name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.MonoidalCategory.MonoidalLeftAction.oppositeLeftAction._proof_13 | Mathlib.CategoryTheory.Monoidal.Action.Opposites | [
"CategoryTheory.Category.assoc",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Iso.op",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.op_inv._simp_1",
"Quiver.Hom.unop",
"CategoryTheory.MonoidalCategory.... | false |
lowerClosure_eq._simp_1 | Mathlib.Order.UpperLower.Closure | [
"Preorder.toLE",
"SetLike.coe",
"IsLowerSet",
"propext",
"LowerSet",
"Eq",
"lowerClosure",
"lowerClosure_eq",
"Preorder",
"Set",
"LowerSet.instSetLike"
] | false |
Nat.ModEq.mul_right_cancel' | Mathlib.Data.Nat.ModEq | [
"Iff.mpr",
"Eq.mpr",
"Dvd.dvd",
"HMul.hMul",
"congrArg",
"HSub.hSub",
"id",
"Ne",
"instMulNat",
"instOfNatNat",
"Int",
"Nat.cast",
"Int.ofNat_ne_zero",
"Int.instDvd",
"Int.instMul",
"Nat.ModEq",
"instHSub",
"instOfNat",
"implies_congr",
"_private.Mathlib.Data.Nat.ModEq.0.Nat.Mo... | true |
HasSSubset.SSubset.trans_eq | Mathlib.Order.RelClasses | [
"HasSSubset",
"HasSSubset.SSubset",
"Eq",
"ssubset_of_ssubset_of_eq"
] | true |
Filter.isBoundedUnder_of | Mathlib.Order.Filter.IsBounded | [
"Filter.map",
"Filter.Eventually",
"Exists",
"Filter.Eventually.of_forall",
"_private.Mathlib.Order.Filter.IsBounded.0.Filter.isBoundedUnder_of.match_1_1",
"Exists.intro",
"Filter.IsBoundedUnder",
"Filter"
] | true |
AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_trans_hom_assoc | Mathlib.AlgebraicGeometry.PullbackCarrier | [
"AlgebraicGeometry.Scheme.Pullback.Triplet.tensorCongr_trans_hom",
"CategoryTheory.Category.assoc",
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CommRingCat",
"Eq.mp",
"CommRingCat.instCategory",
"id",
"AlgebraicGeometry.Scheme.Pullback.Triplet... | true |
Std.ExtTreeMap.contains_insertMany_list | Std.Data.ExtTreeMap.Lemmas | [
"Std.ExtDTreeMap.Const.contains_insertMany_list",
"instForInOfForIn'",
"List.map",
"List.contains",
"Ordering",
"inferInstance",
"Std.TransCmp",
"Id",
"Membership",
"Prod.fst",
"Std.ExtTreeMap.insertMany",
"List",
"Std.ExtTreeMap",
"List.instMembership",
"Std.ExtTreeMap.inner",
"Std.La... | true |
CategoryTheory.Triangulated.Octahedron.casesOn | Mathlib.CategoryTheory.Triangulated.Triangulated | [
"CategoryTheory.Triangulated.Octahedron.mk",
"CategoryTheory.Triangulated.Octahedron",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"CategoryTheory.shiftFunctor",
"Membership.mem",
"Int",
"Int.instAddMonoid",
"CategoryTheory.Pretriangulated.Triangle",
... | false |
StrictConvexOn.convex_lt | Mathlib.Analysis.Convex.Function | [
"Iff.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Trans.trans",
"convex_iff_pairwise_pos",
"Preorder.toLT",
"DistribMulAction.toDistribSMul",
"instTransLTLE",
"covariant_swap_add_of_covariant_add",
"AddMonoid.toAddZeroClass",
"add_le_add",
"PartialOrder.toPreorder",
"setOf"... | true |
HomologicalComplex.homotopyCofiber.sndX.eq_1 | Mathlib.Algebra.Homology.HomotopyCofiber | [
"HomologicalComplex.instCategory",
"HomologicalComplex.homotopyCofiber.X",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"DecidableRel",
"HomologicalComplex",
"ComplexShape",
"CategoryTheory.Limits.biprod",
"dite",
"CategoryTheory.Preadditive",
"CategoryTheory.Limits.biprod.snd",
"Ho... | true |
Lean.Meta.Grind.Origin.key | Lean.Meta.Tactic.Grind.Theorems | [
"_private.Lean.Meta.Tactic.Grind.Theorems.0.Lean.Meta.Grind.instReprOrigin.repr.match_1",
"Lean.Syntax",
"Lean.FVarId",
"Lean.Meta.Grind.Origin",
"Lean.Name",
"Lean.FVarId.name"
] | true |
Lean.Meta.LazyDiscrTree.Key.proj.sizeOf_spec | Lean.Meta.LazyDiscrTree | [
"Lean.Meta.LazyDiscrTree.Key.proj",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Lean.Name",
"Eq.refl",
"instSizeOfNat",
"OfNat.ofNat",
"Eq",
"Lean.Meta.LazyDiscrTree.Key._sizeOf_inst",
"Lean.Meta.LazyDiscrTree.Key"
] | true |
