name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Equiv.swap_apply_of_ne_of_ne | Mathlib.Logic.Equiv.Basic | [
"Equiv.instEquivLike",
"Equiv.swap",
"Ne",
"_private.Mathlib.Logic.Equiv.Basic.0.Equiv.swap_apply_of_ne_of_ne._proof_1_1",
"Equiv.Perm",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike",
"DecidableEq"
] | true |
FreeAddGroup.induction_on | Mathlib.GroupTheory.FreeGroup.Basic | [
"Quot.inductionOn",
"FreeAddGroup.of",
"Prod.mk",
"Bool.recOn",
"FreeAddGroup.instZero",
"FreeAddGroup.instAdd",
"List.cons",
"List",
"instHAdd",
"FreeAddGroup.Red.Step",
"HAdd.hAdd",
"List.recOn",
"Bool",
"_private.Mathlib.GroupTheory.FreeGroup.Basic.0.FreeAddGroup.instAddGroup.match_10",... | true |
StructureGroupoid.symm' | Mathlib.Geometry.Manifold.StructureGroupoid | [
"Membership.mem",
"StructureGroupoid",
"TopologicalSpace",
"StructureGroupoid.members",
"Set.instMembership",
"OpenPartialHomeomorph",
"OpenPartialHomeomorph.symm",
"Set"
] | true |
SimpleGraph.Subgraph.noConfusion | Mathlib.Combinatorics.SimpleGraph.Subgraph | [
"Symmetric",
"SimpleGraph.Subgraph",
"HEq.refl",
"SimpleGraph.Adj",
"SimpleGraph.Subgraph.symm._autoParam",
"Membership.mem",
"SimpleGraph.Subgraph.noConfusionType",
"autoParam",
"SimpleGraph.Subgraph.casesOn",
"SimpleGraph",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Eq",
"Set.instMembership",
... | false |
_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.Cpop.0.Std.Tactic.BVDecide.BVExpr.bitblast.denote_blastExtractAndExtend.go._proof_1_1 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Lemmas.Operations.Cpop | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"HMul.hMul",
"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.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Lea... | false |
Std.Internal.IO.Async.EAsync.lift | Std.Internal.Async.Basic | [
"Std.Internal.IO.Async.BaseAsync.mk",
"EIO",
"Std.Internal.IO.Async.EAsync",
"Std.Internal.IO.Async.BaseAsync.lift",
"EIO.toBaseIO",
"Except"
] | true |
BitVec.shiftLeftZeroExtend | Init.Data.BitVec.Basic | [
"BitVec.shiftLeftZeroExtend._proof_1",
"instPowNat",
"BitVec.ofNatLT",
"BitVec.shiftLeftZeroExtend._proof_2",
"HShiftLeft.hShiftLeft",
"BitVec",
"instOfNatNat",
"BitVec.toNat",
"instNatPowNat",
"instHAdd",
"HPow.hPow",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instHPow",
"instHShif... | true |
CategoryTheory.ObjectProperty.instBraidedFullSubcategoryι._proof_2 | Mathlib.CategoryTheory.Monoidal.Subcategory | [
"Eq.mpr",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ObjectProperty.ι",
"CategoryTheory.ObjectProperty.fullMonoidalSubcategory",
"CategoryTheory.MonoidalCategory",
"id",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"CategoryTheory.ObjectProperty.mon... | false |
PUnit._sizeOf_1._@.Mathlib.Util.CompileInductive.2121875758._hygCtx._hyg.7 | Mathlib.Util.CompileInductive | [
"PUnit.rec",
"instOfNatNat",
"PUnit",
"Nat",
"OfNat.ofNat"
] | false |
UInt8.toUInt64_toUInt32 | Init.Data.UInt.Lemmas | [
"UInt8.toUInt32",
"UInt64",
"UInt8.toUInt64",
"UInt32.toUInt64",
"UInt8",
"Eq",
"rfl"
] | true |
Polynomial.expand_eq_comp_X_pow | Mathlib.Algebra.Polynomial.Expand | [
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"Algebra.id",
"Polynomial",
"Monoid.toPow",
"CommSemiring",
"HPow.hPow",
"Polynomial.semiring",
"Nat",
"Semiring.toMonoid",
"instHPow",
"Polynomial.expand",
"Polynomial.X",
"Eq",
"Polynomial.comp",
... | true |
Profinite.NobelingProof.Products.instLinearOrder._aux_11 | Mathlib.Topology.Category.Profinite.Nobeling.Basic | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"List.instLinearOrder",
"Subtype",
"List.IsChain",
"LinearOrder.toMax",
"Subtype.mk",
"GT.gt",
"List",
"Max.max",
"Subtype.instLinearOrder._proof_6",
"Subtype.val",
"... | false |
_private.Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic.0.AlgebraicGeometry.Proj.awayι_toSpecZero._simp_1_6 | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic | [
