"CharZero",
"Nat.cast_add_one_ne_zero",
"AddMonoidWithOne.toOne",
"AddZero.toZero",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Nat",
"On... | false |
HomotopicalAlgebra.CofibrantObject.HoCat.bifibrantResolution'._proof_1 | Mathlib.AlgebraicTopology.ModelCategory.BifibrantObjectHomotopy | [
"HomotopicalAlgebra.BifibrantObject",
"CategoryTheory.Limits.hasFiniteCoproducts_of_hasFiniteColimits",
"HomotopicalAlgebra.BifibrantObject.HoCat.ιCofibrantObject",
"HomotopicalAlgebra.ModelCategory.cm1a",
"HomotopicalAlgebra.ModelCategory.cm1b",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
... | false |
Lean.StructureFieldInfo.noConfusionType | Lean.Structure | [
"Lean.StructureFieldInfo.casesOn",
"Lean.Expr",
"Lean.StructureFieldInfo",
"Lean.Name",
"Lean.BinderInfo",
"Eq",
"Option"
] | false |
Std.Http.Method._sizeOf_1 | Std.Internal.Http.Data.Method | [
"Std.Http.Method",
"Std.Http.Method.rec",
"instOfNatNat",
"Nat",
"OfNat.ofNat"
] | false |
UInt64.mul_assoc | Init.Data.UInt.Lemmas | [
"BitVec.mul_assoc",
"instMulUInt64",
"HMul.hMul",
"UInt64",
"UInt64.toBitVec_inj",
"BitVec",
"instOfNatNat",
"Nat",
"Iff.mp",
"OfNat.ofNat",
"Eq",
"UInt64.toBitVec",
"instHMul"
] | true |
Batteries.Tactic.TransRelation._sizeOf_1 | Batteries.Tactic.Trans | [
"Batteries.Tactic.TransRelation.rec",
"Lean.Expr",
"Lean.BinderInfo._sizeOf_inst",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"SizeOf.sizeOf",
"Batteries.Tactic.TransRelation",
"instAddNat",
"Lean.Name",
"Lean.BinderInfo",
"OfNat.ofNat",
"Lean.Expr._sizeOf_ins... | false |
EuclideanGeometry.Sphere.secondInter_mem._simp_1 | Mathlib.Geometry.Euclidean.Sphere.SecondInter | [
"EuclideanGeometry.Sphere.secondInter_mem",
"Real",
"Real.instRCLike",
"EuclideanGeometry.Sphere",
"Membership.mem",
"MetricSpace",
"EuclideanGeometry.Sphere.secondInter",
"propext",
"MetricSpace.toPseudoMetricSpace",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Eq",
"InnerProductSpace",
... | false |
Std.DHashMap.Raw.Const.get!_filter_of_getKey?_eq_some | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.DHashMap.Internal.Raw.Const.get!_eq",
"Std.DHashMap.Raw.WF.filter₀",
"Std.DHashMap.Internal.Raw₀.Const.get?",
"congrArg",
"Std.DHashMap.Internal.Raw.filter_eq",
"Std.DHashMap.Internal.Raw₀.getKey?",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw.getKey?_eq",
... | true |
_private.Lean.Meta.InferType.0.Lean.Meta.isArrowProposition'.match_1 | Lean.Meta.InferType | [
"Lean.Expr.letE",
"Lean.Expr",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.bvar",
"Lean.Expr.mdata",
"dite",
"Lean.Expr.forallE",
"_private.Lean.Meta.InferType.0.Lean.Meta.isArrowProposition'._sparseCasesOn_1",
"Lean.MData",
"Nat",
"Eq.ndrec_symm",
"Bool",
"Lean.Name",
"instDecidableEqNa... | false |
PowerBasis.mk.injEq | Mathlib.RingTheory.PowerBasis | [
"PowerBasis",
"PowerBasis.mk",
"CommRing",
"Ring.toNonAssocRing",
"Eq.propIntro",
"CommSemiring.toSemiring",
"Lean.injEq_helper",
"Algebra",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Module.Basis.instFunLike",
"Fin.val",
"NonAssocRing.toNonUnitalNonAssocRing",... | true |
PadicAlgCl.isUltrametricDist | Mathlib.NumberTheory.Padics.Complex | [
"IsUltrametricDist.isUltrametricDist_of_forall_norm_add_le_max_norm",
"NormedCommRing.toSeminormedCommRing",
"Nat.Prime",
"PadicAlgCl.isNonarchimedean",
"Fact",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"NonUnitalSeminormedCommRing.toNonUnitalSeminormedRing",
"Nat",
"SeminormedCommRing.toSemino... | true |
_private.Mathlib.ModelTheory.Basic.0.FirstOrder.Language.isEmpty_empty._simp_1 | Mathlib.ModelTheory.Basic | [
"Sum",
"IsEmpty",
"isEmpty_sum",
"And",
"propext",
"Eq"
] | false |