IterateAddAct.mk._flat_ctor | Mathlib.GroupTheory.GroupAction.IterateAct | [
"IterateAddAct",
"Nat",
"IterateAddAct.mk"
] | false |
ULift.up_ofNat | Mathlib.Algebra.Ring.ULift | [
"ULift.instNatCast",
"ULift",
"NatCast",
"Nat",
"OfNat.ofNat",
"ULift.up",
"Eq",
"instOfNatAtLeastTwo",
"rfl",
"Nat.AtLeastTwo"
] | true |
Lean.Server.Test.Runner.Client.Hyp.isRemoved? | Lean.Server.Test.Runner | [
"Lean.Server.Test.Runner.Client.Hyp",
"Bool",
"Option"
] | true |
Lean.Parser.Term.doLetElse.parenthesizer | Lean.Parser.Do | [
"Lean.Parser.optional.parenthesizer",
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.Parser.Term.doSeqIndent.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.leadingNode.parenthesizer",
"Lean.PrettyPrinter.Paren... | true |
Matrix.kroneckerTMulStarAlgEquiv._proof_2 | Mathlib.RingTheory.MatrixAlgebra | [
"Matrix.instStar",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Matrix.module",
"instDecidableEqProd",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"IsScalarTower",
"Algebra",
"TensorProduct.instStar",
"Algebra.toSMul",
"Matrix.instAlgebra",
"Algebra.toModule",
"Matrix.kroneckerTMulAlgE... | false |
Lean.IR.initFn._@.Lean.Compiler.IR.CompilerM.3612076334._hygCtx._hyg.2 | Lean.Compiler.IR.CompilerM | [
"guard",
"Pure.pure",
"Lean.EnvExtension.AsyncMode.sync",
"Lean.IR.Decl.extern",
"Lean.EnvironmentHeader.isModule",
"instAlternativeOption",
"Lean.Environment.header",
"Bool.not",
"Lean.ExternAttrData.mk",
"Array.push",
"String",
"Lean.getExportNameFor?",
"Lean.SimplePersistentEnvExtensionDe... | false |
Matrix.eRank_toNat_eq_finrank | Mathlib.LinearAlgebra.Matrix.Rank | [
"Pi.Function.module",
"Submodule",
"Semiring.toModule",
"Pi.addCommMonoid",
"Matrix.eRank",
"Matrix",
"Submodule.addCommMonoid",
"Membership.mem",
"Subtype",
"Matrix.cRank",
"Submodule.module",
"Cardinal.toNat_toENat",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUni... | true |
Mathlib.Tactic.BicategoryLike.MkEvalWhiskerLeft | Mathlib.Tactic.CategoryTheory.Coherence.Normalize | [
"Mathlib.Tactic.BicategoryLike.MkEvalWhiskerLeft.mk"
] | true |
_private.Mathlib.Tactic.ProxyType.0.Mathlib.ProxyType.ensureProxyEquiv.match_3 | Mathlib.Tactic.ProxyType | [
"Lean.TSyntax",
"Unit.unit",
"Subarray",
"Option.casesOn",
"Option.some",
"Lean.Expr",
"Prod.mk",
"Lean.Syntax.Term",
"List.cons",
"Option.none",
"Unit",
"Lean.Name",
"Lean.SyntaxNodeKind",
"Prod",
"Prod.casesOn",
"Lean.Name.mkStr1",
"List.nil",
"Option"
] | false |
_private.Init.Data.Array.Lemmas.0.Array.ne_of_not_mem_push._simp_1_1 | Init.Data.Array.Lemmas | [
"not_or",
"And",
"propext",
"Or",
"Eq",
"Not"
] | false |
_private.Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic.0.CFC.sqrt_ringInverse._proof_1_1 | Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Basic | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
StrictConvexOn.slope_lt_of_hasDerivWithinAt | Mathlib.Analysis.Convex.Deriv | [
"NormedCommRing.toSeminormedCommRing",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Set.OrdConnected.mem_nhdsLT",
"instClosedIicTopology",
"Real.partialOrder",
"Real",
"instHSMul",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"instSMulOfMul",
"Real.latt... | true |
Seminorm.mk | Mathlib.Analysis.Seminorm | [
"Norm.norm",
"SeminormedRing.toNorm",
"Real",
"instHSMul",
"HMul.hMul",
"SMul",
"Seminorm",
"AddGroupSeminorm",
"AddGroup",
"AddGroupSeminorm.toFun",
"Real.instMul",
"Seminorm.mk",
"HSMul.hSMul",
"Eq",
"SeminormedRing",
"instHMul"
] | true |
CategoryTheory.IsFiltered.SmallFilteredIntermediate.factoring | Mathlib.CategoryTheory.Filtered.Small | [
"CategoryTheory.Functor",
"CategoryTheory.IsFiltered.SmallFilteredIntermediate.factoring._proof_1",
"CategoryTheory.Functor.comp",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.ObjectProperty.lift",
"CategoryTheory.IsFiltered.SmallFilteredIntermediate._proof_1",
"CategoryTheory.IsFiltered.SmallF... | true |