"CategoryTheory.Iso.comp_inv_eq",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Iso.hom",
"Eq",
"CategoryTheory.Iso.inv",
"CategoryTheory.Category"
] | false |
CategoryTheory.PrelaxFunctor.mkOfHomFunctors._proof_2 | Mathlib.CategoryTheory.Bicategory.Functor.Prelax | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Functor.map",
"CategoryTheory.Bicategory",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Functor.map_comp",
"CategoryTheory.Category.toCategoryStruc... | false |
CategoryTheory.Pretriangulated.Triangle.obj₃ | Mathlib.CategoryTheory.Triangulated.Basic | [
"Int",
"Int.instAddMonoid",
"CategoryTheory.Pretriangulated.Triangle",
"CategoryTheory.HasShift",
"CategoryTheory.Category"
] | true |
LSeriesHasSum_one | Mathlib.NumberTheory.LSeries.Dirichlet | [
"Iff.mpr",
"Real",
"riemannZeta",
"Real.instLT",
"Eq.rec",
"LSeriesHasSum",
"LSeriesSummable.LSeriesHasSum",
"LSeries",
"LSeries_one_eq_riemannZeta",
"Complex.re",
"Real.instOne",
"LSeriesSummable_one_iff",
"Pi.instOne",
"Nat",
"LT.lt",
"One.toOfNat1",
"Complex",
"OfNat.ofNat",
"... | true |
Array.unattach_append | Init.Data.Array.Attach | [
"List.unattach",
"Array.instAppend",
"congrArg",
"List.unattach_toArray",
"Array.casesOn",
"Subtype",
"List.append_toArray",
"List.unattach_append",
"List.toArray",
"Array",
"instHAppendOfAppend",
"List",
"congr",
"True",
"eq_self",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"List.inst... | true |
_private.Mathlib.NumberTheory.DiophantineApproximation.Basic.0.Real.aux₃._simp_1_1 | Mathlib.NumberTheory.DiophantineApproximation.Basic | [
"False",
"eq_false",
"instOfNatNat",
"two_ne_zero",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
parallelepiped | Mathlib.MeasureTheory.Measure.Haar.OfBasis | [
"Real",
"instHSMul",
"Pi.preorder",
"Finset.univ",
"Real.instZero",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Real.semiring",
"DistribSMul.toSMulZeroClass",
"Pi.instZer... | true |
IsCusp.mono | Mathlib.NumberTheory.ModularForms.Cusps | [
"OnePoint.instGLAction",
"_private.Mathlib.NumberTheory.ModularForms.Cusps.0.IsCusp.mono.match_1_1",
"Real",
"instHSMul",
"Matrix.GeneralLinearGroup.IsParabolic",
"Matrix",
"PartialOrder.toPreorder",
"instDecidableEqFin",
"Preorder.toLE",
"Membership.mem",
"Real.semiring",
"Subgroup",
"IsCus... | true |
PowerSeries.constantCoeff_subst_eq_zero | Mathlib.RingTheory.PowerSeries.Substitution | [
"CommRing",
"CommSemiring.toSemiring",
"PowerSeries.HasSubst",
"Algebra",
"MvPowerSeries",
"RingHom",
"MvPowerSeries.constantCoeff",
"PowerSeries.subst",
"MvPowerSeries.subst",
"PowerSeries.constantCoeff",
"PowerSeries.hasSubst_iff",
"MvPowerSeries.instSemiring",
"Unit",
"CommRing.toCommSe... | true |
_private.Mathlib.Algebra.Lie.Submodule.0.LieSubmodule.sSup_image_lieSpan_singleton._simp_1_2 | Mathlib.Algebra.Lie.Submodule | [
"SetLike",
"Membership.mem",
"SetLike.coe",
"SetLike.mem_coe",
"propext",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"Set"
] | false |
_private.Init.Data.Array.Lemmas.0.Array.filter_eq_append_iff._simp_1_1 | Init.Data.Array.Lemmas | [
"Exists",
"instHAppendOfAppend",
"List",
"And",
"List.filter",
"List.filter_eq_append_iff",
"propext",
"Bool",
"List.instAppend",
"Eq",
"HAppend.hAppend"
] | false |
_private.Init.Data.Stream.0.Std.Stream.forIn.visit._unsafe_rec | Init.Data.Stream | [
"Pure.pure",
"Monad.toApplicative",
"Std.Stream.next?",
"Applicative.toPure",
"ForInStep",
"Unit",
"_private.Init.Data.Stream.0.Std.Stream.forIn.visit.match_3",
"_private.Init.Data.Stream.0.Std.Stream.forIn.visit.match_1",
"Monad.toBind",
"_private.Init.Data.Stream.0.Std.Stream.forIn.visit._unsafe... | false |
Lean.Meta.Grind.Arith.Cutsat.ToIntInfo.upperThm? | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToIntInfo | [
"Lean.Meta.Grind.Arith.Cutsat.ToIntInfo",
"Lean.Expr",
"Option"
] | true |
spectralValueTerms_of_natDegree_le | Mathlib.Analysis.Normed.Unbundled.SpectralNorm | [
