name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Nat.sSup_mem | Mathlib.Data.Nat.Lattice | [
"setOf",
"Membership.mem",
"upperBounds",
"Set.Nonempty.csSup_mem",
"Set.Finite.subset",
"LE.le",
"instLENat",
"BddAbove",
"_private.Mathlib.Data.Nat.Lattice.0.Nat.sSup_mem.match_1_1",
"Set.Nonempty",
"Nat",
"Nat.instSupSet",
"ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinear... | true |
Lean.Elab.Term.Do.attachJPs | Lean.Elab.Do.Legacy | [
"Lean.Elab.Term.Do.JPDecl",
"instOfNatNat",
"Array",
"Array.foldr",
"Nat",
"Lean.Elab.Term.Do.Code",
"Lean.Elab.Term.Do.attachJP",
"OfNat.ofNat",
"Array.size"
] | true |
_private.Lean.Meta.LevelDefEq.0.Lean.Meta.strictOccursMax | Lean.Meta.LevelDefEq | [
"Lean.Level",
"_private.Lean.Meta.LevelDefEq.0.Lean.Meta.strictOccursMax.visit.match_1",
"Bool",
"Bool.or",
"Bool.false",
"_private.Lean.Meta.LevelDefEq.0.Lean.Meta.strictOccursMax.visit"
] | true |
_private.Init.Grind.Ordered.Module.0.Lean.Grind.OrderedAdd.zsmul_le_zsmul._simp_1_1 | Init.Grind.Ordered.Module | [
"HSub.hSub",
"Lean.Grind.AddCommMonoid.toZero",
"LE.le",
"LE",
"instHAdd",
"Std.IsPreorder",
"instHSub",
"Lean.Grind.AddCommMonoid.toAdd",
"Lean.Grind.AddCommGroup.toSub",
"propext",
"Lean.Grind.AddCommGroup",
"Zero.toOfNat0",
"Lean.Grind.AddCommGroup.toAddCommMonoid",
"OfNat.ofNat",
"Eq... | false |
CategoryTheory.ShortComplex.isoMk._auto_3 | Mathlib.Algebra.Homology.ShortComplex.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 |
_private.Mathlib.RepresentationTheory.Coinvariants.0.Representation.Coinvariants.instFinite._proof_1 | Mathlib.RepresentationTheory.Coinvariants | [
"Monoid",
"Representation.Coinvariants.ker",
"CommRing",
"Representation",
"instSMulOfMul",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup",
"Module.Finite.quotient",
"instDistribOfSemiring",
"Representation.Coinvariants",
"CommRing.toCommSemiring",
"Distrib.toMul",... | false |
SubAddAction.instInhabited.eq_1 | Mathlib.GroupTheory.GroupAction.SubMulAction | [
"VAdd",
"Bot.bot",
"SubAddAction.instInhabited",
"SubAddAction.instBot",
"SubAddAction",
"Inhabited",
"Eq.refl",
"Eq",
"Inhabited.mk"
] | true |
Std.DTreeMap.Raw.Const.ofList._auto_1 | Std.Data.DTreeMap.Raw.Basic | [
"Lean.Syntax.node",
"Lean.Syntax.ident",
"Array.push",
"String.toRawSubstring",
"Lean.Syntax",
"Array.empty",
"Lean.Syntax.Preresolved",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom",
"List.nil"
] | false |
RingHom.map_iterate_frobenius | Mathlib.Algebra.CharP.Frobenius | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommSemiring.toSemiring",
"MonoidHom.map_iterate_frobenius",
"RingHom",
"ExpChar",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Nat.iterate",
"CommSemiring",
"frobenius",
"RingHom.instFunLike",
"Nat",
"RingHom.toMonoidHom",
"Semiring.toNonAssocSemir... | true |
MeasureTheory.VectorMeasure.Integrable._proof_1 | Mathlib.MeasureTheory.VectorMeasure.Integral | [
"ContinuousLinearMap.instT2Space",
"Real",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"ContinuousLinearMap.topologicalSpace",
"Real.instZero",
"NormedAddCommGroup.toMetricSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClas... | false |
PFunctor.Idx | Mathlib.Data.PFunctor.Univariate.Basic | [
"PFunctor",
"PFunctor.A",
"PFunctor.B",
"Sigma"
] | true |
Lean.Meta.Try.Collector.OrdSet.insert | Lean.Meta.Tactic.Try.Collect | [
"Lean.Meta.Try.Collector.OrdSet.mk",
