name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.Triangulated.TStructure.instIsIsoFunctorETruncGEπBotEInt | Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc | [
"WithBot.instPreorder",
"CategoryTheory.Functor",
"CategoryTheory.IsIso",
"WithTop.instPreorder",
"CategoryTheory.Functor.Additive",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"CategoryTheory.shiftFunctor",
"SemilatticeInf.toPartialOrder",
"CategoryTheory.Functor.id",
"Categor... | true |
MeasureTheory.Measure.IsMulRightInvariant.mk._flat_ctor | Mathlib.MeasureTheory.Group.Defs | [
"MeasureTheory.Measure.IsMulRightInvariant.mk",
"MeasureTheory.Measure",
"HMul.hMul",
"Mul",
"MeasureTheory.Measure.IsMulRightInvariant",
"MeasurableSpace",
"MeasureTheory.Measure.map",
"Eq",
"instHMul"
] | false |
Std.Time.instInhabitedValidDate | Std.Time.Date.ValidDate | [
"Std.Time.ValidDate",
"Std.Time.Day.instOfNatOrdinal",
"Std.Time.instInhabitedValidDate._proof_1",
"Prod.mk",
"Std.Time.Month.Ordinal.Valid",
"Prod.fst",
"Subtype.mk",
"Std.Time.Day.Ordinal",
"Bool",
"Inhabited",
"Prod",
"OfNat.ofNat",
"Prod.snd",
"Std.Time.Month.Ordinal",
"Std.Time.Mont... | true |
Finsupp.lsubtypeDomain_apply | Mathlib.LinearAlgebra.Finsupp.Defs | [
"Finsupp.module",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Membership.mem",
"AddZeroClass.toAddZero",
"Set.Elem",
"LinearMap",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
"AddZero.toZero",
"Semiring",
"AddCommMonoid.toAddMonoid",
"Module",
"Finsupp.subtypeDomain",
"RingHom... | true |
instRingWithIdealFilter._aux_1 | Mathlib.RingTheory.IdealFilter.Topology | [
"AddMonoid.toAddSemigroup",
"WithIdealFilter",
"IdealFilter",
"AddSemigroup.toAdd",
"AddCommMonoid.toAddMonoid",
"Ring.toSemiring",
"Ring",
"Semiring.toAddCommMonoid",
"Add"
] | false |
Module.Relations.instAddCommGroupQuotient._proof_10 | Mathlib.Algebra.Module.Presentation.Basic | [
"Semiring.toModule",
"Submodule.Quotient.addMonoid._proof_8",
"Finsupp.module",
"Ring.toNonAssocRing",
"Module.Relations.Quotient",
"AddMonoid.nsmul_zero._autoParam",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Module.Relations.relation",
"instOfNatNat",
"Module.Relations.instAddCommGrou... | false |
isProperLinearSet_iff | Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Defs | [
"Eq.mpr",
"instVAddOfAdd",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"IsProperLinearSet",
"Set.Finite",
"Exists",
"Set.vaddSet",
"id",
"Set.Finite.coe_toFinset",
"AddSubmonoid",
"AddCommMonoid",
"HVAdd.hVAdd",
"exists_congr",
"And",
"Iff",
"SetLike.coe",
"Finset.instSetLi... | true |
LocallyConstant.mapAddMonoidHom._proof_2 | Mathlib.Topology.LocallyConstant.Algebra | [
"AddMonoidHom.instAddMonoidHomClass",
"congrArg",
"AddZeroClass.toAddZero",
"map_zero",
"LocallyConstant",
"TopologicalSpace",
"AddZero.toZero",
"AddZeroClass",
"LocallyConstant.instAddZeroClass",
"True",
"eq_self",
"LocallyConstant.ext",
"LocallyConstant.map",
"of_eq_true",
"Zero.toOfNa... | false |
RingHom.LocalizationPreserves._proof_1 | Mathlib.RingTheory.LocalProperties.Basic | [
"RingHom.instRingHomClass",
"CommRing",
"CommSemiring.toSemiring",
"RingHom",
"RingHomClass.toMonoidWithZeroHomClass",
"NonAssocSemiring.toMulZeroOneClass",
"MonoidWithZeroHomClass.toMonoidHomClass",
"MulZeroOneClass.toMulOneClass",
"MulOneClass.toMulOne",
"CommRing.toCommSemiring",
"RingHom.ins... | false |
UniformSpace.Core.mkOfBasis._proof_2 | Mathlib.Topology.UniformSpace.Defs | [
"Iff.mpr",
"instMembershipSetFilterBasis",
"Filter.HasBasis.tendsto_iff",
"FilterBasis.hasBasis",
"Membership.mem",
"Exists",
"id",
"HasSubset.Subset",
"And",
"FilterBasis",
"Set.preimage",
"Filter.Tendsto",
"Prod.swap",
"Prod",
"Set.instMembership",
"FilterBasis.filter",
"Set.instHa... | false |
CategoryTheory.PreOneHypercover.Hom.w₁₁ | Mathlib.CategoryTheory.Sites.Hypercover.One | [
"CategoryTheory.PreOneHypercover.Hom.s₁",
"CategoryTheory.PreZeroHypercover.Hom.h₀",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.PreOneHypercover",
"CategoryTheory.PreOneHypercover.I₁",