"Iff.mpr",
"Norm.norm",
"SeminormedRing.toNorm",
"Real.instPow",
"Real",
"Preorder.toLT",
"instHDiv",
"Real.instZero",
"congrArg",
"Real.instDivInvMonoid",
"Real.instSub",
"PartialOrder.toPreorder",
"spectralValueTerms",
"HSub.hSub",
"Decidable",
"Preorder.toLE",
"SeminormedRing.toRi... | true |
Lean.Meta.inferTypeImp | Lean.Meta.InferType | [
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.State",
"Lean.instMonadRecDepthStateRefT'OfMonad",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.MonadQuotation.toMonadRef",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"StateRefT'.instMonadFunctor",
... | true |
FGModuleRepr.instAddCommGroupRepr._aux_1 | Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall | [
"Pi.Function.module",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"Submodule.Quotient.addMonoid._aux_1",
"CommSemiring.toSemiring",
"FGModuleRepr",
"FGModuleRepr.S",
"FGModuleRepr.n",
"NonUnitalNonAssocRing.toNonUnitalNonAssoc... | false |
Bool.bne_false | Init.Data.Bool | [
"bne",
"Bool.instDecidableForallOfDecidablePred",
"of_decide_eq_true",
"id",
"instDecidableEqBool",
"instBEqOfDecidableEq",
"Bool.true",
"Bool",
"Eq.refl",
"Bool.false",
"Decidable.decide",
"Eq"
] | true |
CategoryTheory.Functor.CoconeTypes.IsColimitCore.mk.injEq | Mathlib.CategoryTheory.Limits.Types.ColimitType | [
"CategoryTheory.Functor",
"Eq.propIntro",
"CategoryTheory.Functor.CoconeTypes.IsColimitCore",
"Function.comp",
"CategoryTheory.Functor.CoconeTypes.ι",
"CategoryTheory.Functor.CoconeTypes.pt",
"autoParam",
"CategoryTheory.Functor.CoconeTypes.IsColimitCore.mk.inj",
"CategoryTheory.Functor.CoconeTypes.... | true |
NormedGroup | Mathlib.Analysis.Normed.Group.Defs | [
"NormedGroup.mk"
] | true |
WithTop.conditionallyCompleteLattice | Mathlib.Order.ConditionallyCompleteLattice.Basic | [
"WithTop.instInfSet",
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"ConditionallyCompleteLattice",
"Preorder.toLE",
"WithTop.instSupSet",
"BddAbove",
"Set.Nonempty",
"WithTop.lattice",
"ConditionallyCompleteLattice.mk",
"BddBelow",
"WithTop.isGLB_sInf'",
"ConditionallyCompleteParti... | true |
Std.DHashMap.Internal.Raw₀.fold_eq_foldl_toArray | Std.Data.DHashMap.Internal.RawLemmas | [
"congrArg",
"Std.DHashMap.Raw",
"Std.DHashMap.Internal.Raw₀.fold_eq_foldl_toList",
"Std.DHashMap.Raw.toList",
"Std.DHashMap.Raw.fold",
"Sigma.fst",
"instOfNatNat",
"List.foldl",
"List.toArray",
"Array.foldl",
"Array",
"List.size_toArray",
"Std.DHashMap.Raw.toArray",
"Nat",
"congr",
"St... | true |
_private.Mathlib.GroupTheory.Perm.Sign.0.Equiv.Perm.signAux_inv.match_1_1 | Mathlib.GroupTheory.Perm.Sign | [
"Finset",
"Membership.mem",
"Finset.instSetLike",
"Nat",
"Sigma.mk",
"Sigma.casesOn",
"Equiv.Perm.finPairsLT",
"Fin",
"SetLike.instMembership",
"Sigma"
] | false |
Lean.Elab.instToFormatModifiers._sparseCasesOn_5 | Lean.Elab.DeclModifiers | [
"Nat.ne_of_beq_eq_false",
"Lean.Elab.RecKind.partial",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Elab.RecKind",
"Nat.land",
"Lean.Elab.RecKind.default",
"Nat",
"Bool",
"Eq.refl",
"Lean.Elab.RecKind.rec",
"Lean.Elab.RecKind.nonrec",
"OfNat.ofNat",
"Bool.false",
"Lean.Elab... | false |
_private.Mathlib.NumberTheory.Chebyshev.0.Chebyshev.psi_eq_sum_mul_log_prime._proof_1_16 | Mathlib.NumberTheory.Chebyshev | [
"Lean.RArray.leaf",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Lean.Grind.not_not",
"Lean.Grind.iff_eq",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Finset",
"Classical.byContradiction",
"Preorder.toLE",
"Nat.instLocallyFiniteOrder",
"Membership.mem",
"Finset.mem_Icc",
"Eq.mp",... | false |
Filter.mem_prod_iff_right | Mathlib.Order.Filter.Prod | [
"Filter.instMembership",
"Eq.mpr",
"SProd.sprod",
"congrArg",
"Filter.map",
"Filter.Eventually",
"Iff.rfl",
"Membership.mem",
"Exists",
"id",
"Prod.mk",
"Filter.prod_comm",
"And",
"Iff",
"Set.preimage",
"propext",
"Prod.swap",