Module.Finite.self | Mathlib.RingTheory.Finiteness.Basic | [
"Semiring.toModule",
"Ideal.fg_top",
"Module.Finite.of_fg_top",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semiring",
"Module.Finite",
"Semiring.toNonAssocSemiring"
] | true |
inv_mul_lt_iff₀' | Mathlib.Algebra.Order.GroupWithZero.Unbundled.Basic | [
"CommMonoidWithZero.toCommMonoid",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Preorder.toLT",
"GroupWithZero.toDivisionMonoid",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"CommMonoid.toCommSemigroup",
"DivInvOneMonoid.toInvOneClass",
"MulZeroClass.toMul",
"congrArg",
"Iff.rfl",
"P... | true |
Filter.Germ.instIsCancelMul | Mathlib.Order.Filter.Germ.Basic | [
"IsCancelMul",
"Mul",
"Filter.Germ.instMul",
"IsCancelMul.toIsRightCancelMul",
"IsCancelMul.mk",
"Filter.Germ",
"IsCancelMul.toIsLeftCancelMul",
"Filter.Germ.instIsLeftCancelMul",
"Filter.Germ.instIsRightCancelMul",
"Filter"
] | true |
Lean.parseImports' | Lean.Elab.ParseImportsFast | [
"Pure.pure",
"Lean.ModuleHeader.mk",
"Lean.ParseImports.State.mk",
"Lean.FileMap.toPosition",
"instMonadExceptOfMonadExceptOf",
"Lean.ParseImports.State.isModule",
"Lean.Import",
"Monad.toApplicative",
"String",
"Lean.FileMap",
"MonadExcept.throw",
"IO",
"instMonadExceptOfEIO",
"instMonadE... | true |
Algebra.lmul._proof_3 | Mathlib.Algebra.Algebra.Bilinear | [
"instSMulOfMul",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra",
"Algebra.toModule",
"MulOne.toMul",
"IsScalarTower.left",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"MulOneClass.toMulOne",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Semi... | false |
Filter.high_scores | Mathlib.Order.Filter.AtTopBot.Finite | [
"Mathlib.Tactic.Push.not_and_eq",
"le_refl",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"instDistribLatticeNat",
"Filter.exists_lt_of_tendsto_atTop",
"NoMaxOrder",
"LinearOrder",
"PartialOrder.toPreorder",
"Subtype.casesOn",
"Preorder.toLE",
"Membership.mem",
"Exists",
"SemilatticeInf.to... | true |
LieAlgebra.lieCharacterEquivLinearDual_apply | Mathlib.Algebra.Lie.Character | [
"LieAlgebra.toModule",
"CommRing",
"Equiv.instEquivLike",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Algebra.id",
"Equiv",
"SubtractionMonoid.toSubNegZeroMonoid",
"LieRingModule.toBracket",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toS... | true |
IsDomain.recOn | Mathlib.Algebra.Ring.Defs | [
"Nontrivial",
"IsDomain",
"IsDomain.rec",
"IsCancelMulZero",
"IsDomain.mk",
"instDistribOfSemiring",
"Distrib.toMul",
"Semiring",
"MulZeroClass.toZero",
"instMulZeroClassOfSemiring"
] | false |
FreeCommRing.eq_1 | Mathlib.SetTheory.Cardinal.Free | [
"FreeCommRing",
"Multiset",
"Multiplicative",
"Eq.refl",
"FreeAbelianGroup",
"Eq"
] | true |
_private.Mathlib.Tactic.Simps.Basic.0.Simps.splitOnNotNumber.process._f | Mathlib.Tactic.Simps.Basic | [
"List.head?",
"String",
"instDecidableEqBool",
"List.cons",
"Bool.true",
"instAppendString",
"instHAppendOfAppend",
"List",
"Unit",
"Char.isDigit",
"String.toList",
"_private.Mathlib.Tactic.Simps.Basic.0.Simps.splitOnNotNumber.match_1",
"Bool",
"List.below",
"Char",
"Option.elim",
"B... | false |
CategoryTheory.Limits.colimitFlipCompColimIsoColimitCompColim._proof_1 | Mathlib.CategoryTheory.Limits.Fubini | [
"CategoryTheory.Functor.flip",
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.Limits.colim",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.HasColimit",
"CategoryT... | false |
Std.Tactic.BVDecide.BVExpr.Cache.Inv | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Expr | [
"Std.Sat.AIG.Fanin.gate",
"Std.Sat.AIG.Ref.mk",
"Std.Tactic.BVDecide.BVExpr.Cache.Key",
"instLawfulBEq",
"Vector",
"Vector.instGetElemNatLt",
"Std.Tactic.BVDecide.BVExpr.eval",
"Membership.mem",
"Std.Sat.AIG.Fanin.invert",
"BitVec.getLsbD",
"Std.DHashMap.instMembership",
"Std.Tactic.BVDecide.B... | true |