"CategoryTheory.PreOneHypercover.toPreZeroHypercover",
"CategoryTheory.PreZeroHypercover... | true |
ContinuousOpenMap.id_apply | Mathlib.Topology.Hom.Open | [
"ContinuousOpenMap.instFunLike",
"ContinuousOpenMap.id",
"TopologicalSpace",
"Eq",
"DFunLike.coe",
"rfl",
"ContinuousOpenMap"
] | true |
CategoryTheory.Quiv.isoOfEquiv._proof_5 | Mathlib.CategoryTheory.Category.Quiv | [
"Equiv.instEquivLike",
"Equiv.right_inv",
"CategoryTheory.Quiv.str'",
"Quiver.Hom",
"Quiver.homOfEq",
"CategoryTheory.Quiv.of",
"CategoryTheory.CategoryStruct.id",
"Equiv",
"CategoryTheory.Quiv.isoOfEquiv._proof_3",
"CategoryTheory.Quiv.category",
"CategoryTheory.Bundled.α",
"Prefunctor.ext'",... | false |
CategoryTheory.Functor.opMapTriangleCompTriangleOpEquivalenceInverse | Mathlib.CategoryTheory.Triangulated.Opposite.Functor | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Iso",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Pretriangulated.Triangle",
"CategoryTheory.CatCommSq.iso",
"CategoryTheory.Pretriangulated.Opposi... | true |
Std.DHashMap.Const.get?_filterMap' | Std.Data.DHashMap.Lemmas | [
"Iff.mpr",
"Std.DHashMap.filterMap",
"instLawfulHashableOfLawfulBEq",
"congrArg",
"Option.some",
"LawfulBEq",
"Membership.mem",
"Eq.rec",
"Option.bind",
"Std.DHashMap.instMembership",
"Std.DHashMap.Const.get?",
"Bool.true",
"Std.DHashMap.getKey_eq",
"Std.DHashMap.Const.mem_iff_isSome_get?"... | true |
MulOpposite.instMulActionWithZero._proof_1 | Mathlib.Algebra.GroupWithZero.Action.Opposite | [
"instHSMul",
"SMulWithZero.toSMulZeroClass",
"AddMonoid.toAddZeroClass",
"MulOpposite",
"MulOpposite.instMulAction",
"smul_zero",
"AddZeroClass.toAddZero",
"MulActionWithZero",
"AddZero.toZero",
"MulOpposite.instZero",
"MonoidWithZero",
"MonoidWithZero.toMulZeroOneClass",
"AddMonoid",
"Mon... | false |
Nat.Primrec.below.rec | Mathlib.Computability.Primrec.Basic | [
"Nat.Primrec.below",
"Nat.Primrec",
"Nat.Primrec.left",
"Nat.unpair",
"Nat.Primrec.prec",
"Nat.Primrec.below.pair",
"Nat.Primrec.below.prec",
"Nat.Primrec.below.left",
"Nat.Primrec.below.zero",
"Nat.Primrec.succ",
"Nat.rec",
"instOfNatNat",
"Prod.fst",
"Nat.pair",
"Nat.Primrec.comp",
"... | false |
Nat.pairEquiv.match_1 | Mathlib.Data.Nat.Pairing | [
"Prod.mk",
"Nat",
"Prod",
"Prod.casesOn"
] | false |
_private.Mathlib.GroupTheory.IsSubnormal.0.AddSubgroup.IsSubnormal.isSubnormal_iff.match_1_1.congr_eq_1 | Mathlib.GroupTheory.IsSubnormal | [
"Unit.unit",
"id",
"instOfNatNat",
"heq_of_eq",
"Unit",
"Nat",
"_private.Mathlib.GroupTheory.IsSubnormal.0.AddSubgroup.IsSubnormal.isSubnormal_iff.match_1_1",
"Eq.ndrec",
"Eq.refl",
"HEq",
"OfNat.ofNat",
"Eq.symm",
"Nat.succ",
"Eq",
"Nat.casesOn"
] | true |
CategoryTheory.PreZeroHypercover.pullback₂.congr_simp | Mathlib.CategoryTheory.Sites.Hypercover.Zero | [
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Eq.rec",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.PreZeroHypercover.X",
"CategoryTheory.PreZeroHypercover.pullback₂",
"CategoryTheory.PreZeroHypercover.I₀",
"CategoryTheory.PreZeroHypercover",
... | true |
RootPairing.GeckConstruction.basis._proof_2 | Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Basis | [
"IsDomain",
"Field.toSemifield",
"instIsDomain",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"Field"
] | false |
_private.Mathlib.Data.Ordmap.Invariants.0.Ordnode.all_dual.match_1_1 | Mathlib.Data.Ordmap.Invariants | [
"Ordnode",
"Ordnode.node",
"And.casesOn",
"And",
"Ordnode.dual",
"Nat",
"And.intro",
"Ordnode.All"
] | false |
Std.LawfulLTCmp.eq_lt_iff_lt | Batteries.Classes.Order | [
"Std.LawfulLTCmp",
"Ordering",
"Iff",
"Ordering.lt",
"LT.lt",
"Eq",
"LT"
] | true |
Qq.SortLocalDecls.Context._sizeOf_1 | Qq.SortLocalDecls | [
"Lean.NameMap",
"Qq.SortLocalDecls.Context.rec",
"instSizeOfDefault",
"instOfNatNat",
"instHAdd",
"Qq.SortLocalDecls.Context",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Lean.LocalDecl",
"OfNat.ofNat"
] | false |
CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.D₂._proof_5 | Mathlib.CategoryTheory.Presentable.Directed | [
"CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.hP",
"HasCardinalLT",
"Cardinal.IsRegular",
"Cardinal",
"CategoryTheory.ObjectProperty.HasCardinalLT",
"Fact",
"CategoryTheory.SmallCategory",
"CategoryTheory.IsCardinalFiltered.exists_cardinal_directed.Diagram.P",
"CategoryTheory.I... | false |
AlgebraicGeometry.Proj.awayToSection | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic | [
"SetLike",
"CommRing",
"Opposite",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddGroupWithOne.toAddGroup",
"TopologicalSpace.Opens.instPartialOrder",
"CommSemiring.toSemiring",
"CommRingCat",
"HomogeneousLocalization.homogeneousLocalizat... | true |
Set.infinite_of_forall_exists_lt | Mathlib.Order.Preorder.Finite | [
"OrderDual.instNonempty",
"Preorder.toLT",
"Membership.mem",
"Exists",
"Set.infinite_of_forall_exists_gt",
"And",
"LT.lt",
"Nonempty",
"OrderDual",
"OrderDual.instPreorder",
"Set.instMembership",
"Preorder",
"Set.Infinite",
"Set"
] | true |
Finpartition.ofSubset._proof_1 | Mathlib.Order.Partition.Finpartition | [
"Lattice",
"Finset",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"SemilatticeInf.toPartialOrder",
"id",
"HasSubset.Subset",
"Finpartition.parts",
"Finset.instHasSubset",
"Finpartition.supIndep",
"Finset.SupIndep",
"Finset.SupIndep.subset",
"Finpartition",
"Lattice.toSemilatti... | false |
HomogeneousLocalization.awayMap.congr_simp | Mathlib.RingTheory.GradedAlgebra.HomogeneousLocalization | [
"SetLike",
"CommRing",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"HomogeneousLocalization.awayMap",
"CommSemiring.toSemiring",
"HomogeneousLocalization.homogeneousLocalizationCommRing",
"RingHom",
"Membership.mem",
"Eq.rec",
"AddSubgroupClass.toAddSubmonoidClass",
"AddCommMonoid",
"instDist... | true |
CategoryTheory.HasSubobjectClassifier.isPullback_χ | Mathlib.CategoryTheory.Subobject.Classifier.Defs | [
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Subobject.Classifier.Ω₀",
"CategoryTheory.IsPullback",
"CategoryTheory.HasSubobjectClassifier.χ",
"Nonempty.some",
"CategoryTheory.HasSubobjectClassifier.truth",
"CategoryTheory.Subobject.Classifier.χ₀",
... | true |
SemiconjBy.smul_right_iff._simp_2 | Mathlib.Algebra.Group.Action.Defs | [
"instHSMul",
"instSMulOfMul",
"IsScalarTower",
"SemiconjBy",
"Group",
"Mul",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"MulAction",
"propext",
"Monoid.toSemigroup",
"HSMul.hSMul",
"SemigroupAction.toSMul",
"SemiconjBy.smul_right_iff",
"MulAction.toSemigroupAction",
"Eq",
"SMul... | false |
Nat.decidableLoHiLe._proof_1 | Mathlib.Data.Nat.Init | [
"Iff.rfl",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"Iff",
"forall₂_congr",
"Nat.lt_succ_iff",
"HAdd.hAdd",
"Nat",
"imp_congr",
"LT.lt",
"instAddNat",
"instLTNat",
"OfNat.ofNat"
] | false |
_private.Mathlib.Data.Finset.Disjoint.0.Finset.disjoint_coe._simp_1_1 | Mathlib.Data.Finset.Disjoint | [
"Finset",
"Disjoint",
"Membership.mem",
"Finset.partialOrder",
"Finset.instSetLike",
"propext",
"Finset.disjoint_left",
"Finset.instOrderBot",
"Eq",
"Not",
"SetLike.instMembership"
] | false |
_private.Lean.Compiler.LCNF.FixedParams.0.Lean.Compiler.LCNF.mkFixedParamsMap.match_1 | Lean.Compiler.LCNF.FixedParams | [
"EStateM.Result",
"Lean.Compiler.LCNF.FixedParams.State",
"Unit",
"EStateM.Result.casesOn",
"EStateM.Result.ok",
"EStateM.Result.error"
] | false |
IsPrimitiveRoot.card_primitiveRoots | Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots | [
"Eq.mpr",
"Nat.Coprime",
"Nat.Coprime.symm",
"IsDomain",
"Nat.instMulZeroClass",
"CommRing",
"NeZero.mk",
"Iff.of_eq",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"_private.Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots.0.IsPrimitiveRoot.card_primitiveRoots._simp_1_4",
"Nat.instDecidabl... | true |
CategoryTheory.CostructuredArrow.functor | Mathlib.CategoryTheory.Comma.StructuredArrow.Functor | [
"CategoryTheory.CostructuredArrow.functor._proof_5",
"CategoryTheory.Cat.category",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"CategoryTheory.Functor.toCatHom",
"CategoryTheory.Cat.of",