"Array.push",
"Std.HashSet",
"instDecidableEqBool",
"Array",
"Bool.true",
"Std.HashSet.insert",
"Std.HashSet.contains",
"Lean.Meta.Try.Collector.OrdSet",
"Bool",
"Lean.Meta.Try.Collector.OrdSet.set",
"Hashable",
"_private.Lean.Meta.Tactic.Try.Collect.0.Le... | true |
_private.Mathlib.Data.Multiset.DershowitzManna.0.Multiset.transGen_oneStep_of_isDershowitzMannaLT._simp_1_1 | Mathlib.Data.Multiset.DershowitzManna | [
"Membership.mem",
"Multiset",
"Multiset.instMembership",
"And",
"DecidablePred",
"propext",
"Multiset.mem_filter",
"Eq",
"Multiset.filter"
] | false |
_private.Lean.Meta.Tactic.Grind.Main.0.Lean.Meta.Grind.discharge?.match_1 | Lean.Meta.Tactic.Grind.Main | [
"Option.ctorIdx",
"Option.some",
"Lean.Expr",
"Nat.hasNotBit",
"_private.Lean.Meta.Tactic.Grind.Main.0.Lean.Meta.Grind.mkMethods._sparseCasesOn_1",
"Option"
] | false |
ContinuousMap.instNonUnitalCommCStarAlgebra._proof_6 | Mathlib.Analysis.CStarAlgebra.ContinuousMap | [
"ContinuousMap.instNonUnitalCStarAlgebra",
"NonUnitalCommCStarAlgebra.toNonUnitalCStarAlgebra",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"NonUnitalNonAssocRing.toMul",
"NonUnitalCommCStarAlgebra",
"ContinuousMap",
"NonUnitalNonAssocRing.toAddCommGroup",... | false |
lp.zeroBasis_repr_symm_apply_coe | Mathlib.Analysis.Normed.Lp.lpSpace | [
"Finsupp.instFunLike",
"LinearEquiv.symm",
"Semiring.toModule",
"NormedRing.toRing",
"Finsupp.module",
"AddCommGroup.toAddCommMonoid",
"instAddCommGroupPreLp",
"lp.instModuleSubtypePreLpMemAddSubgroup",
"AddCommGroup.toAddGroup",
"Membership.mem",
"NormedRing.toNonUnitalNormedRing",
"Subtype",... | true |
Mathlib.Tactic.Monoidal.instMkEvalWhiskerLeftMonoidalM.match_1 | Mathlib.Tactic.CategoryTheory.Monoidal.Normalize | [
"Option.ctorIdx",
"Lean.Expr.const",
"Option.some",
"Nat.hasNotBit",
"Mathlib.Tactic.Monoidal.Context.instCat",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Mathlib.Tactic.Monoidal.Context.C",
"Mathlib.Tactic.Monoidal.instMkEvalWhiskerLeftMonoidalM._sparseCasesOn_1",
"Mathlib.Tactic.Monoidal.Context... | false |
isClosed_Ioo_iff | Mathlib.Topology.Order.DenselyOrdered | [
"OrderTopology",
"Preorder.toLT",
"congrArg",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Set.Finite",
"IsClosed.closure_eq",
"le_of_not_gt",
"SemilatticeInf.toPartialOrder",
"OrderClosedTopology.to_t2Space",
"Eq.mp",
"DistribLattice.toLattice",
"LT.lt.le",
"LE.le",
"Or... | true |
_private.Mathlib.Algebra.Module.Submodule.Union.0.Submodule.iUnion_ssubset_of_forall_ne_top_of_card_lt._simp_1_1 | Mathlib.Algebra.Module.Submodule.Union | [
"Set.univ",
"HasSSubset.SSubset",
"Set.instHasSSubset",
"Ne",
"propext",
"Set.ssubset_univ_iff",
"Eq",
"Set"
] | false |
Submonoid.smulDistribClass | Mathlib.Algebra.Group.Submonoid.MulAction | [
"SetLike",
"SMul",
"SMulDistribClass",
"Membership.mem",
"Subtype",
"Submonoid.instSMulSubtypeMem",
"SMulDistribClass.smul_distrib_smul",
"SMulDistribClass.mk",
"Subtype.val",
"SetLike.instMembership"
] | true |
UInt8.mod_eq_of_lt | Init.Data.UInt.Lemmas | [
"instModUInt8",
"instHMod",
"instLTUInt8",
"instOfNatNat",
"BitVec.toNat",
"Nat.mod_eq_of_lt",
"UInt8.toBitVec",
"HMod.hMod",
"Nat",
"LT.lt",
"Iff.mp",
"UInt8.toNat_inj",
"UInt8.toNat",
"OfNat.ofNat",
"UInt8",
"Eq"
] | true |
Aesop.RuleBuilderInput.noConfusion | Aesop.Builder.Basic | [
"Aesop.RuleBuilderInput.noConfusionType",
"Aesop.RuleBuilderOptions",