CategoryTheory.ObjectProperty.ι_obj_lift_map | Mathlib.CategoryTheory.ObjectProperty.FullSubcategory | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ObjectProperty.ι",
"CategoryTheory.ObjectProperty.lift",
"CategoryTheory.Functor.map",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ObjectProperty.FullSubcategory",
"CategoryTheory.Object... | true |
CategoryTheory.Triangulated.TStructure.isLE_of_le | Mathlib.CategoryTheory.Triangulated.TStructure.Basic | [
"CategoryTheory.Triangulated.TStructure.le_of_isLE",
"CategoryTheory.Triangulated.TStructure.IsLE",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Triangulated.TStructure.le_monotone",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Triangulated.TStructure.isLE_of_le._auto_1",
"Int",
"Int.instAddMo... | true |
groupHomology.H1CoresCoinfOfTrivial_g_epi | Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | [
"Rep.V",
"CommRing",
"CategoryTheory.Epi",
"Representation.IsTrivial",
"ModuleCat",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Subgroup.subtype",
"Module.End.instSemiring",
"Group",
"Rep.hV1",
"Membership.mem",
"Subtype",
"_private.Ma... | true |
CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.cc._proof_2 | Mathlib.Algebra.Homology.SpectralObject.SpectralSequence | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Abelian.SpectralObject.E",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore.i₃",
"CategoryTheory.Abelian.SpectralObject.SpectralSequenceDataCore.le₀₁'",
"CategoryTheory.Abelian.SpectralObject.mapFourδ₄Toδ₃'",
"CategoryTheory.CategorySt... | false |
Asymptotics.isBigOWith_norm_right._simp_1 | Mathlib.Analysis.Asymptotics.Defs | [
"Norm.norm",
"Real",
"Asymptotics.isBigOWith_norm_right",
"SeminormedAddCommGroup",
"Asymptotics.IsBigOWith",
"Norm",
"SeminormedAddCommGroup.toNorm",
"propext",
"Eq",
"Filter",
"Real.norm"
] | false |
Metric.smul_eball | Mathlib.Topology.MetricSpace.IsometricSMul | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"instHSMul",
"IsometryEquiv.constSMul",
"IsIsometricSMul",
"Group",
"IsometryEquiv.image_eball",
"DivInvMonoid.toMonoid",
"Metric.eball",
"PseudoEMetricSpace",
"Group.toDivInvMonoid",
"WeakPseudoEMetricSpace.toEDist",
"PseudoEMetricSpace.toUniform... | true |
_private.Mathlib.Analysis.InnerProductSpace.Defs.0.InnerProductSpace.Core.«term_†» | Mathlib.Analysis.InnerProductSpace.Defs | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.Name.anonymous",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat",
"Lean.TrailingParserDescr"
] | true |
PerfectClosure.of | Mathlib.FieldTheory.PerfectClosure | [
"MulOne.toOne",
"CommRing",
"Nat.Prime",
"RingHom.mk",
"CommSemiring.toSemiring",
"OneHom.mk",
"AddGroupWithOne.toAddMonoidWithOne",
"PerfectClosure.of._proof_4",
"RingHom",
"Fact",
"Prod.mk",
"MonoidHom.mk",
"NonAssocSemiring.toMulZeroOneClass",
"instOfNatNat",
"MulZeroOneClass.toMulOne... | true |
SSet.Truncated.IsStrictSegal.mk | Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"Opposite",
"SSet.Truncated.spine",
"SSet.Truncated",
"SSet.Truncated.IsStrictSegal",
"instOfNatNat",
"LE.le",
"instLENat",
"autoParam",
"SSet.Truncated.IsStrictSegal.mk",
"instHAdd",
"HAdd.hAdd",
"SimplexCategory.mk",
"Opposite.op",
"N... | true |
CategoryTheory.Adjunction.CoreHomEquivUnitCounit.recOn | Mathlib.CategoryTheory.Adjunction.Basic | [
"CategoryTheory.Functor",
"Equiv.instEquivLike",
"CategoryTheory.Adjunction.CoreHomEquivUnitCounit",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Adjunction.CoreHomEquivUnitCounit.mk",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functo... | false |
CategoryTheory.FunctorToTypes.naturality_symm | Mathlib.CategoryTheory.Types.Basic | [
"Eq.mpr",
"CategoryTheory.Functor",
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Equiv.symm_apply_apply",
"CategoryTheory.ConcreteCategory.hom",
"TypeCat.instFunLikeFun",
"Function.comp",
"Exists",
"id",
"Equiv",
"C... | true |