"CategoryTheory.CostructuredArrow",
"Catego... | true |
Lean.Syntax.node5 | Init.Prelude | [
"Lean.Syntax.node",
"Lean.SourceInfo",
"Lean.Syntax",
"Array.mkArray5",
"Lean.SyntaxNodeKind"
] | true |
SSet.StrictSegal.isPointwiseRightKanExtensionAt._proof_4 | Mathlib.AlgebraicTopology.SimplicialSet.Coskeletal | [
"CategoryTheory.Functor.op",
"Eq.mpr",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"CategoryTheory.Functor",
"SSet.StrictSegal.isPointwiseRightKanExtensionAt.lift._proof_4",
"CategoryTheory.Limits.Cone",
"Fin.castSucc_le_succ",
"SSet.Path",
"Opposite",
"Eq... | false |
_private.Lean.Meta.Sym.Simp.Forall.0.Lean.Meta.Sym.Simp.mkForallCongrFor | Lean.Meta.Sym.Simp.Forall | [
"Array.instAppend",
"Lean.mkAppN",
"Lean.mkSort",
"instMonadControlTOfPure",
"Lean.Meta.State",
"Lean.Meta.withLocalDeclD",
"Lean.mkApp6",
"Lean.mkApp2",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instOfNatNat",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Meta.getLevel",
"Applicative.t... | true |
Lean.Meta.Grind.Arith.Cutsat.Search.State.noConfusion | Lean.Meta.Tactic.Grind.Arith.Cutsat.SearchM | [
"Lean.Meta.Grind.Arith.Cutsat.Search.State",
"Lean.PArray",
"Lean.Meta.Grind.Arith.Cutsat.Search.State.casesOn",
"Lean.Meta.Grind.Arith.Cutsat.Search.State.noConfusionType",
"Bool",
"Eq.ndrec",
"Lean.Meta.Grind.Arith.Cutsat.Case",
"Eq.refl",
"Lean.FVarIdSet",
"Eq"
] | false |
Std.ExtTreeMap.getKey!_eq_of_contains | Std.Data.ExtTreeMap.Lemmas | [
"Ordering",
"Std.TransCmp",
"Std.ExtTreeMap.getKey!",
"Bool.true",
"Std.ExtTreeMap",
"Std.LawfulEqCmp",
"Std.ExtTreeMap.inner",
"Bool",
"Inhabited",
"Std.ExtTreeMap.contains",
"Std.ExtDTreeMap.getKey!_eq_of_contains",
"Eq"
] | true |
_private.Mathlib.Algebra.Homology.ShortComplex.Homology.0.CategoryTheory.ShortComplex.HomologyMapData.instSubsingleton._simp_1 | Mathlib.Algebra.Homology.ShortComplex.Homology | [
"True",
"propext",
"Subsingleton",
"Eq",
"eq_iff_true_of_subsingleton"
] | false |
Mathlib.Tactic.BicategoryLike.Mor₁._sizeOf_1 | Mathlib.Tactic.CategoryTheory.Coherence.Datatypes | [
"Lean.Expr",
"Mathlib.Tactic.BicategoryLike.Mor₁.rec",
"instOfNatNat",
"Mathlib.Tactic.BicategoryLike.Obj",
"Mathlib.Tactic.BicategoryLike.Atom₁",
"Mathlib.Tactic.BicategoryLike.Mor₁",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Mathlib.Tactic.BicategoryLike.Atom₁._sizeOf_i... | false |
HomogeneousIdeal.toIdeal_sup | Mathlib.RingTheory.GradedAlgebra.Homogeneous.Ideal | [
"SetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Lattice.toSemilatticeSup",
"Semiring.toModule",
"Submodule.completeLattice",
"AddMonoid.toAddZeroClass",
"AddSubmonoidClass",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"AddCommMonoidWithOne.toAddMonoidWithOne",
... | true |
Rat.mk'.sizeOf_spec | Init.Data.Rat.Basic | [
"Nat.Coprime",
"Rat.den_nz._autoParam",
"Rat",
"instSizeOfDefault",
"Rat.reduced._autoParam",
"Ne",
"instOfNatNat",
"Int",
"autoParam",
"instHAdd",
"Rat._sizeOf_inst",
"HAdd.hAdd",
"Nat",
"Int._sizeOf_inst",
"Int.natAbs",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"instSizeOfNat",... | true |
CategoryTheory.Functor.mapCommMonNatIso._proof_4 | Mathlib.CategoryTheory.Monoidal.CommMon_ | [
"CategoryTheory.CommMon.instCategory",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
"CategoryTheory.Iso",
"CategoryTheory.Functor.map",
"Categor... | false |
_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_15 | Mathlib.Combinatorics.SimpleGraph.Walk.Counting | [
"_private.Mathlib.Combinatorics.SimpleGraph.Walk.Counting.0.SimpleGraph.coe_finsetWalkLength_eq._proof_1_13",
"Eq.refl"
] | false |
LinearMap.BilinForm.mem_orthogonal_iff._simp_1 | Mathlib.LinearAlgebra.BilinearForm.Orthogonal | [
"Submodule",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"Membership.mem",
"LinearMap.BilinForm.IsOrtho",
"AddCommMonoid",
"CommSemiring",
"Submodule.setLike",
"LinearMap.BilinForm.mem_orthogonal_iff",
"propext",
"Module",
"LinearMap.BilinForm.orthogonal",
"Eq",
"SetLike.instMembersh... | false |