"Filter.mem_prod_iff_left",
"Prod",
"Filter.instSPr... | true |
Multiset.Ioc_self | Mathlib.Order.Interval.Multiset | [
"Eq.mpr",
"congrArg",
"Finset",
"Multiset",
"id",
"Finset.Ioc_self",
"Finset.val",
"Finset.instEmptyCollection",
"LocallyFiniteOrder",
"Zero.toOfNat0",
"Eq.refl",
"Finset.empty_val",
"Multiset.Ioc",
"EmptyCollection.emptyCollection",
"OfNat.ofNat",
"Eq",
"Multiset.Ioc.eq_1",
"Preor... | true |
homeomorphSphereProd._proof_11 | Mathlib.Analysis.Normed.Module.Ball.RadialEquiv | [
"Continuous.comp'",
"Real",
"Metric.ne_of_mem_sphere",
"Set.Ioi",
"instHSMul",
"Preorder.toLT",
"Continuous",
"NormedSpace.toIsBoundedSMul",
"Membership.mem.out",
"NormedSpace",
"continuous_subtype_val",
"Real.instZero",
"instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors",
"DistribMulAction.... | false |
Std.Time.Internal.UnitVal.ediv | Std.Time.Internal.UnitVal | [
"Int.cast",
"Rat.instMul",
"HMul.hMul",
"Std.Time.Internal.UnitVal.ofInt",
"Rat",
"Std.Time.Internal.UnitVal",
"Rat.instIntCast",
"Int",
"Std.Time.Internal.UnitVal.val",
"Int.ediv",
"instHMul"
] | true |
_private.Lean.Elab.PreDefinition.Eqns.0.Lean.Elab.Eqns.splitMatch?.go | Lean.Elab.PreDefinition.Eqns | [
"Inhabited.default",
"Lean.MVarId",
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.ExprSet",
"Array",
"List",
"Lean.Meta.instInhabitedMetaM",
"Lean.Name",
"Option"
] | true |
_private.Mathlib.Topology.MetricSpace.Bounded.0.Mathlib.Meta.Positivity.evalDiam._sparseCasesOn_1 | Mathlib.Topology.MetricSpace.Bounded | [
"Lean.Level.ctorIdx",
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Lean.Level.mvar",
"Lean.Level.param",
"Nat.hasNotBit",
"Lean.Level.imax",
"instOfNatNat",
"Lean.Level",
"Nat.land",
"Lean.Level.zero",
"Nat",
"Bool",
"Lean.Level.rec",
"Lean.Name",
"Eq.refl",
"Lean.Level.succ",
"OfN... | false |
isLocalHom_equiv | Mathlib.Algebra.Group.Units.Equiv | [
"Monoid",
"Monoid.toMulOneClass",
"IsUnit",
"IsLocalHom.mk",
"MulOne.toMul",
"imp_self._simp_1",
"MulEquivClass",
"MulOneClass.toMulOne",
"EquivLike",
"implies_congr",
"True",
"MulEquiv.isUnit_map._simp_2",
"of_eq_true",
"IsLocalHom",
"Eq.refl",
"implies_true",
"DFunLike.coe",
"Eq.... | true |
Born.instConcreteCategoryLocallyBoundedMapCarrier._proof_2 | Mathlib.Topology.Category.Born | [
"Born",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"id",
"Born.instLargeCategory",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"Eq"
] | false |
Circle.instSMulCommClass_left | Mathlib.Analysis.Complex.Circle | [
"_private.Mathlib.Analysis.Complex.Circle.0.Circle.instSMulCommClass_left._proof_1",
"SMul",
"Circle",
"Complex",
"Circle.instSMul",
"SMulCommClass"
] | true |
Std.TreeMap.distinct_keys_toList | Std.Data.TreeMap.Lemmas | [
"List.Pairwise",
"Std.TreeMap.inner",
"Ordering",
"Ordering.eq",
"Std.DTreeMap.Const.distinct_keys_toList",
"Std.TransCmp",
"Prod.fst",
"Prod",
"Eq",
"Not",
"Std.TreeMap",
"Std.TreeMap.toList"
] | true |
ProjectiveSpectrum.union_zeroLocus | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Topology | [
"SetLike",
"Eq.mpr",
"CommRing",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"Nat.instAddMonoid",
"AddSubmonoidClass",
"Set.instUnion",
"id",
"Ideal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"CommRing.... | true |
CategoryTheory.AddMod.id.eq_1 | Mathlib.CategoryTheory.Monoidal.Mod | [
"CategoryTheory.AddMod.id._proof_1",
"CategoryTheory.AddMod.id",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.AddMod",
"CategoryTheory.MonoidalCategory.MonoidalLeftAction",
"CategoryTheory.AddMonObj",
"CategoryTheory.AddMod.Hom",
"Eq.refl",
"CategoryTheory... | true |
CategoryTheory.MorphismProperty.RightFraction.cases | Mathlib.CategoryTheory.Localization.CalculusOfFractions | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.MorphismProperty.RightFraction.mk",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.RightFraction",
"Exists",
"CategoryTheory.MorphismProperty.RightFraction.f",