_private.Mathlib.Order.WellFoundedSet.0.Set.WellFoundedOn.exists_maximal.match_1_1 | Mathlib.Order.WellFoundedSet | [
"Set.univ",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Subtype",
"Exists.casesOn",
"Exists.intro",
"Maximal",
"Set.instMembership",
"Preorder",
"Subtype.preorder",
"Set"
] | false |
Equiv.Perm.extendDomain_eq_one_iff._simp_1 | Mathlib.Algebra.Group.End | [
"Equiv.Perm.instOne",
"Equiv.Perm.extendDomain",
"Equiv",
"Subtype",
"Equiv.Perm",
"DecidablePred",
"propext",
"One.toOfNat1",
"Equiv.Perm.extendDomain_eq_one_iff",
"OfNat.ofNat",
"Eq"
] | false |
_private.Mathlib.Algebra.Order.CauSeq.Basic.0.CauSeq.not_limZero_of_pos.match_1_1 | Mathlib.Algebra.Order.CauSeq.Basic | [
"Preorder.toLT",
"AddGroupWithOne.toAddGroup",
"abs",
"LinearOrder",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"DivisionRing.toRing",
"LE.le",
"Field.toSemifield",
"And.casesOn",
... | false |
Sym2.fromRel_top_iff | Mathlib.Data.Sym.Sym2 | [
"Eq.mpr",
"Symmetric",
"Sym2.mk",
"congrArg",
"Set.mem_univ._simp_1",
"Sym2.fromRel_top",
"Set.univ",
"iff_true",
"true_iff",
"Membership.mem",
"Eq.mp",
"id",
"funext",
"Iff",
"BooleanAlgebra.toTop",
"True",
"Iff.intro",
"Sym2.fromRel_prop",
"propext",
"Eq.ndrec",
"congrFun'"... | true |
Module.finrank_directSum | Mathlib.LinearAlgebra.Dimension.Constructions | [
"Nat.instMulZeroOneClass",
"Finset.univ",
"instAddCommMonoidDirectSum",
"Cardinal",
"rank_directSum",
"DirectSum.instModule",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"_private.Mathlib.LinearAlgebra.Dimension.Constructions.0.Module.finrank_directSum._simp_1_1",
"Cardinal.commSemiring",
... | true |
_private.Mathlib.Tactic.Ring.Basic.0.Mathlib.Tactic.Ring.ExBase.evalNatCast.match_3 | Mathlib.Tactic.Ring.Basic | [
"Mathlib.Tactic.Ring.Common.Result.mk",
"Lean.Expr.const",
"Mathlib.Tactic.Ring.Common.Result",
"Mathlib.Tactic.Ring.ExSum",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Mathlib.Tactic.Ring.Common.Result.casesOn",
"Qq.Quoted.unsafeMk",
"Lean.Name.mkStr2",
"Lean.Expr.app",
"Lean... | false |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.ediv_lt_natAbs_self_of_lt_neg_one_of_lt_neg_one._simp_1_3 | Init.Data.Int.DivMod.Lemmas | [
"Int",
"Int.instLTInt",
"instHAdd",
"Int.add_lt_add_iff_right",
"HAdd.hAdd",
"LT.lt",
"propext",
"Int.instAdd",
"Eq"
] | false |
_private.Batteries.Linter.UnreachableTactic.0.Batteries.Linter.UnreachableTactic.ignoreTacticKindsRef._proof_1 | Batteries.Linter.UnreachableTactic | [
"Lean.NameHashSet.instInhabited",
"Lean.NameHashSet",
"ST.instNonemptyRef",
"IO.RealWorld",
"instNonemptyOfInhabited",
"Nonempty",
"ST.Ref"
] | false |
Polynomial.isIntegral_isLocalization_polynomial_quotient | Mathlib.RingTheory.Jacobson.Ring | [
"AddGroup.toSubtractionMonoid",
"Polynomial.monic_X_sub_C",
"WithBot.instPreorder",
"Ideal.Quotient.commSemiring",
"Eq.mpr",
"Polynomial.C",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"MulOne.toOne",
"Submodule.Quotient.instZeroQuotient",
"Nat.instMulZeroClass",
"Co... | true |
CategoryTheory.ExponentiableMorphism.pushforwardComp | Mathlib.CategoryTheory.LocallyCartesianClosed.ExponentiableMorphism | [
"CategoryTheory.Over",
"CategoryTheory.Functor",
"CategoryTheory.ChosenPullbacksAlong",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ExponentiableMorphism.pushforward",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.ExponentiableMorphism.... | true |
_private.Batteries.Data.PairingHeap.0.Batteries.PairingHeapImp.Heap.foldM.match_1.eq_2 | Batteries.Data.PairingHeap | [
"Batteries.PairingHeapImp.Heap.foldM.match_1",
"Option.some",
"Prod.mk",
"Option.none",
"Batteries.PairingHeapImp.Heap",
"Eq.refl",
"Prod",
"Eq",
"Option"
] | true |
Lean.Elab.Command.removeFunctorPostfix | Lean.Elab.Coinductive | [
"Lean.Name.getPrefix",
"Lean.Name",
"Lean.Name.modifyBase"
] | true |
CategoryTheory.GradedObject.mapIso_hom | Mathlib.CategoryTheory.GradedObject | [