_private.Mathlib.ModelTheory.Complexity.0.FirstOrder.Language.BoundedFormula.realize_toPrenexImp._simp_1_2 | Mathlib.ModelTheory.Complexity | [
"FirstOrder.Language.BoundedFormula.imp",
"FirstOrder.Language.BoundedFormula.Realize",
"FirstOrder.Language.Structure",
"Nat",
"propext",
"FirstOrder.Language",
"FirstOrder.Language.BoundedFormula",
"FirstOrder.Language.BoundedFormula.realize_imp",
"Fin",
"Eq"
] | false |
sdiff_sdiff_le | Mathlib.Order.Heyting.Basic | [
"Iff.mpr",
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"GeneralizedCoheytingAlgebra",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"LE.le",
"SDiff.sdiff",
"Max.max",
"GeneralizedCoheytingAlgebra.toLattice",
"sdiff_le_iff",
"GeneralizedCoheytingAlgebra.... | true |
Lean.PrettyPrinter.Formatter.categoryFormatter | Lean.PrettyPrinter.Formatter | [
"Lean.PrettyPrinter.Formatter",
"Lean.PrettyPrinter.Formatter.fill",
"Lean.PrettyPrinter.Formatter.categoryFormatterCore",
"Int",
"Option.none",
"Lean.Name",
"Lean.PrettyPrinter.Formatter.indent"
] | true |
CategoryTheory.ComposableArrows.Exact.cokerIsoKer_hom_fac | Mathlib.Algebra.Homology.ExactSequenceFour | [
"CategoryTheory.ComposableArrows.IsComplex.cokerToKer'._proof_2",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ComposableArrows.map'._proof_8",
"PartialOrder.toPreorder",
"CategoryTheory.ComposableArrows.IsComplex.cokerToKer'_fac._proof_2",
"CategoryTheory.ComposableArrows.Exa... | true |
_private.Init.Data.Array.Basic.0.Array.takeWhile.go._unary._proof_1 | Init.Data.Array.Basic | [
"Array.push",
"InvImage",
"HSub.hSub",
"PSigma.casesOn",
"id",
"instSubNat",
"instOfNatNat",
"Array",
"GetElem.getElem",
"instHAdd",
"instHSub",
"Array.instGetElemNatLtSize",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Nat.sub_succ_lt_self",
"PSigma.mk",
"instAddNat",
"instLTNat",
"OfNat.ofN... | false |
AddGrpCat.limitAddGroup._aux_17 | Mathlib.Algebra.Category.Grp.Limits | [
"CategoryTheory.Functor",
"instHSMul",
"CategoryTheory.Limits.Types.Small.limitCone",
"AddGrpCat.instCategory",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.comp",
"AddZeroClass.toAddZero",
"Set.Elem",
"Int",
"CategoryTheory.Limits.Cone.pt",
"AddGrpCat",
"AddGroup.toSubNegMonoid",
"Ad... | false |
Std.Time.Modifier.F | Std.Time.Format.Basic | [
"Std.Time.Modifier.F",
"Std.Time.Number",
"Std.Time.Modifier"
] | true |
StateRefT'.run | Init.Control.StateRef | [
"Pure.pure",
"Monad.toApplicative",
"ST.Ref.get",
"Prod.mk",
"MonadLiftT",
"Applicative.toPure",
"ST",
"StateRefT'",
"Monad.toBind",
"Bind.bind",
"ST.mkRef",
"Prod",
"ST.Ref",
"Monad"
] | true |
IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers | Mathlib.RingTheory.DedekindDomain.AdicValuation | [
"Int.instAddCommGroup",
"Multiplicative.linearOrder",
"CommRing",
"IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers._proof_1",
"Int.instLinearOrder",
"IsFractionRing",
"Valued.v",
"IsDedekindDomain.HeightOneSpectrum",
"Algebra",
"IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers._... | true |
LinearOrderedAddCommGroup.negGen_eq_of_top | Mathlib.Algebra.Order.Group.Cyclic | [
"Nontrivial",
"AddSubgroup.instNontrivialSubtypeMemTop",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"AddCommGroup.toAddGroup",
"LinearOrderedAddCommGroup.negGen",
"SemilatticeInf.toPartialOrder",
"AddCommGroup",
"DistribLattice.toLattice",
"AddSubgroup",
"AddGrou... | true |
IsCompl.sup_eq_top | Mathlib.Order.Disjoint | [
"Lattice",
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeSup.toMax",
"IsCompl",
"OrderTop.toTop",
"Max.max",
"BoundedOrder.toOrderTop",
"SemilatticeSup.toPartialOrder",
"Top.top",
"IsCompl.codisjoint",
"BoundedOrder",
"Eq",
"Codisjoint.eq_top"
] | true |
ENNReal.one_le_coe_iff._simp_1 | Mathlib.Data.ENNReal.Basic | [
"ENNReal.ofNNReal",
"PartialOrder.toPreorder",