"CategoryTheory.MorphismProperty.RightFraction.X'... | true |
_private.Mathlib.Algebra.Central.End.0.LinearEquiv.conjAlgEquiv_ext_iff._simp_1_3 | Mathlib.Algebra.Central.End | [
"LinearMap.comp_assoc",
"RingHom",
"RingHomCompTriple",
"LinearMap",
"AddCommMonoid",
"LinearMap.comp",
"Semiring",
"Module",
"Eq.symm",
"Semiring.toNonAssocSemiring",
"Eq"
] | false |
CategoryTheory.Comon.instMonoidalForget._proof_6 | Mathlib.CategoryTheory.Monoidal.Comon_ | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Mon.Hom.hom",
"Quiver.Hom.unop",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Comon.MonOpOpToComonObj",
"... | false |
CategoryTheory.CountableAB4.mk._flat_ctor | Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic | [
"CategoryTheory.HasExactColimitsOfShape",
"CategoryTheory.Limits.instHasCoproductsOfShapeOfHasCountableCoproductsOfCountable",
"CategoryTheory.Limits.HasCountableCoproducts",
"CategoryTheory.discreteCategory",
"CategoryTheory.CountableAB4",
"Countable",
"CategoryTheory.CountableAB4.mk",
"CategoryTheor... | false |
Lean.Lsp.CodeActionContext._sizeOf_inst | Lean.Data.Lsp.CodeActions | [
"SizeOf.mk",
"Lean.Lsp.CodeActionContext._sizeOf_1",
"SizeOf",
"Lean.Lsp.CodeActionContext"
] | false |
Lean.Parser.Command.mixfix._regBuiltin.Lean.Parser.Command.namedName.parenthesizer_67 | Lean.Parser.Syntax | [
"Lean.Name.mkStr5",
"Lean.Parser.Command.namedName.parenthesizer",
"IO",
"Lean.PrettyPrinter.Parenthesizer",
"Lean.PrettyPrinter.parenthesizerAttribute",
"Unit",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
MeasureTheory.Submartingale.sum_smul_sub | Mathlib.Probability.Martingale.Basic | [
"MeasureTheory.ae",
"NormedCommRing.toNormedRing",
"Real.instIsOrderedRing",
"Norm.norm",
"Eq.mpr",
"IsOrderedModule.toPosSMulMono",
"le_refl",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHSMul",
"smul_le_smul_of_nonneg_right",
"MeasureTheory.Measure",
"CompleteSpace",
"Pi.addCommMo... | true |
PiTensorProduct.instSemiring._proof_4 | Mathlib.RingTheory.PiTensorProduct | [
"instSMulOfMul",
"IsScalarTower.right",
"IsScalarTower",
"Algebra",
"Algebra.toSMul",
"instDistribOfSemiring",
"CommSemiring",
"Distrib.toMul",
"Semiring"
] | false |
Equiv.prodShear._proof_4 | Mathlib.Logic.Equiv.Prod | [
"Equiv.instEquivLike",
"Equiv",
"Prod.mk",
"Prod.fst",
"Function.RightInverse",
"Equiv.symm",
"Prod",
"Prod.snd",
"DFunLike.coe",
"_private.Mathlib.Logic.Equiv.Prod.0.Equiv.prodShear._proof_3",
"EquivLike.toFunLike"
] | false |
CategoryTheory.ShortComplex.SnakeInput.exact_C₂_up | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.SnakeInput.L₂",
"CategoryTheory.ShortComplex.SnakeInput.L₀",
"CategoryTheory.ShortComplex.mk",
"CategoryTheory.ShortComplex.SnakeInput",
"CategoryTheory.Abelian",
"CategoryTheory.ShortComplex.SnakeInput.v₀₁",
"CategoryTheory.ShortCom... | true |
FormalMultilinearSeries.rightInv._proof_21 | Mathlib.Analysis.Analytic.Inverse | [
"AddMonoid.toAddSemigroup",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"AddSemigroup.toAdd",
"ContinuousMultilinearMap.instAddCommGroup._proof_7",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"AddGroup.toSubNegMonoid",
"SeminormedAddCommGroup.toAddCommGroup",
"SubNegMonoid.toAdd... | false |
Aesop.Rule.map | Aesop.Rule.Basic | [
"Aesop.Rule.name",
"Aesop.Rule",
"Aesop.Rule.pattern?",
"Aesop.Rule.tac",
"Aesop.Rule.extra",
"Aesop.Rule.mk",
"Aesop.Rule.indexingMode"
] | true |
Set.subset_compl_iff_disjoint_left | Mathlib.Order.BooleanAlgebra.Set | [
"Compl.compl",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"BiheytingAlgebra.toHeytingAlgebra",
"HasSubset.Subset",
"BiheytingAlgebra.toCoheytingAlgebra",
"Set.instCompl",
"BooleanAlgebra.toBiheytingAlgebra",
"Iff",
"Set.instBooleanAlgebra",
"le_compl_iff_disjoint_left",
"CoheytingAlgebra.toG... | true |
Polynomial.coeToPowerSeries | Mathlib.RingTheory.PowerSeries.Basic | [
"Coe.mk",
"Polynomial",
"Polynomial.toPowerSeries",