"CategoryTheory.GradedObject.HasMap",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso",
"CategoryTheory.GradedObject.mapMap",
"CategoryTheory.GradedObject.categoryOfGradedObjects",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.GradedObject",
"Ca... | true |
Equiv.sumArrowEquivProdArrow_symm_apply_inl | Mathlib.Logic.Equiv.Prod | [
"Equiv.instEquivLike",
"Sum",
"Equiv",
"Prod.mk",
"Sum.inl",
"Equiv.symm",
"Prod",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike",
"Equiv.sumArrowEquivProdArrow"
] | true |
Lean.Meta.Grind.Arith.Cutsat.VarInfo.maxDvdCoeff | Lean.Meta.Tactic.Grind.Arith.Cutsat.ReorderVars | [
"Nat",
"Lean.Meta.Grind.Arith.Cutsat.VarInfo"
] | true |
Lean.Meta.Grind.AC.DiseqCnstr.setUnsat | Lean.Meta.Tactic.Grind.AC.Proof | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.AC.DiseqCnstr",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.Grind.AC.ProofM.State",
"_private.Lean.Meta.Tactic.Grind.AC.Proof.0.Lean.Meta.Grind.AC.withProofContext",
"instMonadLiftT",
"Lean.mkApp4",
"Lean.Meta.Sym... | true |
Std.Iterators.PostconditionT.operation_pure | Init.Data.Iterators.PostconditionMonad | [
"Pure.pure",
"Monad.toApplicative",
"Eq.rec",
"Std.Iterators.PostconditionT.Property",
"Subtype",
"Std.Iterators.PostconditionT.property_pure",
"Applicative.toPure",
"Std.Iterators.PostconditionT.operation",
"Subtype.mk",
"Std.Iterators.instMonadPostconditionT",
"Std.Iterators.PostconditionT",
... | true |
IsTopologicalAddGroup.toHSpace._proof_4 | Mathlib.Topology.Homotopy.HSpaces | [
"AddZeroClass.toAddZero",
"zero_add",
"AddZero.toZero",
"instHAdd",
"AddZeroClass",
"HAdd.hAdd",
"AddZero.toAdd",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
LocalizedModule.smulOfIsLocalization._proof_2 | Mathlib.Algebra.Module.LocalizedModule.Basic | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Iff.mpr",
"Eq.mpr",
"IsLocalization.sec",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semigroup.toMul",
"instHSMul",
"Trans.trans",
"Mathlib.Tactic.Ring.Common.mul_congr",
"Submonoid.mul",
"HMul.hMul",
"Nat.rawCast",
"IsLocalization",
"LocalizedMo... | false |
Nat.prod_Icc_factorial | Mathlib.Data.Nat.Factorial.SuperFactorial | [
"Nat.superFactorial",
"Nat.instLocallyFiniteOrder",
"Nat.brecOn",
"instOfNatNat",
"Finset.Icc",
"Finset.prod",
"Nat.prod_Icc_factorial._f",
"Nat.factorial",
"Nat.instPreorder",
"Nat",
"Nat.instCommMonoid",
"OfNat.ofNat",
"Eq"
] | true |
CategoryTheory.PreGaloisCategory.PointedGaloisObject.cocone._proof_12 | Mathlib.CategoryTheory.Galois.Prorepresentability | [
"CategoryTheory.Functor.op",
"Eq.mpr",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.coyoneda",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.PreGaloisCategory.PointedGaloisObject... | false |
Hindman.FS.below.rec | Mathlib.Combinatorics.Hindman | [
"Hindman.FS.tail'",
"Hindman.FS.cons'",
"Hindman.FS.below",
"Hindman.FS.below.head'",
"AddSemigroup",
"Stream'",
"instHAdd",
"AddSemigroup.toAdd",
"HAdd.hAdd",
"Hindman.FS.below.tail'",
"Hindman.FS",
"Stream'.tail",
"Hindman.FS.below.cons'",
"Stream'.head",
"Hindman.FS.head'"
] | false |
AntivaryOn.eq_1 | Mathlib.Order.Monotone.Monovary | [
"Preorder.toLT",
"Preorder.toLE",
"Membership.mem",
"AntivaryOn",
"LE.le",
"LT.lt",
"Eq.refl",
"Eq",
"Set.instMembership",
"Preorder",
"Set"
] | true |
Matrix.transposeᵣ.eq_1 | Mathlib.Data.Matrix.Reflection | [
"Equiv.instEquivLike",
"Matrix",
"Matrix.of",
"Equiv",
"instOfNatNat",
"Nat",
"Matrix.vecEmpty",
"Eq.refl",
"OfNat.ofNat",
"Fin",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike",
"Matrix.transposeᵣ"
] | true |
instReprExcept.match_1 | Init.Data.ToString.Basic | [
"Except.ok",
"Except.error",
"Nat",
"Except.casesOn",
"Except"
] | false |
Similar.exists_pos_dist_eq | Mathlib.Topology.MetricSpace.Similarity | [
"Real",
"HMul.hMul",
"Real.instZero",
"Similar",
"Real.instLT",
"Exists",
"And",