"Lean.Syntax.Term",
"Aesop.RuleBuilderInput.casesOn",
"Eq.ndrec",
"Eq.refl",
"Aesop.PhaseSpec",
"Eq",
"Aesop.RuleBuilderInput"
] | false |
_private.Std.Data.DHashMap.Internal.AssocList.Lemmas.0.Std.DHashMap.Internal.AssocList.replace.eq_2 | Std.Data.DHashMap.Internal.AssocList.Lemmas | [
"cond",
"BEq.beq",
"Std.DHashMap.Internal.AssocList.replace",
"Eq.refl",
"Std.DHashMap.Internal.AssocList",
"Std.DHashMap.Internal.AssocList.cons",
"BEq",
"Eq"
] | true |
CategoryTheory.Dial.rightUnitorImpl._proof_1 | Mathlib.CategoryTheory.Dialectica.Monoidal | [
"CategoryTheory.Limits.prod.rightUnitor",
"congrArg",
"inf_of_le_left",
"le_top._simp_2",
"CategoryTheory.Dial.tensorUnitImpl._proof_1",
"CategoryTheory.Limits.prod.fst",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"CategoryTheory.Dial.tensorObjImpl._proof_3",
"C... | false |
NumberField.mixedEmbedding.convexBodySum_volume_eq_zero_of_le_zero | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody | [
"instInnerProductSpaceRealComplex",
"Set.ext",
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"NumberField.mixedEmbedding.convexBodySumFun",
"Real.partialOrder",
"Re... | true |
iUnion_Iic_eq_Iio_of_lt_of_tendsto | Mathlib.Topology.Order.OrderClosed | [
"IsLUB.range_of_tendsto",
"Eq.mpr",
"False",
"Set.mem_range",
"Preorder.toLT",
"congrArg",
"Filter.NeBot",
"PartialOrder.toPreorder",
"le_of_lt",
"Set.biUnion_range",
"Membership.mem",
"Exists",
"SemilatticeInf.toPartialOrder",
"nhds",
"DistribLattice.toLattice",
"id",
"Conditionally... | true |
CategoryTheory.Limits.HasBiproductsOfShape.colimIsoLim_inv_app | Mathlib.CategoryTheory.Limits.Shapes.Biproducts | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasCoproduct_of_hasBiproduct",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasBiproduct... | true |
MonadControlT | Init.Control.Basic | [
"MonadControlT.mk"
] | true |
Matrix.conjTranspose_reindex | Mathlib.LinearAlgebra.Matrix.ConjTranspose | [
"Equiv.instEquivLike",
"Matrix",
"Equiv",
"Star",
"Matrix.reindex",
"Matrix.conjTranspose",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
Lean.Parser.Attr.tactic_alt.parenthesizer | Lean.Parser.Attr | [
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.Parser.ident.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.leadingNode.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer.andthen.parenthesizer",
"Bool.true",
"... | true |
Sum.map_surjective | Mathlib.Data.Sum.Basic | [
"Sum.inr_injective",
"Sum.ctorIdx",
"Sum.map",
"HEq.refl",
"False.elim",
"Sum.inl_injective",
"Function.Surjective.sumMap",
"noConfusion_of_Nat",
"Exists",
"Sum.casesOn",
"Sum",
"Eq.casesOn",
"Sum.inl",
"And",
"Iff",
"Exists.casesOn",
"Sum.inr",
"And.intro",
"Iff.intro",
"Exist... | true |
LinearMap.BilinForm.Equivalent.symm | Mathlib.LinearAlgebra.BilinearForm.IsometryEquiv | [
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"Nonempty.elim",
"LinearMap.BilinForm.Equivalent",
"Nonempty.intro",
"AddCommMonoid",
"CommSemiring",
"Module",
"LinearMap.BilinForm.IsometryEquiv.symm",
"LinearMap.BilinForm.IsometryEquiv"
] | true |
_private.Mathlib.RingTheory.Valuation.ValuativeRel.Basic.0.ValuativeRel.ext.match_1 | Mathlib.RingTheory.Valuation.ValuativeRel.Basic | [
"CommRing",
"HMul.hMul",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"Distrib.toAdd",
"instDistribOfSemiring",
"AddMonoidWithOne.toOne",
"instHAdd",