"Preorder.toLE",
"NNReal",
"LE.le",
"NNReal.instPartialOrder",
"ENNReal.instLE",
"ENNReal",
"propext",
"One.toOfNat1",
"ENNReal.instOne",
"ENNReal.one_le_coe_iff",
"OfNat.ofNat",
"Eq",
"NNReal.instOne"
] | false |
MeasureTheory.crossing_eq_crossing_of_lowerCrossingTime_lt | Mathlib.Probability.Martingale.Upcrossing | [
"Eq.mpr",
"MeasureTheory.upperCrossingTime_succ_eq",
"Nat.instCanonicallyOrderedAdd",
"lt_of_le_of_lt",
"MeasureTheory.lowerCrossingTime.eq_1",
"Real",
"Nat.recAux",
"Preorder.toLT",
"le_rfl",
"_private.Mathlib.Probability.Martingale.Upcrossing.0.MeasureTheory.crossing_eq_crossing_of_lowerCrossing... | true |
Std.Time.instHSubOffsetOffset_41 | Std.Time.Date.Basic | [
"Rat.instOfNat",
"Rat",
"Std.Time.Week.Offset.toDays",
"Std.Time.Day.Offset",
"Std.Time.Internal.UnitVal.sub",
"HSub.mk",
"OfNat.ofNat",
"Std.Time.Week.Offset",
"HSub"
] | true |
CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse._proof_6 | Mathlib.CategoryTheory.Localization.Construction | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Localization.Construction.WhiskeringLeftEquivalence.inverse._proof_2",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.eqToHom",
"CategoryTheory.MorphismProperty.Q",
"CategoryTheory.Functor.category",
... | false |
Filter.HasBasis.forall_iff | Mathlib.Order.Filter.Bases.Basic | [
"Filter.instMembership",
"Filter.HasBasis.mem_iff",
"Membership.mem",
"Exists",
"HasSubset.Subset",
"_private.Mathlib.Order.Filter.Bases.Basic.0.Filter.HasBasis.forall_iff.match_1_1",
"And",
"Filter.HasBasis",
"Iff",
"Iff.intro",
"Iff.mp",
"Filter.HasBasis.mem_of_mem",
"Filter",
"Set.instH... | true |
String.Pos.noConfusionType | Init.Data.String.Defs | [
"String",
"String.Pos.casesOn",
"String.Pos.Raw",
"String.Pos",
"String.Pos.Raw.IsValid",
"Eq"
] | false |
AddGroup.ofLeftAxioms._proof_3 | Mathlib.Algebra.Group.MinimalAxioms | [
"Zero.zero",
"Add.mk",
"Add.add",
"instOfNatNat",
"AddSemigroup.mk",
"nsmulRecAuto",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Zero.mk",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Add",
"Zero"
] | false |
covariant_le_of_covariant_lt | Mathlib.Algebra.Order.Monoid.Unbundled.Defs | [
"LE.le.eq_or_lt",
"Preorder.toLT",
"le_rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"LT.lt.le",
"LE.le",
"Covariant",
"Or.casesOn",
"LT.lt",
"Eq.ndrec",
"Or",
"Eq"
] | true |
CategoryTheory.Functor.LaxBraided.mk | Mathlib.CategoryTheory.Monoidal.Braided.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.LaxBraided.braided._autoParam",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.LaxBraided.mk",
"autoParam",
"CategoryTheory.Functor.map",
"CategoryTheory.BraidedCategory",
"Categor... | true |
Finite.of_addSubgroup_quotient | Mathlib.GroupTheory.QuotientGroup.Finite | [
"Eq.mpr",
"congrArg",
"Finite",
"finite_iff_addSubgroup_quotient",
"Membership.mem",
"id",
"Subtype",
"AddSubgroup",
"HasQuotient.Quotient",
"And",
"AddGroup",
"AddSubgroup.instSetLike",
"QuotientAddGroup.instHasQuotientAddSubgroup",
"And.intro",
"propext",
"Eq",
"SetLike.instMembers... | true |
Lean.Elab.Term.Context.declName? | Lean.Elab.Term.TermElabM | [
"Lean.Elab.Term.Context",
"Lean.Name",
"Option"
] | true |
_private.Mathlib.NumberTheory.LSeries.PrimesInAP.0.ArithmeticFunction.vonMangoldt.summable_residueClass_non_primes_div._simp_1_2 | Mathlib.NumberTheory.LSeries.PrimesInAP | [
"GroupWithZero.toMonoidWithZero",
"instHDiv",
"GroupWithZero.toDivInvMonoid",
"GroupWithZero",
"HDiv.hDiv",
"MonoidWithZero.toMulZeroOneClass",
"propext",
"DivInvMonoid.toDiv",
"Zero.toOfNat0",
"Or",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq",
"div_eq_zero_iff",
"MulZeroClass.... | false |
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