_private.Lean.Elab.DocString.Builtin.Keywords.0.Lean.Doc.containsAtom' | Lean.Elab.DocString.Builtin.Keywords | [
"Inhabited.default",
"String",
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Meta.instInhabitedMetaM",
"Option"
] | true |
AlgHom.ker_kerSquareLift | Mathlib.RingTheory.Ideal.Cotangent | [
"Submodule",
"RingHom.instRingHomClass",
"CommRing",
"Ideal.cotangentIdeal",
"Semiring.toModule",
"CommSemiring.toSemiring",
"Ideal.Quotient.mk",
"AlgHom",
"LinearMap.instFunLike",
"Algebra",
"RingHom",
"Membership.mem",
"Exists",
"Algebra.id",
"Ideal.instAlgebraQuotient",
"Submodule.i... | true |
Multiset.prod | Mathlib.Algebra.BigOperators.Group.Multiset.Defs | [
"MulOne.toOne",
"Multiset.foldr",
"HMul.hMul",
"Monoid.toMulOneClass",
"Multiset.prod._proof_1",
"Multiset",
"MulOne.toMul",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"One.toOfNat1",
"OfNat.ofNat",
"CommMonoid",
"instHMul"
] | true |
_private.Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions.0.SimpleGraph.cycleGraph.tricoloring._proof_9 | Mathlib.Combinatorics.SimpleGraph.Coloring.Constructions | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Lean.Omega.Int.le_of_not_lt",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy",
"Lean... | false |
_private.Mathlib.Algebra.Category.ModuleCat.Kernels.0.ModuleCat.kernelIsLimit._simp_1 | Mathlib.Algebra.Category.ModuleCat.Kernels | [
"outParam",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.comp_apply",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.ConcreteCategory",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq.symm",
"Eq",
"DFunLike... | false |
Lean.Grind.ConfigInteractive._sizeOf_1 | Init.Grind.Config | [
"Lean.Grind.Config",
"Lean.Grind.ConfigInteractive.rec",
"Lean.Grind.Config._sizeOf_inst",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Lean.Grind.ConfigInteractive",
"OfNat.ofNat"
] | false |
_private.Mathlib.Data.Fin.Tuple.Basic.0.Fin.init_update_castSucc._simp_1_2 | Mathlib.Data.Fin.Tuple.Basic | [
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Fin.castSucc_inj",
"Nat",
"propext",
"instAddNat",
"Fin.castSucc",
"OfNat.ofNat",
"Fin",
"Eq"
] | false |
_private.Mathlib.Algebra.Homology.HomotopyCategory.MappingCone.0.CochainComplex.mappingCone.ext_cochain_to_iff._proof_1_2 | Mathlib.Algebra.Homology.HomotopyCategory.MappingCone | [
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"congrArg",
"Int.Linear.eq_norm",
"Classical.byContradiction",
"Eq.mp",
"Lean.RArray.branch",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"Int.instNegInt",
"instOfNatNat",
"Int",
"Int.Linear.Poly.num",
"Int.instMul",
... | false |
BorelSpace.measurable_eq | Mathlib.MeasureTheory.Constructions.BorelSpace.Basic | [
"BorelSpace",
"borel",
"MeasurableSpace",
"TopologicalSpace",
"Eq"
] | true |
Mathlib.Ineq.relImpRelData | Mathlib.Tactic.LinearCombination.Lemmas | [
"Mathlib.Ineq",
"Mathlib.Ineq.lt",
"Option.some",
"Prod.mk",
"Option.none",
"Unit",
"Mathlib.Ineq.eq",
"_private.Mathlib.Tactic.LinearCombination.Lemmas.0.Mathlib.Ineq.addRelRelData.match_1",
"Lean.Name",
"Mathlib.Ineq.le",
"Prod",
"Lean.Name.mkStr4",
"Option"
] | true |
CategoryTheory.ShortComplex.homologyι_comp_asIsoHomologyι_inv | Mathlib.Algebra.Homology.ShortComplex.Homology | [
"CategoryTheory.ShortComplex.opcycles",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.asIsoHomologyι",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.HasHomology",
"CategoryTheory.CategoryStruct.id",
"Categ... | true |
CategoryTheory.ObjectProperty.IsTriangulatedClosed₁.casesOn | Mathlib.CategoryTheory.Triangulated.Subcategory | [
"CategoryTheory.Functor.Additive",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"CategoryTheory.Pretriangulated.Triangle.obj₃",
"CategoryTheory.shiftFunctor",
"Membership.mem",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Pretriangulated.Triangle",
"CategoryTheory.Preadditive",
"CategoryTheory.O... | false |
Partrec.to₂ | Mathlib.Computability.Partrec | [
"Part",
"PFun",
"_private.Mathlib.Computability.Partrec.0.Partrec.to₂.match_1_1",
"Prod.mk",
"Prod.fst",
