name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
String.toList.eq_1 | Init.Data.String.Basic | [
"String",
"Array.toList",
"List",
"String.toList",
"Eq.refl",
"Char",
"Eq",
"String.Internal.toArray"
] | true |
SchwartzMap.evalCLM._proof_3 | Mathlib.Analysis.Distribution.SchwartzSpace.Basic | [
"ContinuousLinearMap.toNormedSpace._proof_1",
"NormedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"NormedField.toField",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"... | false |
CoxeterMatrix.ext | Mathlib.GroupTheory.Coxeter.Matrix | [
"Matrix",
"HEq.refl",
"CoxeterMatrix.M",
"Eq.casesOn",
"CoxeterMatrix.diagonal._autoParam",
"Ne",
"instOfNatNat",
"CoxeterMatrix",
"autoParam",
"CoxeterMatrix.off_diagonal._autoParam",
"CoxeterMatrix.isSymm._autoParam",
"Nat",
"_private.Mathlib.GroupTheory.Coxeter.Matrix.0.CoxeterMatrix.ext.... | true |
Invertible.mulRight | Mathlib.Algebra.Group.Invertible.Basic | [
"Monoid",
"invertibleOfMulInvertible",
"MulOne.toOne",
"HMul.hMul",
"Monoid.toMulOneClass",
"Equiv.mk",
"Equiv",
"MulOne.toMul",
"invertibleMul",
"Invertible.mulRight._proof_2",
"MulOneClass.toMulOne",
"Invertible",
"Invertible.mulRight._proof_1",
"instHMul"
] | true |
Multiset.right_notMem_Ioo | Mathlib.Order.Interval.Multiset | [
"Finset.right_notMem_Ioo",
"Membership.mem",
"Multiset",
"Multiset.Ioo",
"Multiset.instMembership",
"LocallyFiniteOrder",
"Not",
"Preorder"
] | true |
_private.Lean.Server.FileWorker.SetupFile.0.Lean.Server.FileWorker.runLakeSetupFile._sparseCasesOn_1 | Lean.Server.FileWorker.SetupFile | [
"Nat.ne_of_beq_eq_false",
"Lean.Lsp.DependencyBuildMode.once",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Lsp.DependencyBuildMode.ctorIdx",
"Lean.Lsp.DependencyBuildMode.always",
"Nat.land",
"Nat",
"Lean.Lsp.DependencyBuildMode.never",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.... | false |
WeierstrassCurve.coe_variableChange_Δ' | Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange | [
"Units.val",
"WeierstrassCurve.Δ",
"CommRing",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"WeierstrassCurve.IsElliptic",
"congrArg",
"CommSemiring.toSemiring",
"WeierstrassCurve.instIsEllipticHSMulVariableChange",
"WeierstrassCurv... | true |
Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.clearRupUnits | Std.Tactic.BVDecide.LRAT.Internal.Formula.Implementation | [
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.insert.match_1",
"instOfNatNat",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula",
"List.toArray",
"Array.foldl",
"Array",
"Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.mk",
"Nat",
"Std.Tactic.BVDecide.LRAT.Internal.Assignment",
"Std.Tactic.B... | true |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.0._auto_452 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
instDecidableEqZNum.decEq._proof_10 | Mathlib.Data.Num.Basic | [
"False",
"ZNum",
"PosNum",
"ZNum.neg",
"ZNum.neg.noConfusion",
"Eq",
"Not"
] | false |
AbstractCompletion.closure_range | Mathlib.Topology.UniformSpace.AbstractCompletion | [
"UniformSpace",
"AbstractCompletion",
"AbstractCompletion.dense",
"Set.univ",
"AbstractCompletion.space",
"AbstractCompletion.uniformStruct",
"AbstractCompletion.coe",
"DenseRange.closure_range",
"closure",
"Set.range",
"UniformSpace.toTopologicalSpace",
"Eq",
"Set"
] | true |
Lean.KVMap.entries | Lean.Data.KVMap | [
"List",
"Lean.Name",
"Lean.DataValue",
"Prod",
"Lean.KVMap"
] | true |
ULift.leftCancelMonoid.eq_1 | Mathlib.Algebra.Group.ULift | [
"MulOne.toOne",
"ULift.leftCancelMonoid._proof_3",
"Equiv.instEquivLike",
"ULift.leftCancelMonoid",
"Monoid.toMulOneClass",
"ULift.commSemigroup._proof_1",
"ULift",
"Equiv.ulift",
"Equiv",
"MulOne.toMul",
"LeftCancelMonoid.toMonoid",
"ULift.one",
"ULift.leftCancelMonoid._proof_1",
"Monoid.... | true |
Aesop.LocalRuleSet.simprocsArray | Aesop.RuleSet | [
"Array",