"PseudoMetricSpace",
"Real.instMul",
"LT.lt",
"Iff.mp",
"Zero.toOfNat0",
"Dist.dist",
"PseudoMetricSpace.toDist",
"OfNat.ofNat",
"Eq",
"similar_iff_exists_pos_dist_eq",
"instHMul",
"PseudoMetricSpace... | true |
CategoryTheory.Bicategory.InducedBicategory.Hom.noConfusion | Mathlib.CategoryTheory.Bicategory.InducedBicategory | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Bicategory.InducedBicategory.Hom.noConfusionType",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory",
"CategoryTheory.Bicategory.InducedBicategory",
"CategoryTheory.Bicategory.InducedBicategory.... | false |
CategoryTheory.CreatesColimitsOfShape.mk | Mathlib.CategoryTheory.Limits.Creates | [
"CategoryTheory.CreatesColimitsOfShape.mk",
"CategoryTheory.Functor",
"CategoryTheory.CreatesColimitsOfShape",
"CategoryTheory.CreatesColimit",
"autoParam",
"CategoryTheory.CreatesColimitsOfShape.CreatesColimit._autoParam",
"CategoryTheory.Category"
] | true |
Asymptotics.IsLittleO.sum_congr | Mathlib.Analysis.Asymptotics.Defs | [
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"Trans.trans",
"SeminormedAddCommGroup",
"Real.lattice",
"Finset.sum_cons",
"Finset.cons_induction",
"abs",
"Finset.cons",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"true_or",
"Finset",
"AddMonoid.toAddZeroClass",
... | true |
Lean.Elab.Term.MutualClosure.LetRecClosure | Lean.Elab.MutualDef | [
"Lean.Elab.Term.MutualClosure.LetRecClosure.mk"
] | true |
LinearMap.coprod_inl | Mathlib.LinearAlgebra.Prod | [
"LinearMap.coprod",
"LinearMap.inl",
"SemilinearMapClass.distribMulActionSemiHomClass",
"LinearMap.ext",
"congrArg",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"RingHom",
"AddZeroClass.toAddZero",
"map_zero",
"LinearMap.semilinearMapClass",
"Prod.mk",
"LinearMap",
"AddCommMonoid"... | true |
_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0._auto_266 | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Interval.coeHom.match_1 | Mathlib.Order.Interval.Basic | [
"Unit.unit",
"PartialOrder.toPreorder",
"Option.casesOn",
"Preorder.toLE",
"Option.some",
"PartialOrder",
"Interval",
"Option.none",
"Unit",
"NonemptyInterval"
] | false |
_private.Mathlib.Algebra.Order.GroupWithZero.Canonical.0.WithZero.map'_mono._simp_1_1 | Mathlib.Algebra.Order.GroupWithZero.Canonical | [
"WithZero.instZero",
"And",
"WithZero.forall",
"WithZero",
"WithZero.coe",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
Std.TreeSet.Equiv.of_forall_mem_iff | Std.Data.TreeSet.Lemmas | [
"Std.TreeSet",
"Membership.mem",
"Ordering",
"Std.TreeSet.inner",
"Std.TransCmp",
"Iff",
"Std.LawfulEqCmp",
"Std.TreeSet.Equiv.mk",
"Std.TreeSet.Equiv",
"Std.TreeMap.Equiv.of_forall_mem_unit_iff",
"Std.TreeSet.instMembership"
] | true |
List.Nodup.pairwise_coe | Mathlib.Data.Set.Pairwise.List | [
"_private.Mathlib.Data.Set.Pairwise.List.0.List.Nodup.pairwise_coe._simp_1_1",
"False",
"Std.Symm",
"List.Pairwise",
"congrArg",
"setOf",
"Membership.mem",
"Eq.mp",
"Insert.insert",
"Ne",
"Ne.symm",
"List.rec",
"imp_iff_right",
"List.not_mem_nil._simp_1",
"Set.Pairwise",
"ne_of_mem_of_... | true |
OpenNormalAddSubgroup.instLatticeOfSeparatelyContinuousAdd._proof_2 | Mathlib.Topology.Algebra.OpenSubgroup | [
"SemilatticeInf.inf_le_right",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"LE.le",
"SemilatticeInf.inf",
"TopologicalSpace",
"AddGroup",
"OpenNormalAddSubgroup.instSemilatticeInfOpenNormalAddSubgroup",
"OpenNormalAddSubgroup"
] | false |
TopologicalSpace.CompactOpens.instBooleanAlgebra._proof_6 | Mathlib.Topology.Sets.Compacts | [
"TopologicalSpace.CompactOpens.instGeneralizedBooleanAlgebra",
"TopologicalSpace.CompactOpens.instPartialOrder",
"TopologicalSpace.CompactOpens.instCompl",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"TopologicalSpace.CompactOpens.instHImp",
"Function.Injective.booleanAlgebra._proof_13",
"Compl.compl... | false |
Heyting.Regular.instBooleanAlgebra._proof_9 | Mathlib.Order.Heyting.Regular | [