"Primcodable.prod",
"Partrec.of_eq",
"Primcodable",
"Prod",
"Eq",
"Prod.snd",
"Partrec₂",
"rfl",
"Partrec"
] | true |
CategoryTheory.Adjunction.leftAdjointCompNatTrans_app | Mathlib.CategoryTheory.Adjunction.CompositionIso | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Adjunction.unit",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Adjunction.comp_counit_... | true |
Set.Iic.isCompl_iff | Mathlib.Order.LatticeIntervals | [
"Eq.mpr",
"Lattice",
"Codisjoint",
"Lattice.toSemilatticeSup",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"OrderBot",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"Set.Elem",
"isCompl_iff",
"id",
"Set.Iic.disjoint_iff"... | true |
Std.HashSet.Raw.Equiv.beq_congr | Std.Data.HashSet.RawLemmas | [
"Std.HashSet.Raw.inner",
"Std.HashSet.Raw.WF",
"instBEqOfDecidableEq",
"LawfulHashable",
"Std.HashSet.Raw.Equiv",
"Std.HashSet.Raw.instBEqOfHashable",
"BEq.beq",
"Unit",
"EquivBEq",
"Std.HashSet.Raw.WF.out",
"Bool",
"Hashable",
"Std.HashMap.Raw.Equiv.beq_congr",
"instDecidableEqPUnit",
"... | true |
_private.Mathlib.Analysis.InnerProductSpace.Symmetric.0.Submodule.isSymmetricProjection_projection_iff._simp_1_3 | Mathlib.Analysis.InnerProductSpace.Symmetric | [
"Submodule",
"Submodule.projection",
"AddCommGroup.toAddCommMonoid",
"Submodule.completeLattice",
"Module.End.instMul",
"CompleteLattice.toBoundedOrder",
"AddCommGroup",
"Submodule.instPartialOrder",
"LinearMap",
"IsCompl",
"IsIdempotentElem",
"True",
"eq_true",
"Module",
"RingHom.id",
... | false |
RingSeminormClass.toSubmultiplicativeHomClass | Mathlib.Algebra.Order.Hom.Basic | [
"NonUnitalNonAssocRing",
"outParam",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"instDistribOfSemiring",
"SubmultiplicativeHomClass",
"Distrib.toMul",
"Semiring",
"NonUnitalNonAssocSemiring.toDistrib",
"FunLike",
"RingSemi... | true |
MonadLiftT.noConfusion | Init.Prelude | [
"HEq.refl",
"MonadLiftT",
"MonadLiftT.noConfusionType",
"MonadLiftT.casesOn",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Eq"
] | false |
Lean.Meta.Grind.Arith.CommRing.isField | Lean.Meta.Tactic.Grind.Arith.CommRing.RingM | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.Arith.CommRing.CommRing.fieldInst?",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.Arith.CommRing.RingM",
"Lean.Meta.Grind.Arith.CommRing.RingM.Context",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.Sym.Context",
"ReaderT.instMonad",
"Lean.Met... | true |
Algebra.instIsStandardSmoothOfSubsingleton | Mathlib.RingTheory.Smooth.StandardSmooth | [
"CommRing",
"Algebra.IsStandardSmooth",
"CommSemiring.toSemiring",
"Finite",
"Algebra",
"Exists",
"inferInstance",
"Finite.of_fintype",
"Nonempty.intro",
"And",
"Unit",
"CommRing.toCommSemiring",
"Algebra.SubmersivePresentation",
"PUnit.fintype",
"And.intro",
"Algebra.IsStandardSmooth.... | true |
Metric.Snowflaking.mk | Mathlib.Topology.MetricSpace.Snowflaking | [
"Real.instLE",
"Real",
"Real.instZero",
"Real.instLT",
"Metric.Snowflaking.mk",
"LE.le",
"Real.instOne",
"LT.lt",
"One.toOfNat1",
"Zero.toOfNat0",
"Metric.Snowflaking",
"OfNat.ofNat"
] | true |
ZSpan.map | Mathlib.Algebra.Module.ZLattice.Basic | [
"Set.range_comp",
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"NormedSpace",
"congrArg",
"LinearEquiv.restrictScalars",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"Module.Basis.map",
"LinearMap.instFunLike",
"Function.comp",
"Membership.mem",
"NormedField.toField",
"AddC... | true |
Set.union_inter_compl_right_subset | Mathlib.Order.BooleanAlgebra.Set | [
"Set.union_empty",
"congrArg",
"Compl.compl",
"Set.instUnion",
"HasSubset.Subset",
"Set.instInter",
"Set.instCompl",
"Inter.inter",
"True",
"Set.inter_compl_self",
"Set.instEmptyCollection",
"of_eq_true",
"congrFun'",
"Union.union",
"EmptyCollection.emptyCollection",
"Set.union_inter_d... | true |
QuaternionAlgebra.lift._proof_2 | Mathlib.Algebra.QuaternionBasis | [
"RingHom.instRingHomClass",
"CommRing",
"instHSMul",
"QuaternionAlgebra.imI",
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"congrArg",