"Aesop.LocalRuleSet",
"Lean.Meta.Simp.Simprocs",
"Lean.Name",
"Prod"
] | true |
isTotallyDisconnected_iff_lt | Mathlib.Topology.Order.IntermediateValue | [
"Eq.mpr",
"False",
"OrderTopology",
"Preorder.toLT",
"le_rfl",
"_private.Mathlib.Topology.Order.IntermediateValue.0.isTotallyDisconnected_iff_lt._simp_1_4",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"_private.Mathlib.Topology.Order.IntermediateValue.0.isTotallyDisconnected_iff_lt._si... | true |
LieModule.chainTop | Mathlib.Algebra.Lie.Weights.Chain | [
"IsDomain",
"CommRing",
"instHSMul",
"LieModule.Weight.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"LieModule.chainTop._proof_1",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LieRing.IsNilpotent",
"Module.IsTorsionFree",
"AddGro... | true |
_private.Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin.0.ContinuousAlternatingMap.alternatizeUncurryFinCLM.aux._proof_10 | Mathlib.Analysis.Normed.Module.Alternating.Uncurry.Fin | [
"NormedField.toField",
"RingHomCompTriple",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring"
] | false |
groupHomology.chains₁ToCoinvariantsKer | Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree | [
"Submodule",
"Representation.Coinvariants.ker",
"Rep.V",
"CommRing",
"Finsupp.module",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"CommSemiring.toSemiring",
"groupHomology.chains₁ToCoinvariantsKer._proof_1",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Group",
"Rep... | true |
FreeSimplexQuiver.homRel.δ_comp_δ | Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic | [
"FreeSimplexQuiver.homRel",
"CategoryTheory.CategoryStruct.toQuiver",
"Fin.succ",
"CategoryTheory.Paths.categoryPaths",
"FreeSimplexQuiver.mk",
"CategoryTheory.Paths",
"FreeSimplexQuiver.homRel.δ_comp_δ",
"instOfNatNat",
"LE.le",
"instLEFin",
"instHAdd",
"FreeSimplexQuiver.quiv",
"FreeSimple... | true |
CategoryTheory.HasLiftingProperty.transfiniteComposition.SqStruct.w₂ | Mathlib.CategoryTheory.SmallObject.TransfiniteCompositionLifting | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"LinearOrder",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"Preorder.toLE",
"OrderBot",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLatti... | true |
ContinuousMultilinearMap.norm_iteratedFDerivComponent_le | Mathlib.Analysis.Normed.Module.Multilinear.Basic | [
"Fintype.card_congr",
"Real.instIsOrderedRing",
"Norm.norm",
"Finset.card_univ",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"instDecidableNot",
"NormedCommRing.toSeminormedCommRing",
"Real.partialOrder",
"Real.instLE",
"Real",
"Trans.trans",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Se... | true |
small_iff | Mathlib.Logic.Small.Defs | [
"Exists",
"Equiv",
"Small.mk",
"Iff",
"Iff.intro",
"Nonempty",
"Small.casesOn",
"Small"
] | true |
_private.Mathlib.Algebra.Order.Star.Basic.0.MulOpposite.instStarOrderedRing._simp_1 | Mathlib.Algebra.Order.Star.Basic | [
"Set.image",
"Set.range",
"Eq.symm",
"Set.range_comp'",
"Eq",
"Set"
] | false |
Mathlib.Tactic.Widget.homType? | Mathlib.Tactic.Widget.CommDiag | [
"Pure.pure",
"instAlternativeOption",
"_private.Mathlib.Tactic.Widget.CommDiag.0.Mathlib.Tactic.Widget.homType?.match_1",
"Lean.Expr",
"Prod.mk",
"Applicative.toPure",
"Option.none",
"Alternative.toApplicative",
"Lean.Name.mkStr2",
"Lean.Expr.app4?",
"Prod",
"Option"
] | true |
MulActionWithZero.toMulAction | Mathlib.Algebra.GroupWithZero.Action.Defs | [
"MulActionWithZero",
"MonoidWithZero",
"MulAction",
"MonoidWithZero.toMonoid",
"Zero"
] | true |
Vector.set._proof_1 | Init.Data.Vector.Basic | [
"Vector",
"congrArg",
"Nat",
"LT.lt",
"True",
"Vector.size_toArray",
"eq_true",
"of_eq_true",
"instLTNat",
"Array.size",
"Vector.toArray",
"Eq.trans"
] | false |
subset_refl | Mathlib.Order.RelClasses | [
"HasSubset.Subset",
"Std.Refl",
"HasSubset",
"refl"
] | true |