"Semiring",
"PowerSeries",
"Coe"
] | true |
Mathlib.Tactic.Qify.nnratCast_le._simp_1 | Mathlib.Data.NNRat.Defs | [
"Mathlib.Tactic.Qify.nnratCast_le",
"Rat",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"NNRat",
"LE.le",
"Rat.instLE",
"Rat.instNNRatCast",
"propext",
"NNRat.cast",
"Eq",
"instDistribLatticeOfLinearOrder",
"instLinearOrderNNRat... | false |
_private.Lean.Meta.Tactic.Grind.Arith.Cutsat.ToInt.0.Lean.Meta.Grind.Arith.Cutsat.toInt' | Lean.Meta.Tactic.Grind.Arith.Cutsat.ToInt | [
"Inhabited.default",
"Lean.Meta.Grind.Arith.Cutsat.ToIntM.Context",
"Lean.Meta.Grind.Arith.Cutsat.ToIntM",
"Lean.Meta.Grind.instInhabitedGoalM",
"Lean.Expr",
"instInhabitedReaderT",
"Prod",
"Lean.Meta.Grind.GoalM"
] | true |
fderivWithin_continuousAlternatingMap_apply_const_apply | Mathlib.Analysis.Calculus.FDeriv.CompCLM | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"ContinuousAlternatingMap.instAddCommGroup._proof_7",
"Fintype.ofFinite",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"ContinuousLinearMap.flipAlternating",
"NormedSpace... | true |
CategoryTheory.Limits.HasColimitsOfShape | Mathlib.CategoryTheory.Limits.HasLimits | [
"CategoryTheory.Limits.HasColimitsOfShape.mk",
"CategoryTheory.Category"
] | true |
CharP.natCast_injOn_Iio | Mathlib.Algebra.CharP.Basic | [
"IsRightCancelAdd",
"AddMonoid.toAddSemigroup",
"Membership.mem",
"AddMonoidWithOne.toNatCast",
"Nat.cast",
"Nat.ModEq.eq_of_lt_of_lt",
"AddSemigroup.toAdd",
"CharP.natCast_eq_natCast",
"Nat.ModEq",
"Nat.instPreorder",
"Nat",
"Iff.mp",
"CharP",
"AddMonoidWithOne.toAddMonoid",
"Set.InjOn"... | true |
_private.Mathlib.Algebra.Group.Pointwise.Finset.Basic.0.Finset.Nonempty.pow.match_1_1 | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
CategoryTheory.Limits.BinaryBicone.toBiconeFunctor._proof_5 | Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | [
"CategoryTheory.Limits.Bicone.mk",
"CategoryTheory.Limits.BinaryBicone.fst",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.BinaryBicone.category",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.BinaryBiconeMorphism.winr",
"CategoryTheory.Limits.Binary... | false |
AddMonCat.hasForgetToAddSemigroup | Mathlib.Algebra.Category.MonCat.Adjunctions | [
"AddMonCat.instConcreteCategoryAddMonoidHomCarrier",
"CategoryTheory.HasForget₂.mk",
"AddMonoid.toAddSemigroup",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddMonoidHom.toAddHom",
"AddSemigrp.str",
"AddHom",
"CategoryTheory.Functor.mk",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toA... | true |
CauSeq.coe_sup._simp_1 | Mathlib.Algebra.Order.CauSeq.Basic | [
"Lattice.toSemilatticeSup",
"AddGroupWithOne.toAddGroup",
"abs",
"LinearOrder",
"CauSeq.coe_sup",
"IsStrictOrderedRing",
"Field.toDivisionRing",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"DivisionRing.toRing",
"Field.toSemifield",
"Semifield.toDivis... | false |
Real.arsinh_surjective | Mathlib.Analysis.SpecialFunctions.Arsinh | [
"Real",
"Real.arsinh",
"Real.sinhEquiv",
"Equiv.surjective",
"Equiv.symm",
"Function.Surjective"
] | true |
_private.Mathlib.Tactic.Linter.HaveLetLinter.0.Mathlib.Linter.haveLet.toFormat_propTypes | Mathlib.Tactic.Linter.HaveLetLinter | [
"Pure.pure",
"Lean.Meta.ppExpr",
"Lean.instantiateMVars",
"_private.Mathlib.Tactic.Linter.HaveLetLinter.0.Mathlib.Linter.haveLet.toFormat_propTypes.match_1",
"ReaderT",
"Lean.Meta.State",
"Array.filterMapM",
"Option.some",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"EIO",
"instDecidable... | true |
Subgroup.index_eq_zero_of_relIndex_eq_zero | Mathlib.GroupTheory.Index | [
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"Subgroup",
"instOfNatNat",
"Subgroup.relIndex",
"le_top",
"Nat",
"BoundedOrder.toOrderTop",
"Subgroup.index",
"Subgroup.instPartialOrder",
"Subgroup.instCompleteLattice",
"Subgroup.instTop",
"Top.top"... | true |
Mathlib.Meta.Positivity.ite_ne_zero_of_pos_of_ne_zero | Mathlib.Tactic.Positivity.Basic | [