"ValuativeRel.casesOn",
"CommRing.toCommSemiring",
"Distrib.toMul",
"HAdd.hAdd",
"One.toOfNat1",
"Zero.toOfNat0",
"Val... | false |
Module.Basis.prod_apply_inl_fst | Mathlib.LinearAlgebra.Basis.Prod | [
"Finsupp.instFunLike",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"Finsupp.module",
"Finsupp.ext",
"congrArg",
"Sum.inl_injective",
"AddMonoid.toAddZeroClass",
"Finsupp.single_apply_left",
"AddZeroClass.toAddZero",
"Sum",
"id",
"Sum.inl",
"AddCommMonoidWith... | true |
UInt8.toInt8_ofNat' | Init.Data.SInt.Lemmas | [
"Int8",
"UInt8.toInt8",
"Nat",
"Int8.ofNat",
"UInt8.ofNat",
"Eq",
"rfl"
] | true |
GradeOrder.wellFoundedGT | Mathlib.Order.Grade | [
"Preorder.toLT",
"StrictMono.wellFoundedGT",
"WellFoundedGT",
"GradeOrder.grade",
"GradeOrder.grade_strictMono",
"Preorder",
"GradeOrder"
] | true |
WeierstrassCurve.Affine.instDecidableEqPoint.decEq._proof_6 | Mathlib.AlgebraicGeometry.EllipticCurve.Affine.Point | [
"False",
"CommRing",
"WeierstrassCurve.Affine.Point.some.noConfusion",
"WeierstrassCurve.Affine.Nonsingular",
"WeierstrassCurve.Affine.Point.some",
"WeierstrassCurve.Affine",
"eq_of_heq",
"WeierstrassCurve.Affine.Point",
"HEq",
"Eq",
"Not"
] | false |
_private.Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit.0.CategoryTheory.coherentTopology.preimageDiagram.eq_1 | Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit | [
"CategoryTheory.Functor",
"CategoryTheory.Preregular",
"_private.Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit.0.CategoryTheory.coherentTopology.struct.X",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom.op",
"CategoryTheory.FinitaryExtensive",
"CategoryTheory.Functor.categor... | true |
IsSimpleRing.of_surjective | Mathlib.RingTheory.SimpleRing.Congr | [
"Nontrivial",
"RingHom.instRingHomClass",
"RingEquiv.mapTwoSidedIdeal",
"TwoSidedIdeal",
"RingEquiv.ofBijective",
"IsSimpleRing",
"RingHom",
"CompleteLattice.toBoundedOrder",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"NonAssocRing",
"TwoSidedIdeal.instCompleteLattic... | true |
Std.HashSet.getD_union_of_not_mem_left | Std.Data.HashSet.Lemmas | [
"Std.HashSet.instMembership",
"Std.HashSet",
"Membership.mem",
"Std.HashSet.getD",
"Std.HashSet.instUnion",
"LawfulHashable",
"Unit",
"EquivBEq",
"Std.HashSet.inner",
"Hashable",
"Union.union",
"Std.HashMap.getKeyD_union_of_not_mem_left",
"BEq",
"Eq",
"Not"
] | true |
Lean.Parser.Term.set_option.parenthesizer | Lean.Parser.Command | [
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.Parser.identWithPartialTrailingDot.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer.leadingNode.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer.andthen.parenthesize... | true |
CircularPartialOrder.toCircularPreorder | Mathlib.Order.Circular | [
"CircularPreorder",
"CircularPartialOrder"
] | true |
ModuleCon.mk.noConfusion | Mathlib.Algebra.Module.Congruence.Defs | [
"AddCon",
"instHSMul",
"HEq.refl",
"SMul",
"ModuleCon.mk",
"id",
"AddCon.toSetoid",
"heq_of_eq",
"Eq.refl",
"HEq",
"HSMul.hSMul",
"ModuleCon.noConfusion",
"Eq",
"ModuleCon",
"Add",
"Setoid.r"
] | false |
MonoidHom.compLeftContinuousBounded_apply | Mathlib.Topology.ContinuousMap.Bounded.Basic | [
"Monoid",
"BoundedContinuousFunction.comp",
"LipschitzWith",
"MonoidHom.instFunLike",
"PseudoMetricSpace.toBornology",
"BoundedContinuousFunction.instMulOneClass",
"MonoidHom",
"BoundedMul",