MeromorphicOn.mono_set | Mathlib.Analysis.Meromorphic.Basic | [
"NormedSpace",
"Membership.mem",
"MeromorphicOn",
"HasSubset.Subset",
"NontriviallyNormedField",
"NontriviallyNormedField.toNormedField",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Set.instMembership",
"NormedAddCommGroup",
"Set.instHasSubset",
"Set"
] | true |
Lean.Meta.Grind.AC.instInhabitedEqCnstr | Lean.Meta.Tactic.Grind.AC.Types | [
"Inhabited.default",
"Lean.Meta.Grind.AC.EqCnstr",
"Lean.Grind.AC.instInhabitedSeq",
"instOfNatNat",
"Lean.Meta.Grind.AC.EqCnstrProof",
"Nat",
"Inhabited",
"Lean.Grind.AC.Seq",
"OfNat.ofNat",
"Lean.Meta.Grind.AC.EqCnstr.mk",
"Lean.Meta.Grind.AC.instInhabitedEqCnstrProof",
"Inhabited.mk"
] | true |
Std.Tactic.BVDecide.BVExpr.bitblast.blastConst._proof_4 | Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Const | [
"LE.le",
"instLENat",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"instDecidableEqNat",
"instLTNat",
"Eq",
"Not",
"_private.Std.Tactic.BVDecide.Bitblast.BVExpr.Circuit.Impl.Const.0.Std.Tactic.BVDecide.BVExpr.bitblast.blastConst._proof_3"
] | false |
Lean.Meta.Config.assignSyntheticOpaque | Lean.Meta.Basic | [
"Bool",
"Lean.Meta.Config"
] | true |
IO.Error.permissionDenied.inj | Init.System.IOError | [
"String",
"IO.Error.permissionDenied",
"And",
"And.intro",
"IO.Error.permissionDenied.noConfusion",
"UInt32",
"IO.Error",
"Eq",
"Option"
] | true |
Fin.natAdd_natAdd | Init.Data.Fin.Lemmas | [
"Fin.natAdd",
"Fin.ext",
"Fin.val",
"instHAdd",
"Fin.cast",
"HAdd.hAdd",
"Nat",
"Nat.add_assoc",
"instAddNat",
"Eq.symm",
"Fin",
"Eq"
] | true |
AnalyticWithinAt.exists_hasFTaylorSeriesUpToOn | Mathlib.Analysis.Calculus.FDeriv.Analytic | [
"Filter.instMembership",
"NormedCommRing.toSeminormedCommRing",
"AnalyticOn",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CompleteSpace",
"inter_mem_nhdsWithin",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"AnalyticOnNhd.iteratedFDeriv",... | true |
MeasureTheory.AEEqFun.coeFn_posPart | Mathlib.MeasureTheory.Function.AEEqFun | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"Lattice.toSemilatticeSup",
"MeasureTheory.AEEqFun.posPart._proof_1",
"MeasureTheory.AEEqFun.cast",
"LinearOrder",
"MeasureTheory.AEEqFun.coeFn_comp",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"DistribLattice.... | true |
CategoryTheory.Bicategory.leftUnitor | Mathlib.CategoryTheory.Bicategory.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Bicategory.homCategory"
] | true |
CategoryTheory.shiftFunctorAdd'.eq_1 | Mathlib.CategoryTheory.Shift.Basic | [
"CategoryTheory.Functor",
"AddMonoid.toAddSemigroup",
"CategoryTheory.Functor.category",
"CategoryTheory.eqToIso",
"CategoryTheory.Functor.comp",
"CategoryTheory.shiftFunctor",
"CategoryTheory.Iso",
"CategoryTheory.shiftFunctorAdd'",
"CategoryTheory.shiftFunctorAdd",
"instHAdd",
"AddSemigroup.to... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected.0.SimpleGraph.ConnectedComponent.walk_toSimpleGraph._unary._proof_10 | Mathlib.Combinatorics.SimpleGraph.Connectivity.Connected | [
"HEq.refl",
"SimpleGraph.Walk",
"SimpleGraph",
"HEq"
] | false |
DivisibleHull.mk_add_mk | Mathlib.GroupTheory.DivisibleHull | [
"PNat.val",
"instHSMul",
"Submonoid.mul",
"HMul.hMul",
"instLinearOrderPNat",
"LocalizedModule.mk_add_mk",
"CommSemiring.toSemiring",
"PartialOrder.toPreorder",
"AddMonoid.toNSMul",
"DivisibleHull",
"Membership.mem",
"nonZeroDivisors",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLat... | true |
MulActionHom.instCommSemiring | Mathlib.GroupTheory.GroupAction.Hom | [
"Monoid",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"MulActionHom.instCommSemiring._proof_1",
"SMul",
"AddMonoid.toAddZeroClass",
"MulActionHom.instSemiring",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddCommMonoidWith... | true |
CategoryTheory.Limits.ChosenPullback₃.hp₁._autoParam | Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