"CommSemiring.toSemiring",
"QuaternionAlgebra.Basis.self",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Module.toMulActionWithZero",
"Q... | false |
Complex.addCommGroup._proof_6 | Mathlib.Data.Complex.Basic | [
"HSub.hSub",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Eq.refl",
"Complex.instSub",
"Complex.instAdd",
"Complex",
"Eq",
"Complex.instNeg",
"Neg.neg"
] | false |
_private.Mathlib.RingTheory.Invariant.Basic.0.fixed_of_fixed1_aux2 | Mathlib.RingTheory.Invariant.Basic | [
"Eq.mpr",
"RingHom.instRingHomClass",
"Submodule.instAddCommMonoidWithOne",
"Submodule.Quotient.instZeroQuotient",
"CommRing",
"instHSMul",
"Semiring.toModule",
"HMul.hMul",
"_private.Mathlib.RingTheory.Invariant.Basic.0.fixed_of_fixed1_aux1",
"Algebra.algebraMap",
"MulZeroClass.toMul",
"Monoi... | true |
Homeomorph.coe_sumComm | Mathlib.Topology.Constructions.SumProd | [
"Homeomorph.sumComm",
"Sum.swap",
"Sum",
"instTopologicalSpaceSum",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"Homeomorph",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
Path.delayReflLeft | Mathlib.Topology.Homotopy.HSpaces | [
"Real",
"Path.symm",
"Set.Elem",
"Path.delayReflRight",
"TopologicalSpace",
"Path",
"unitInterval"
] | true |
VectorField.mpullback_neg_apply | Mathlib.Geometry.Manifold.VectorField.Pullback | [
"NegZeroClass.toNeg",
"Pi.instNeg",
"mfderiv",
"SemilinearMapClass.distribMulActionSemiHomClass",
"NormedSpace",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"instAddCommGroupTangentSpace",
"ContinuousLinearMap.funLike",
"AddCommGroup.toAddGroup",
"RingHom",
"NormedField.toField",
"instModule... | true |
CategoryTheory.coherentTopology.equivalence' | Mathlib.CategoryTheory.Sites.Coherent.SheafComparison | [
"CategoryTheory.Functor.op",
"CategoryTheory.coherentTopology.equivalence'._proof_2",
"CategoryTheory.Functor",
"CategoryTheory.Preregular",
"Opposite",
"CategoryTheory.coherentTopology.equivalence'._proof_3",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.FinitaryExtensive",
"CategoryThe... | true |
instFunLikeContMDiffMonoidMorphism._proof_1 | Mathlib.Geometry.Manifold.Algebra.Monoid | [
"Monoid",
"MulOne.toOne",
"MonoidHom.instFunLike",
"NormedSpace",
"MonoidHom",
"Monoid.toMulOneClass",
"ContMDiff",
"Eq.rec",
"TopologicalSpace",
"ModelWithCorners",
"MulOneClass.toMulOne",
"ContMDiffMonoidMorphism.mk",
"OneHom.toFun",
"ENat",
"ContMDiffMonoidMorphism.toMonoidHom",
"Mo... | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getKeyD_insertMany_list_of_contains_eq_false._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
cfc_add_const._auto_3 | 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 |
panicCore | Init.Prelude | [
"Inhabited.default",
"String",
"Inhabited"
] | true |
locallyConvexSpace_iff_exists_convex_subset | Mathlib.Topology.Algebra.Module.LocallyConvex | [
"Filter.instMembership",
"locallyConvexSpace_iff",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"Exists",
"nhds",
"AddZeroClass.toAddZero",
"PartialOrder",
"id",
"DistribSMul.toSMulZeroClass",
"HasSubset.Subset",
"LocallyConvexSpace",
"AddCommMonoid",
"... | true |
MulChar.inv._proof_1 | Mathlib.NumberTheory.MulChar.Basic | [
"congrArg",
"MonoidWithZeroHom.funLike",
"IsUnit",
"MulChar",
"MulChar.instFunLike",
"CommMonoidWithZero.toMonoidWithZero",
"MonoidWithZeroHom",
"MonoidWithZero.toMulZeroOneClass",
"CommMonoid.toMonoid",
"CommMonoidWithZero",
"True",
"eq_self",
"MulChar.map_nonunit",
"of_eq_true",
"Zero.... | false |
SlashInvariantForm.const_toFun | Mathlib.NumberTheory.ModularForms.SlashInvariantForms | [
"SlashInvariantForm",
"Real",
"Subgroup.HasDetOne",
"SlashInvariantForm.const",
"Matrix",
"instDecidableEqFin",
"SlashInvariantForm.funLike",
"Real.semiring",
"Subgroup",
"instOfNatNat",
"Int",
"Units.instGroup",
"Real.commRing",
"Fin.fintype",
"instOfNat",
"UpperHalfPlane",
"Nat",
... | true |
Partition.ctorIdx | Mathlib.Order.Partition.Basic | [
"Partition",
"Nat",
"CompleteLattice"
] | false |
Finset.preimage_neg | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"Eq.mpr",