"Monoid.toMulOneClass",
"PseudoMetricSpace.toUniformSpace",
"MulOne.toMul",
"NNReal",
"TopologicalSpa... | true |
LinearOrderedAddCommMonoidWithTop.toIsOrderedAddMonoid | Mathlib.Algebra.Order.AddGroupWithTop | [
"PartialOrder.toPreorder",
"LinearOrderedAddCommMonoidWithTop",
"LinearOrder.toPartialOrder",
"LinearOrderedAddCommMonoidWithTop.toAddCommMonoid",
"LinearOrderedAddCommMonoidWithTop.toLinearOrder",
"IsOrderedAddMonoid"
] | true |
IsAntichain.sperner | Mathlib.Combinatorics.SetFamily.LYM | [
"Iff.mpr",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Trans.trans",
"Preorder.toLT",
"Nat.choose",
"NNRat.instInv",
"instHDiv",
"Nat.cast_pos",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"... | true |
Batteries.BinomialHeap.Imp.FindMin.WF.casesOn | Batteries.Data.BinomialHeap.Basic | [
"Batteries.BinomialHeap.Imp.FindMin.WF",
"Batteries.BinomialHeap.Imp.Heap.WF",
"Batteries.BinomialHeap.Imp.FindMin.val",
"Batteries.BinomialHeap.Imp.Heap",
"Batteries.BinomialHeap.Imp.FindMin",
"Batteries.BinomialHeap.Imp.FindMin.WF.mk",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Batteries... | false |
_private.Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality.0.InnerProductGeometry.angle_eq_angle_add_angle_iff._proof_1_2 | Mathlib.Geometry.Euclidean.Angle.Unoriented.TriangleInequality | [
"of_eq_false",
"Lean.RArray.leaf",
"Lean.Grind.Field.toCommRing",
"False",
"Real",
"Lean.Grind.not_not",
"Real.pi",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"eq_false",
"Lean.Grind.iff_eq",
"Real.instZero",
"Real.instRCLike",
"InnerProductGeometry.angle",
"Classical.byCont... | false |
Std.Iterators.Types.TakeWhile.PlausibleStep.recOn | Std.Data.Iterators.Combinators.Monadic.TakeWhile | [
"Std.Iterators.Types.TakeWhile.PlausibleStep",
"Std.Iterators.Types.TakeWhile.inner",
"Std.IterStep",
"ULift",
"Std.IterM.IsPlausibleStep",
"Std.Iterators.PostconditionT.Property",
"Std.IterStep.skip",
"Std.Iterators.Types.TakeWhile.PlausibleStep.yield",
"Std.IterM.internalState",
"Std.Iterator",
... | false |
CategoryTheory.uliftFunctor | Mathlib.CategoryTheory.Types.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.mk",
"ULift",
"TypeCat.instFunLikeFun",
"TypeCat.ofHom",
"CategoryTheory.uliftFunctor._proof_1",
"TypeCat.Fun",
"CategoryTheory.types",
"CategoryTheo... | true |
CategoryTheory.Limits.Types.chosenEnd_def | Mathlib.CategoryTheory.Limits.Types.End | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.Types.end_",
"CategoryTheory.types",
"CategoryTheory.Category.opposite",
"CategoryTheory.Limits.chosenEnd",
"Eq",
"CategoryTheory.Limits.instChosenEndsType",
"rfl",
"CategoryTheory.Category"
] | true |
Rep.standardComplex.forget₂ToModuleCat | Mathlib.RepresentationTheory.Homological.Resolution | [
"Monoid",
"Rep.V",
"CommRing",
"HomologicalComplex.instCategory",
"Nat.instOne",
"ModuleCat",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"LinearMap.instFunLike",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Rep.standardComple... | true |
_private.Mathlib.Analysis.BoxIntegral.Partition.Additive.0.Option.elim'.match_1.eq_2 | Mathlib.Analysis.BoxIntegral.Partition.Additive | [
"Unit.unit",
"Option.some",
"Option.none",
"Unit",
"Eq.refl",
"Eq",
"Option.elim'.match_1",
"Option"
] | true |
Std.DTreeMap.Internal.Impl.Const.entryAtIdxD_eq_getD_entryAtIdx? | Std.Data.DTreeMap.Internal.Model | [
"Ordering.gt",
"Eq.mpr",