LawfulBitraversable.mk | Mathlib.Control.Bitraversable.Basic | [
"Pure.pure",
"Bitraversable",
"Monad.toApplicative",
"ApplicativeTransformation",
"LawfulBitraversable.mk",
"LawfulBitraversable",
"Function.comp",
"Functor.Comp.instApplicativeComp",
"Bitraversable.toBifunctor",
"Bifunctor.bimap",
"Id",
"Applicative.toPure",
"Applicative",
"LawfulBifuncto... | true |
unitary.linearIsometryEquiv_coe_symm_apply | Mathlib.Analysis.InnerProductSpace.Adjoint | [
"InnerProductSpace.toNormedSpace",
"MulEquiv.instEquivLike",
"LinearIsometryEquiv.instGroup",
"CompleteSpace",
"Submonoid.mul",
"Monoid.toMulOneClass",
"AddCommGroup.toAddCommMonoid",
"unitary",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField"... | true |
CategoryTheory.Pretriangulated.TriangleOpEquivalence.unitIso | Mathlib.CategoryTheory.Triangulated.Opposite.Triangle | [
"CategoryTheory.Functor",
"CategoryTheory.Equivalence.unitIso",
"Opposite",
"CategoryTheory.Pretriangulated.TriangleOpEquivalence.inverse",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Iso.op",
"CategoryTheory.Pretriangulated.Triangle.obj₁",
"CategoryTheory.Pretriangulated.Triangle.obj₃",... | true |
NonUnitalRingHom.rangeRestrict_surjective | Mathlib.RingTheory.NonUnitalSubring.Basic | [
"NonUnitalNonAssocRing",
"NonUnitalSubring.instSetLike",
"NonUnitalRingHom.mem_range",
"_private.Mathlib.RingTheory.NonUnitalSubring.Basic.0.NonUnitalRingHom.rangeRestrict_surjective.match_1_3",
"NonUnitalSubring",
"Membership.mem",
"Exists",
"Subtype",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemi... | true |
_private.Init.Data.Nat.Power2.Basic.0.Nat.nextPowerOfTwo.go._unary._proof_2 | Init.Data.Nat.Power2.Basic | [
"HMul.hMul",
"of_decide_eq_true",
"_private.Init.Data.Nat.Power2.Basic.0.Nat.nextPowerOfTwo.go._unary._proof_1",
"InvImage",
"HSub.hSub",
"Nat.mul_pos",
"PSigma.casesOn",
"id",
"instSubNat",
"instMulNat",
"instOfNatNat",
"Bool.true",
"GT.gt",
"instHSub",
"Nat",
"LT.lt",
"PSigma.mk",
... | false |
LowerSet.sdiff_lt_left._simp_1 | Mathlib.Order.UpperLower.Closure | [
"Preorder.toLT",
"LowerSet.sdiff",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"LowerSet.sdiff_lt_left",
"LowerSet.instPartialOrder",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"SetLike.coe",... | false |
GrpCat.instCreatesLimitsOfSizeUliftFunctor._proof_1 | Mathlib.Algebra.Category.Grp.Ulift | [
"GrpCat.instConcreteCategoryMonoidHomCarrier",
"CategoryTheory.Functor",
"GrpCat",
"MonoidHom.instFunLike",
"MonoidHom",
"GrpCat.str",
"Monoid.toMulOneClass",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.HasLimit",
"Membership.mem",
"small_subtype",
"UnivLE.small",
"DivInvMonoid.toM... | false |
WType._sizeOf_1 | Mathlib.Data.W.Basic | [
"WType",
"instOfNatNat",
"WType.rec",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"SizeOf",
"OfNat.ofNat"
] | false |
Std.instDecidableEqRci | Init.Data.Range.Polymorphic.PRange | [
"Std.Rci",
"Std.instDecidableEqRci.decEq",
"DecidableEq"
] | true |
Function.LeftInverse.rightInverse_of_surjective | Mathlib.Logic.Function.Basic | [
"Function.LeftInverse",
"_private.Mathlib.Logic.Function.Basic.0.Function.LeftInverse.rightInverse_of_surjective.match_1_1",
"Exists",
"Eq.rec",
"congr_arg",
"Function.RightInverse",
"Eq",
"Function.Surjective"
] | true |
_private.Lean.Meta.Tactic.Grind.Proof.0.Lean.Meta.Grind.mkHCongrProof'._unsafe_rec | Lean.Meta.Tactic.Grind.Proof | [
"Lean.Meta.Grind.GrindM",
"Lean.mkAppN",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.State",
"ReaderT",
"instMonadControlTOfPure",
"String",
"Lean.Meta.Sym.isSameExpr",
"Lean.Meta.State",
"Lean.Meta.CongrTheorem",
"Lean.Meta.Grind.instInhabitedGoalM",
"instMonadLiftT",
"Lean.Meta.Sym.Context",
... | false |
BooleanSubalgebra.map._proof_3 | Mathlib.Order.BooleanSubalgebra | [
"BooleanAlgebra",
"BooleanSubalgebra",
"SupClosed.image",