"congrArg",
"Function.Injective.injOn",
"Finset",
"neg_injective",
"id",
"Finset.coe_neg",
"Finset.coe_preimage",
"Finset.coe_injective",
"InvolutiveNeg",
"SetLike.coe",
"Set.preimage",
"Finset.instSetLike",
"Set.neg_preimage",
"Finset.preimage",
"Set.neg",
"Finset.neg",
... | true |
_private.Lean.Meta.ExprDefEq.0.Lean.Meta.isDefEqProj.isDefEqSingleton.match_1 | Lean.Meta.ExprDefEq | [
"Lean.ConstructorVal",
"Option.ctorIdx",
"_private.Lean.Meta.ExprDefEq.0.Lean.Meta.isEtaUnassignedMVar._sparseCasesOn_1",
"Option.some",
"Nat.hasNotBit",
"Option"
] | false |
exists_covby_infinite_Ici_of_infinite_Ici | Mathlib.Order.Atoms.Finite | [
"Mathlib.Tactic.Push.not_exists._simp_1",
"Set.Finite.not_infinite",
"Mathlib.Tactic.Push.not_and_eq",
"Preorder.toLT",
"Set.Ici",
"IsStronglyAtomic",
"CovBy",
"Classical.byContradiction",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Set.Finite",
"Membership.mem",
"Exists",
"Par... | true |
Matrix.diagonal_kroneckerTMul_diagonal | Mathlib.LinearAlgebra.Matrix.Kronecker | [
"instDecidableEqProd",
"CommSemiring.toSemiring",
"Matrix",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"TensorProduct.tmul_zero",
"TensorProduct.zero_tmul",
"Prod.fst",
"AddCommMonoid",
"CommSemiring",
"AddZero.toZero",
"Matrix.kroneckerMap_diagonal_diagonal",
"Matrix.kroneckerMap... | true |
TensorProduct.sum_tmul_eq_zero_of_vanishesTrivially | Mathlib.LinearAlgebra.TensorProduct.Vanishing | [
"Eq.mpr",
"_private.Mathlib.LinearAlgebra.TensorProduct.Vanishing.0.TensorProduct.sum_tmul_eq_zero_of_vanishesTrivially._simp_1_3",
"CommRing",
"TensorProduct.leftHasSMul",
"instHSMul",
"instSMulOfMul",
"Finset.univ",
"congrArg",
"CommSemiring.toSemiring",
"_private.Mathlib.LinearAlgebra.TensorPro... | true |
Substring.Raw.ValidFor.extract | Batteries.Data.String.Lemmas | [
"String.toList_ofList",
"Substring.Raw.extract",
"Eq.mpr",
"Substring.Raw.str",
"List.append_assoc",
"congrArg",
"Substring.Raw.mk",
"String",
"Exists",
"Eq.mp",
"Substring.Raw.ValidFor",
"id",
"String.Pos.Raw",
"Substring.Raw",
"instAppendString",
"instHAppendOfAppend",
"List",
"S... | true |
Batteries.HashMap.toArray | Batteries.Data.HashMap.Basic | [
"Array",
"Batteries.HashMap.inner",
"Hashable",
"Std.HashMap.toArray",
"Prod",
"BEq",
"Batteries.HashMap"
] | true |
_private.Mathlib.Data.List.Basic.0.List.length_eq_four.match_1_3 | Mathlib.Data.List.Basic | [
"Exists",
"List.cons",
"List",
"Exists.casesOn",
"Exists.intro",
"Eq",
"List.nil"
] | false |
Mathlib.Tactic.FieldSimp.Sign.minus.inj | Mathlib.Tactic.FieldSimp.Lemmas | [
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"Mathlib.Tactic.FieldSimp.Sign.minus",
"List.cons",
"Qq.Quoted",
"Mathlib.Tactic.FieldSimp.Sign",
"Mathlib.Tactic.FieldSimp.Sign.minus.noConfusion",
"Lean.Expr.app",
"Lean.Level.succ",
"Lean.Name.mkStr1",
"Eq",
"List.nil"
] | true |
Valued.noConfusion | Mathlib.Topology.Algebra.Valued.ValuationTopology | [
"Filter.instMembership",
"UniformSpace",
"Units.val",
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Preorder.toLT",
"ValuationClass.toMonoidWithZeroHomClass",
"AddGroupWithOne.toAddGroup",
"WithZero.instMonoidWithZero",
"HEq.refl",
"Monoid... | false |
PosNum.size._unsafe_rec | Mathlib.Data.Num.Basic | [
"PosNum.size._unsafe_rec",
"instOnePosNum",
"PosNum.succ",
"Unit",
"One.toOfNat1",
"PosNum",
"OfNat.ofNat",
"PosNum.pred'.match_1"
] | false |
Aesop.Frontend.Feature.builder.sizeOf_spec | Aesop.Frontend.RuleExpr | [
"Aesop.Frontend.Feature._sizeOf_inst",
"instOfNatNat",
"Aesop.Frontend.DBuilderName",
"Aesop.Frontend.Feature.builder",
"instHAdd",
"Aesop.Frontend.Feature",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Aesop.Frontend.DBuilderName._sizeOf_inst"
] | true |
CategoryTheory.ShortComplex.LeftHomologyData.ofIsColimitCokernelCofork | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.ShortComplex.LeftHomologyData.ofIsColimitCokernelCofork._proof_3",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParal... | true |
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