"Preorder.toLT",
"Decidable",
"Ne",
"LT.lt.ne'",
"LT.lt",
"Mathlib.Meta.Positivity.ite_ne_zero",
"Zero.toOfNat0",
"OfNat.ofNat",
"Preorder",
"Zero",
"ite"
] | true |
AddGroupExtension.mk.sizeOf_spec | Mathlib.GroupTheory.GroupExtension.Defs | [
"AddMonoidHom._sizeOf_inst",
"AddGroupExtension",
"AddMonoid.toAddZeroClass",
"instSizeOfDefault",
"AddMonoidHom.range",
"AddZeroClass.toAddZero",
"AddGroupExtension.mk",
"instOfNatNat",
"AddGroupExtension._sizeOf_inst",
"AddSubgroup",
"instHAdd",
"AddGroup",
"AddGroup.toSubNegMonoid",
"HA... | true |
Lean.Elab.Term.LVal.ctorElim | Lean.Elab.Term.TermElabM | [
"String",
"Lean.Elab.Term.LVal",
"Lean.Syntax",
"Lean.Elab.Term.LVal.fieldIdx",
"Nat",
"Eq.ndrec",
"Lean.Name",
"Lean.Elab.Term.LVal.casesOn",
"PULift.down",
"Eq",
"Lean.Elab.Term.LVal.ctorElimType",
"Lean.Elab.Term.LVal.ctorIdx",
"Option",
"Lean.Elab.Term.LVal.fieldName"
] | false |
_private.Mathlib.Data.Set.Finite.Powerset.0.Set.Finite.finite_subsets._simp_1_1 | Mathlib.Data.Set.Finite.Powerset | [
"Finset",
"Set.Finite",
"HasSubset.Subset",
"Set.Finite.subset_toFinset",
"SetLike.coe",
"Finset.instSetLike",
"Set.Finite.toFinset",
"propext",
"Finset.instHasSubset",
"Eq",
"Set.instHasSubset",
"Set"
] | false |
semicontinuousWithinAt_univ_iff | Mathlib.Topology.Semicontinuity.Defs | [
"nhdsWithin_univ",
"congrArg",
"Set.univ",
"nhdsWithin",
"Filter.Eventually",
"nhds",
"iff_self",
"TopologicalSpace",
"Iff",
"implies_congr",
"True",
"of_eq_true",
"Eq.refl",
"congrFun'",
"SemicontinuousAt",
"Filter",
"Eq.trans",
"SemicontinuousWithinAt",
"forall_congr"
] | true |
_private.Mathlib.Algebra.Module.LocalizedModule.Basic.0.IsLocalizedModule.of_restrictScalars._simp_1_2 | Mathlib.Algebra.Module.LocalizedModule.Basic | [
"Module.End.instMonoid",
"LinearMap.instFunLike",
"IsUnit",
"Module.End.isUnit_iff",
"AddCommMonoid",
"propext",
"Function.Bijective",
"Semiring",
"Module.End",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe"
] | false |
AddSubmonoid.LocalizationMap.map_spec | Mathlib.GroupTheory.MonoidLocalization.Maps | [
"AddSubmonoid.LocalizationMap.map",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddSubmonoid.LocalizationMap",
"AddZeroClass.toAddZero",
"Subtype",
"AddSubmonoid.LocalizationMap.instFunLike",
"AddSubmonoid",
"AddSubmonoid.LocalizationMap.toAddMonoidHom",
"Prod.fst",
"AddCommMonoid",
"Subtyp... | true |
CategoryTheory.Functor.representableByUliftFunctorEquiv._proof_2 | Mathlib.CategoryTheory.Yoneda | [
"CategoryTheory.Functor",
"Function.LeftInverse",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"Equiv.trans",
"Quiver.Hom.op",
"ULift",
"CategoryTheory.Functor.comp",
"TypeCat.instFunLikeFun",
... | false |
AlgEquiv.mk.sizeOf_spec | Mathlib.Algebra.Algebra.Equiv | [
"HMul.hMul",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"AlgEquiv._sizeOf_inst",
"Algebra",
"RingHom",
"Equiv",
"Distrib.toAdd",
"instOfNatNat",
"Equiv.toFun",
"AlgEquiv.mk",
"instDistribOfSemiring",
"CommSemiring",
"instHAdd",
"RingHom.instFunLike",
"Distrib.toMul",
"AlgEquiv"... | true |
OrthonormalBasis.equiv_self_rfl | Mathlib.Analysis.InnerProductSpace.PiL2 | [
"LinearIsometryEquiv.instEquivLike",
"InnerProductSpace.toNormedSpace",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"LinearIsometryEquiv.refl",
"NormedSpace.toModule",
"Module.Basis.ext_linearIsometryEquiv",
"NormedField.toField",
"OrthonormalBasis.equiv",
"Module.Basis.instFunLike",
"Field.toSe... | true |
Lean.Lsp.SemanticTokenType.typeParameter.sizeOf_spec | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SemanticTokenType.typeParameter",
"Lean.Lsp.SemanticTokenType",
"instOfNatNat",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Lean.Lsp.SemanticTokenType._sizeOf_inst"
] | true |
_private.Mathlib.Algebra.Order.Star.Basic.0.StarOrderedRing.of_nonneg_iff._simp_1_1 | Mathlib.Algebra.Order.Star.Basic | [
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"SubNegMonoid.toSub",