"Lattice.toSemilatticeSup",
"SupBotHomClass.toSupHomClass",
"BoundedLatticeHom.instFunLike",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"BooleanAlgebra.toBoundedOrder",
"SemilatticeSup... | false |
real_inner_I_smul_self | Mathlib.Analysis.InnerProductSpace.Basic | [
"Norm.norm",
"InnerProductSpace.toNormedSpace",
"Real",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"SeminormedAddGroup.toAddGroup",
"SeminormedAddCommGroup",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"Inner.inner",
"sub_self",
"Real.instZero",
"Real.instAddMonoid",
"inner... | true |
CategoryTheory.sectionsFunctorNatIsoCoyoneda | Mathlib.CategoryTheory.Yoneda | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.coyoneda",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Unique",
"CategoryTheory.Functor.category",
"Set.Elem",
"CategoryTheory.Iso",
"CategoryTheory.sectionsFunctorNatIsoCoyoneda._proof_1",
"Equiv.toIso",
"Opposite.op",
"Cate... | true |
WithOne | Mathlib.Algebra.Group.WithOne.Defs | [
"Option"
] | true |
Representation.free | Mathlib.RepresentationTheory.Basic | [
"Monoid",
"Representation",
"Semiring.toModule",
"Finsupp.module",
"CommSemiring.toSemiring",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Finsupp.instAddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Representation.finsupp",
"NonAssocSemiring.toNonUnitalNonAssocSemir... | true |
Lean.Parser.Tactic.Grind.mbtc | Init.Grind.Interactive | [
"Lean.ParserDescr.nonReservedSymbol",
"Lean.Name.mkStr5",
"instOfNatNat",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"OfNat.ofNat",
"Bool.false"
] | true |
Primrec.subtype_val_iff | Mathlib.Computability.Primrec.Basic | [
"Eq.mpr",
"Option.casesOn",
"Option.some",
"Option.encodable",
"id",
"Subtype",
"instOfNatNat",
"Primrec",
"Option.none",
"Option.map",
"Iff",
"DecidablePred",
"Nat",
"Primrec.comp",
"Iff.intro",
"Primcodable.toEncodable",
"Primcodable",
"Eq.refl",
"Encodable.encode",
"Encodabl... | true |
Lean.Grind.CommRing.Poly.mulMonC.go | Init.Grind.Ring.CommSolver | [
"cond",
"Lean.Grind.CommRing.Poly",
"HMul.hMul",
"Lean.Grind.CommRing.Poly.add",
"Int.instDecidableEq",
"Lean.Grind.CommRing.Poly.below",
"instHMod",
"Lean.Grind.CommRing.Poly.denote.match_1",
"Int",
"instBEqOfDecidableEq",
"Nat.cast",
"Int.instMul",
"Lean.Grind.CommRing.Mon.mul",
"HMod.hM... | true |
Equiv.simpleGraph._proof_1 | Mathlib.Combinatorics.SimpleGraph.Maps | [
"Equiv.instEquivLike",
"Equiv.symm_comp_self",
"congrArg",
"Function.comp",
"id",
"Equiv",
"SimpleGraph",
"SimpleGraph.comap",
"SimpleGraph.comap_id",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"Eq.trans",
"EquivLike.toFunLike"
] | false |
Path.Homotopy.hcomp._proof_8 | Mathlib.Topology.Homotopy.Path | [
"Real.instIsOrderedRing",
"Path.Homotopy",
"Real.partialOrder",
"Real",
"Continuous",
"instHDiv",
"Continuous.continuousOn",
"HMul.hMul",
"Set.Icc.instZero",
"Path.Homotopy.hcomp._proof_3",
"Path.Homotopy.hcomp._proof_7",
"Real.instZero",
"Real.instDivInvMonoid",
"Real.instSub",
"Continu... | false |
Std.DHashMap.Raw.Const.all_eq_false_iff_exists_mem_get | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Std.DHashMap.Raw.Const.get",
"Std.DHashMap.Raw",
"LawfulBEq",
"Membership.mem",
"Exists",
"Std.DHashMap.Raw.Const.all_eq_false_iff_exists_contains_get",
"Iff",
"Bool",
"Hashable",
"Bool.false",
"BEq",
"Eq",
"Std.DH... | true |
Lean.Elab.Tactic.ElimApp.Result.motive | Lean.Elab.Tactic.Induction | [
"Lean.Elab.Tactic.ElimApp.Result",
"Lean.MVarId"
] | true |
ModularForm.coe_eq_zero_iff._simp_1 | Mathlib.NumberTheory.ModularForms.Basic | [
"ModularForm",
"Real",
"Matrix",
"instDecidableEqFin",
"ModularForm.instZero",
"Complex.instZero",
"Real.semiring",
"Pi.instZero",
"Subgroup",
"instOfNatNat",
"Int",
"Units.instGroup",
"ModularForm.coe_eq_zero_iff",
"Fin.fintype",
"UpperHalfPlane",
"Nat",
"propext",
"Zero.toOfNat0"... | false |