"Lattice.toSemilatticeSup",
"Heyting.Regular.instCompl",
"Compl.compl",
"OrderBot.toBot",
"Heyting.Regular.lattice",
"PartialOrder.toPreorder",
"Heyting.Regular.instBooleanAlgebra._proof_6",
"Preorder.toLE",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"Heyting.Regular.coe_le_coe",
"Heyting.Re... | false |
Complex.UnitDisc.coe_neg._simp_1 | Mathlib.Analysis.Complex.UnitDisc.Basic | [
"NegZeroClass.toNeg",
"Complex.UnitDisc.coe_neg",
"SemigroupWithZero.toMulZeroClass",
"Complex.UnitDisc.instSemigroupWithZero",
"MulZeroClass.negZeroClass",
"Complex.UnitDisc",
"Complex.UnitDisc.coe",
"Complex",
"Eq.symm",
"Eq",
"Complex.UnitDisc.instHasDistribNeg",
"Complex.instNeg",
"Neg.n... | false |
ProperCone.mem_dual._simp_1 | Mathlib.Analysis.Convex.Cone.Dual | [
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"ClosedIciTopology",
"IsOrderedRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"ProperCone",
"ProperCone.mem_dual",
"ProperCone.instSe... | false |
SeparationQuotient.instNonUnitalNormedRing._proof_2 | Mathlib.Analysis.Normed.Ring.Lemmas | [
"Norm.norm",
"NonUnitalSeminormedRing",
"Real.instLE",
"Real",
"HMul.hMul",
"SeparationQuotient.instNormedAddCommGroup",
"NonUnitalNonAssocRing.toMul",
"SeparationQuotient.instNonUnitalRing",
"PseudoMetricSpace.toUniformSpace",
"NonUnitalRing.toNonUnitalNonAssocRing",
"inferInstance",
"insepar... | false |
_private.Mathlib.Computability.Primrec.Basic.0.Primrec.nat_div._simp_1_2 | Mathlib.Computability.Primrec.Basic | [
"Preorder.toLT",
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"Ne",
"IsBotZeroClass",
"LT.lt",
"propext",
"Zero.toOfNat0",
"zero_lt_iff",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
PseudoMetricSpace.ofPreNNDist._proof_9 | Mathlib.Topology.Metrizable.Uniformity | [
"Iff.mpr",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"List.zipWith",
"Real.instLE",
"Real",
"iInf",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"LE.le.trans_eq",
"Real.instZero",
"NNReal.coe_eq_zero",
"List.sum",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | false |
analyticOnNhd_const | Mathlib.Analysis.Analytic.Constructions | [
"NormedSpace",
"AnalyticOnNhd",
"Membership.mem",
"analyticAt_const",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Set.instMembership",
"NormedAddCommGroup",
"Set"
] | true |
_private.Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol.0.jacobiSym.eq_zero_iff_not_coprime._simp_1_5 | Mathlib.NumberTheory.LegendreSymbol.JacobiSymbol | [
"And",
"and_assoc",
"propext",
"Eq"
] | false |
_private.Mathlib.Topology.MetricSpace.Isometry.0.isometry_iff_nndist_eq._simp_1_2 | Mathlib.Topology.MetricSpace.Isometry | [
"ENNReal.ofNNReal",
"ENNReal.coe_inj",
"NNReal",
"ENNReal",
"propext",
"Eq"
] | false |
Semiring.directSumGSemiring._proof_3 | Mathlib.Algebra.DirectSum.Ring | [
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"GradedMonoid.GMonoid.toGMul",
"AddSemigroup.toAdd",
"GradedMonoid.GMonoid.mul_assoc",
"AddMonoid",
"Semiring.toMonoid",
"GradedMonoid",
"Semiring",
"GradedMonoid.GMul.toMul",
"Eq",
"Monoid.gMonoid",
"instHMul"
] | false |
LieHom.prod._proof_1 | Mathlib.Algebra.Lie.Prod | [
"LieHom",
"LieAlgebra.toModule",
"CommRing",
"LieRing.toAddCommGroup",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Bracket.bracket",
"LieHom.map_lie",
"LinearMap.toAddHom",
"Prod.mk",
"LieRingModule.toBracket",
"LieAlgebra.Prod.instLieAlgebra",
"LieRing",
"Com... | false |
ProfiniteGrp.ofProfinite._proof_1 | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic | [
"TotallyDisconnectedSpace",
"CompactSpace",
"TopCat.str",
"CompHausLike.is_compact",
"Profinite",
"TopCat.carrier",
"TopCat",
"CompHausLike.toTop"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getKeyD_inter._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 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.