"instHAdd",
"instHSub",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"propext",
"AddZero.toAdd",
"SubNegMonoid.toAddMonoid",
"Eq.symm",
"Eq",
"sub_eq_iff_eq_ad... | false |
Module.Basis.eval_range | Mathlib.LinearAlgebra.Dual.Basis | [
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Finite",
"Submodule.map_top",
"AddMonoid.toAddZeroClass",
"Module.Basis.toDual",
"LinearMap.range_comp",
"Classical.propDecidable",
"AddZeroClass.t... | true |
ProbabilityTheory.IsKolmogorovProcess.casesOn | Mathlib.Probability.Process.Kolmogorov | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Real",
"ENNReal.ofNNReal",
"MeasureTheory.Measure",
"HMul.hMul",
"Real.instZero",
"CommSemiring.toSemiring",
"ENNReal.instPowReal",
"Measurable",
"instTopologicalSpaceProd",
"Real.instLT",
"ProbabilityTheory.IsKolmogorovProcess",
"borel",
"Pr... | false |
CompleteLattice.ωScottContinuous.iSup | Mathlib.Order.BourbakiWitt | [
"ChainCompletePartialOrder.instOfCompleteLattice",
"congrArg",
"iSup",
"PartialOrder.toPreorder",
"Monotone",
"eq_of_forall_ge_iff",
"Preorder.toLE",
"forall_comm",
"iSup_le_iff._simp_2",
"OmegaCompletePartialOrder.ωScottContinuous.map_ωSup",
"LE.le",
"ChainCompletePartialOrder.instOmegaComple... | true |
_private.Std.Do.PostCond.0.Std.Do.PostShape.args.match_1.eq_1 | Std.Do.PostCond | [
"Unit.unit",
"Std.Do.PostShape.except",
"Std.Do.PostShape.args.match_1",
"Std.Do.PostShape.arg",
"Std.Do.PostShape",
"Std.Do.PostShape.pure",
"Unit",
"Eq.refl",
"Eq"
] | true |
NzsNum.ctorElimType | Mathlib.Data.Num.Bitwise | [
"cond",
"Nat.ble",
"PULift",
"NzsNum.msb",
"Nat",
"NzsNum.bit",
"Bool",
"NzsNum"
] | false |
WellOrder.rec | Mathlib.SetTheory.Ordinal.Basic | [
"IsWellOrder",
"WellOrder.mk",
"WellOrder"
] | false |
_private.Init.Data.UInt.Bitwise.0.USize.and_le_left._simp_1_1 | Init.Data.UInt.Bitwise | [
"instLEUSize",
"USize.le_iff_toNat_le",
"LE.le",
"instLENat",
"USize.toNat",
"Nat",
"propext",
"Eq",
"USize"
] | false |
CategoryTheory.obj_μ_inv_app | Mathlib.CategoryTheory.Monoidal.End | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.μ_δ_app_assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.Monoidal.map_associator",
"CategoryTheory.MonoidalCa... | true |
_private.Mathlib.Algebra.Lie.Normalizer.0.LieSubmodule.normalizer_inf._simp_1_1 | Mathlib.Algebra.Lie.Normalizer | [
"And",
"propext",
"Eq.symm",
"Eq",
"forall_and"
] | false |
PartOrd.Hom.ctorIdx | Mathlib.Order.Category.PartOrd | [
"PartOrd.Hom",
"Nat",
"PartOrd"
] | false |
_private.Mathlib.RingTheory.QuasiFinite.Weakly.0.Algebra.WeaklyQuasiFiniteAt.of_algHom_localization._simp_1_1 | Mathlib.RingTheory.QuasiFinite.Weakly | [
"CommSemiring.toSemiring",
"IsUnit",
"Algebra",
"Membership.mem",
"Subtype",
"Ideal",
"MulZeroOneClass.toMulOneClass",
"instMulZeroOneClassOfSemiring",
"CommSemiring",
"IsLocalization.mk'",
"IsLocalization.AtPrime",
"Ideal.IsPrime",
"Semiring.toMonoid",
"propext",
"IsLocalization.AtPrime... | false |
Lean.Server.LoadedILean._sizeOf_inst | Lean.Server.References | [
"SizeOf.mk",
"Lean.Server.LoadedILean._sizeOf_1",
"Lean.Server.LoadedILean",
"SizeOf"
] | false |
Matrix.det_one_add_X_smul | Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff | [
"add_mul",
"Eq.mpr",
"Polynomial.C",
"Polynomial.eval",
"Matrix.smul",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Polynomial.instOne",
"Semigroup.toMul",
"eval_det_add_X_smul",
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Matrix.add",
"instSMulOfMul",
"Poly... | true |
Lean.MVarId.setTag | Lean.Meta.Tactic.Util | [
"Lean.Meta.State.mk",
"Lean.Core.instMonadLiftIOCoreM",
"IO.instMonadLiftSTRealWorldBaseIO",
"modify",
"Lean.Meta.State.mctx",
"Lean.Meta.State",
"instMonadLiftT",
"Lean.MetavarContext.setMVarUserName",
"IO",
"StateRefT'.instMonadStateOfOfMonadLiftTST",
"Lean.MVarId",
"Lean.Meta.MetaM",
"IO.... | true |
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