Submodule.subtypeₗᵢ_toContinuousLinearMap | Mathlib.Analysis.Normed.Operator.LinearIsometry | [
"Submodule.subtypeL",
"Submodule",
"SeminormedAddCommGroup",
"AddCommGroup.toAddCommMonoid",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"Subtype",
"Submodule.module",
"ContinuousLinearMap",
"SeminormedAddCommGroup.toPseudoMetricSpace",
"SeminormedAddCommGroup.toAddCommGroup",
"Submo... | true |
Differential.logDeriv.eq_1 | Mathlib.FieldTheory.Differential.Basic | [
"Derivation",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Field.toDivisionRing",
"DivisionRing.toDivInvMonoid",
"Differential",
"HDiv.hDiv",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"I... | true |
Array.toList_mapFinIdxM | Init.Data.Array.MapIdx | [
"Eq.mpr",
"congrArg",
"Monad.toApplicative",
"LawfulApplicative.toLawfulFunctor",
"id",
"LawfulMonad",
"Array.toList",
"List.toArray",
"List.mapFinIdxM_toArray",
"Array",
"List",
"Nat",
"LT.lt",
"True",
"eq_self",
"List.mapFinIdxM",
"id_map'",
"of_eq_true",
"Applicative.toFunctor... | true |
IsCompact.exists_isGLB | Mathlib.Topology.Order.Compact | [
"IsCompact.exists_isLeast",
"lowerBounds",
"LinearOrder",
"PartialOrder.toPreorder",
"IsLeast.isGLB",
"Preorder.toLE",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Exists.imp",
"ClosedIicTopology",
"IsLeast",
"TopologicalSpace",
"And",
"Set.... | true |
_private.Init.Data.Nat.Basic.0.Nat.exists_eq_succ_of_ne_zero.match_1_1 | Init.Data.Nat.Basic | [
"False",
"False.elim",
"Ne",
"instOfNatNat",
"instHAdd",
"absurd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Nat.zero",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq",
"Nat.casesOn"
] | false |
CategoryTheory.ShortComplex.SnakeInput.Hom.comp | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.ShortComplex.SnakeInput.Hom.comp._proof_3",
"CategoryTheory.ShortComplex.SnakeInput.L₃",
"CategoryTheory.ShortComplex.SnakeInput.Hom.comp._proof_2",
"CategoryTheory.ShortComplex.SnakeInput.L₂",
"CategoryTheory.ShortComplex.SnakeInput.L₀",
"Category... | true |
CategoryTheory.ReflPrefunctor.«_aux_Mathlib_Combinatorics_Quiver_ReflQuiver___macroRules_CategoryTheory_ReflPrefunctor_term_⥤rq__1» | Mathlib.Combinatorics.Quiver.ReflQuiver | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr3",... | false |
Nat.Pseudoperfect.eq_1 | Mathlib.NumberTheory.FactorisationProperties | [
"Finset",
"Exists",
"HasSubset.Subset",
"instOfNatNat",
"Nat.properDivisors",
"And",
"Nat",
"LT.lt",
"Finset.instHasSubset",
"Nat.Pseudoperfect",
"Nat.instAddCommMonoid",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
"Eq",
"Finset.sum"
] | true |
Finset.smul_sum | Mathlib.Algebra.BigOperators.GroupWithZero.Action | [
"instHSMul",
"AddMonoidHom.instAddMonoidHomClass",
"Finset",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"map_sum",
"AddCommMonoid",
"AddZero.toZero",
"DistribSMul",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"AddCommMonoid.toAddMonoid",
"AddMonoidHom",... | true |
OrderMonoidIso.val_inv_unitsWithZero_symm_apply | Mathlib.Algebra.Order.Hom.MonoidWithZero | [
"Units.val",
"GroupWithZero.toMonoidWithZero",
"GroupWithZero.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"WithZero.instMonoidWithZero",
"OrderMonoidIso.unitsWithZero",
"Group",
"DivisionMonoid.toDivInvOneMonoid",
"Units",
"MulOne.toMul",
"DivInvMonoid.toMonoid"... | true |
ContMDiffOn.clm_bundle_apply₂ | Mathlib.Geometry.Manifold.VectorBundle.Hom | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toNormedSpace._proof_1",
"ContinuousLinearMap.toNormedAddCommGroup",
"ContinuousLinearMap.continuousSMul",
"RingHomSurjective.ids",
"Prod.normedSpace",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedR... | true |
CategoryTheory.Limits.BinaryCofan.isColimitMk._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | [
"CategoryTheory.Limits.BinaryCofan.inr",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.WalkingPair.right",
"CategoryTheory.Limits.WalkingPair",
"CategoryTheory.Limits.BinaryC... | false |
Finsupp.lsingle_range_le_ker_lapply | Mathlib.LinearAlgebra.Finsupp.Span | [
"Iff.mpr",
"_private.Mathlib.LinearAlgebra.Finsupp.Span.0.Finsupp.lsingle_range_le_ker_lapply._simp_1_3",
"Eq.mpr",
"Disjoint.le_bot",
"Submodule",
"RingHomSurjective.ids",
"iInf",
"_private.Mathlib.LinearAlgebra.Finsupp.Span.0.Finsupp.lsingle_range_le_ker_lapply._simp_1_4",
"Finsupp.module",
"Com... | true |
CategoryTheory.ShortComplex.homMk_τ₁ | Mathlib.Algebra.Homology.ShortComplex.Basic | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.Hom.τ₁",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.X₁",
"CategoryTheory.ShortComplex.homMk",
"CategoryTheory.CategoryStruct.comp",
"Eq.refl",
"CategoryTh... | true |
Matroid.IsCircuit.eq_fundCircuit_of_subset | Mathlib.Combinatorics.Matroid.Circuit | [
"Matroid.Indep.mem_closure_iff",
"subset_refl._simp_1",
"Eq.mpr",
"Matroid.Dep",
"Set.diff_subset",
"Matroid.fundCircuit_eq_sInter",
"congrArg",
"Matroid.E",
"Matroid.Dep.superset",
"False.elim",
"setOf",
"Membership.mem",
"Matroid.IsCircuit.diff_singleton_isBasis",
"Set.insert_eq_of_mem",... | true |
LieDerivation.exp_map_apply | Mathlib.Algebra.Lie.Derivation.Basic | [
"LieAlgebra.toModule",
"Module.End.instRing",
"CommRing",
"DFunLike.congr_fun",
"Module.End.instMonoid",
"LieDerivation",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LieEquiv",
"Rat",
"LinearMap.instFunLike",
"lieA... | true |
Lean.Elab.Structural.EqnInfo._sizeOf_1 | Lean.Elab.PreDefinition.Structural.Eqns | [
"Lean.Elab.Structural.EqnInfo.rec",
"Lean.Elab.FixedParamPerms._sizeOf_inst",
"Lean.Elab.FixedParamPerms",
"Lean.Expr",
"instOfNatNat",
"Array._sizeOf_inst",
"Array",
"List",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Lean.Elab.Structural.EqnInfo",
"Nat",
"List._sizeOf_inst",
"Size... | false |
Std.IterM.Equiv.of_morphism | Std.Data.Iterators.Lemmas.Equivalence.Basic | [
"_private.Std.Data.Iterators.Lemmas.Equivalence.Basic.0.Std.IterM.Equiv.of_morphism._simp_1_2",
"Std.Iterators.HetT.pure",
"Iff.mpr",
"Eq.mpr",
"Std.BundledIterM.step",
"bind_congr",
"Std.IterStep",
"Quot.sound",
"Std.Iterators.HetT.pure_bind",
"Iff.of_eq",
"congrArg",
"Std.Shrink",
"Monad.t... | true |
MonadReaderOf.read | Init.Prelude | [
"semiOutParam",
"MonadReaderOf"
] | true |
Ideal.Pure.eq_1 | Mathlib.RingTheory.Ideal.Pure | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Submodule.Quotient.module",
"Ideal",
"Module.Flat",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Has... | true |
Asymptotics.transIsEquivalentIsLittleO | Mathlib.Analysis.Asymptotics.AsymptoticEquivalent | [
"Asymptotics.IsEquivalent.trans_isLittleO",
"Norm",
"Trans",
"Asymptotics.IsEquivalent",
"NormedAddCommGroup.toNorm",
"Asymptotics.IsLittleO",
"Trans.mk",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"Filter",
"NormedAddCommGroup"
] | true |
CategoryTheory.PreOneHypercover.cylinder_X | Mathlib.CategoryTheory.Sites.Hypercover.Homotopy | [
"CategoryTheory.PreOneHypercover.cylinder",
"CategoryTheory.PreOneHypercover",
"CategoryTheory.PreOneHypercover.I₁",
"CategoryTheory.PreOneHypercover.toPreZeroHypercover",
"CategoryTheory.PreZeroHypercover.X",
"Sigma.fst",
"CategoryTheory.PreOneHypercover.Hom.toHom",
"CategoryTheory.PreZeroHypercover.... | true |
CategoryTheory.CostructuredArrow.ιCompGrothendieckPrecompFunctorToCommaCompFst_hom_app | Mathlib.CategoryTheory.Comma.StructuredArrow.Functor | [
"CategoryTheory.Cat.category",
"CategoryTheory.Functor",
"CategoryTheory.Grothendieck.ι",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CostructuredArrow.grothendieckPrecompFunctorToComma",
"CategoryTheory.Comma.fst",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma... | true |
Homeomorph.ext | Mathlib.Topology.Homeomorph.Defs | [
"DFunLike.ext",
"TopologicalSpace",
"Homeomorph.instEquivLike",
"Homeomorph",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
Std.DHashMap.Internal.Raw₀.Const.getKeyD_filter | Std.Data.DHashMap.Internal.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Option.pfilter",
"Std.DHashMap.Raw.WF.filter₀",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.DHashMap.Internal.Raw.WF.out",
"congrArg",
"Std.Internal.List.getKeyD",
"Std.DHashMap.Internal.Raw₀.getKey?",
"Std.DHashMap.Raw",
"Opt... | true |
Submodule.IsLattice.smul | Mathlib.Algebra.Module.Lattice | [
"Units.val",
"Eq.mpr",
"Submodule.pointwiseDistribMulAction",
"Submodule",
"Finite.Set.finite_image",
"IsScalarTower.to_smulCommClass'",
"Units.instMulAction",
"CommRing",
"instHSMul",
"trivial",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Units.smulCommClass_... | true |
Algebra.Generators.localizationAway._proof_5 | Mathlib.RingTheory.Extension.Generators | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"AlgHom.algHomClass",
"MvPolynomial.aeval",
"CommSemiring.toSemiring",
"AlgHom",
"AlgHom.funLike",
"AddMonoidAlgebra.algebra",
"IsLocalization.Away",
"Finsupp.instAddMonoid",
"AddMonoidAlgebra.commSemiring",
"Algebra",
"Nat.i... | false |
TensorProduct.mapOfCompatibleSMul | Mathlib.LinearAlgebra.TensorProduct.Basic | [
"TensorProduct.CompatibleSMul",
"TensorProduct.mapOfCompatibleSMul._proof_3",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"TensorProduct.addCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LinearMap.toAddHo... | true |
_private.Mathlib.Algebra.Homology.SpectralSequence.ComplexShape.0.ComplexShape.spectralSequenceFin._proof_4 | Mathlib.Algebra.Homology.SpectralSequence.ComplexShape | [
"Int.Linear.eq_of_core",
"Lean.RArray.leaf",
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"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",
... | false |
_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.pow_sub_le_descFactorial.match_1_1 | Mathlib.Data.Nat.Factorial.Basic | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
BitVec.toNat_shiftConcat_eq_of_lt | Init.Data.BitVec.Lemmas | [
"instPowNat",
"Eq.mpr",
"Nat.shiftLeft_eq",
"Nat.pow_lt_pow_of_lt",
"HMul.hMul",
"congrArg",
"Bool.toNat",
"HShiftLeft.hShiftLeft",
"BitVec",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.toNat_shiftConcat_eq_of_lt._proof_1_3",
"id",
"Nat.instMod",
"instHMod",
"instMulNat",
"instOfNatNat",
... | true |
CategoryTheory.Limits.MulticospanIndex.sectionsEquiv._proof_3 | Mathlib.CategoryTheory.Limits.Types.Multiequalizer | [
"CategoryTheory.Limits.MulticospanShape.snd",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Limits.WalkingMulticospan.instSmallCategory",
"CategoryTheory.Limits.MulticospanIndex.sections.val",
"CategoryTheory.Limits.Walk... | false |
MeasureTheory.ComplexMeasure.absolutelyContinuous_ennreal_iff | Mathlib.MeasureTheory.Measure.Complex | [
"LinearMap.toAddMonoidHom",
"Complex.imLm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"Complex.instNormedAddCommGroup",
"ENNReal.instAd... | true |
IsSymmetricRel.iInter | Mathlib.Topology.UniformSpace.Defs | [
"Eq.mpr",
"SetRel",
"congrArg",
"Set.iInter",
"id",
"funext",
"Set.preimage",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"Set.preimage_iInter",
"Prod.swap",
"IsSymmetricRel.eq",
"IsSymmetricRel",
"Prod",
"Eq",
"Eq.trans",
"Set"
] | true |
_private.Lean.Compiler.LCNF.JoinPoints.0.Lean.Compiler.LCNF.JoinPointFinder.removeCandidatesInArg | Lean.Compiler.LCNF.JoinPoints | [
"Lean.Compiler.LCNF.Arg",
"ReaderT.instMonad",
"Lean.Compiler.LCNF.JoinPointFinder.FindCtx",
"IO.RealWorld",
"_private.Lean.Compiler.LCNF.JoinPoints.0.Lean.Compiler.LCNF.JoinPointFinder.eraseCandidate",
"Lean.Compiler.LCNF.Purity.pure",
"Unit",
"Lean.Compiler.LCNF.instTraverseFVarArg",
"Lean.Compile... | true |
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