"congrArg",
"Std.DTreeMap.Internal.Impl.Const.entryAtIdx?.induct_unfolding",
"HSub.hSub",
"Option.getD",
"Std.DTreeMap.Internal.Impl.Const.entryAtIdxD",
"Option.some",
"Ordering",
"Ordering.eq",
"Std.DTreeMap.Internal.Impl.size",
"Std.DTreeMap.Internal.Impl.inner",
"... | true |
Int64.le_minValue_iff | Init.Data.SInt.Lemmas | [
"Int64",
"Int64.minValue_le",
"LE.le",
"Int64.le_antisymm",
"Int64.le_refl._simp_1",
"Iff",
"Int64.minValue",
"Iff.intro",
"of_eq_true",
"Eq.ndrec",
"Eq.symm",
"Eq",
"instLEInt64"
] | true |
TensorProduct.instInner | Mathlib.Analysis.InnerProductSpace.TensorProduct | [
"InnerProductSpace.toNormedSpace",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Inner.mk",
"AddCommGroup.toAddCommMonoid",
"TensorProduct.addCommMonoid",
"NormedSpace.toModule",
"LinearMap.instFunLike",
"NormedField.toField",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemi... | true |
MeasureTheory.integral_union_ae | Mathlib.MeasureTheory.Integral.Bochner.Set | [
"Real",
"MeasureTheory.Measure",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"MeasureTheory.NullMeasurableSet",
"PseudoMetricSpace.toUniformSpace",
"Set.instUnion",
"MeasureTheory.Measure.restrict",
"SeminormedAddGroup.toContinuousENorm",
"MeasureTheory.IntegrableOn",
"MeasureTheory.AEDisjoin... | true |
Nat.le.below.refl | Init.Prelude | [
"Nat.le.below",
"Nat.le",
"Nat",
"Nat.le.refl",
"Nat.le.below.refl"
] | true |
Batteries.PairingHeapImp.Heap.foldTreeM._unsafe_rec | Batteries.Data.PairingHeap | [
"Pure.pure",
"Batteries.PairingHeapImp.Heap.foldTreeM._unsafe_rec",
"Monad.toApplicative",
"Batteries.PairingHeapImp.Heap.size.match_1",
"Applicative.toPure",
"Unit",
"Batteries.PairingHeapImp.Heap",
"Monad.toBind",
"Bind.bind",
"Monad"
] | false |
Mathlib.Linter.TextBased.UnicodeLinter.replaceDisallowed | Mathlib.Tactic.Linter.TextBased.UnicodeLinter | [
"String",
"Option.some",
"_private.Mathlib.Tactic.Linter.TextBased.UnicodeLinter.0.Mathlib.Linter.TextBased.UnicodeLinter.replaceDisallowed.match_1",
"Option.none",
"Unit",
"Char",
"Option"
] | true |
_private.Mathlib.NumberTheory.Divisors.0.Nat.filter_dvd_eq_properDivisors._simp_1_5 | Mathlib.NumberTheory.Divisors | [
"And",
"Iff",
"and_congr_left_iff",
"propext",
"Eq"
] | false |
invMonoidHom.eq_1 | Mathlib.Algebra.Group.Hom.Basic | [
"MulOne.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Monoid.toMulOneClass",
"invMonoidHom",
"mul_inv",
"OneHom.mk",
"DivisionCommMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"DivInvMonoid.toMonoid",
"MonoidHom.mk",
"DivisionMonoid.toDivInvMono... | true |
_private.Mathlib.Data.Nat.Prime.Defs.0.Nat.prime_iff_not_exists_mul_eq._simp_1_6 | Mathlib.Data.Nat.Prime.Defs | [
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"not_lt",
"LT.lt",
"propext",
"LinearOrder.toPartialOrder",
"Eq",
"Not"
] | false |
LeanSearchClient.LoogleResult.recOn | LeanSearchClient.LoogleSyntax | [
"LeanSearchClient.LoogleResult.empty",
"String",
"Array",
"List",
"LeanSearchClient.LoogleResult",
"LeanSearchClient.LoogleResult.rec",
"LeanSearchClient.LoogleResult.failure",
"LeanSearchClient.SearchResult",
"LeanSearchClient.LoogleResult.success",
"Option"
] | false |
Std.Tactic.BVDecide.BVPred.rec | Std.Tactic.BVDecide.Bitblast.BVExpr.Basic | [
"Std.Tactic.BVDecide.BVPred.getLsbD",
"Std.Tactic.BVDecide.BVPred.bin",
"Nat",
"Std.Tactic.BVDecide.BVBinPred",
"Std.Tactic.BVDecide.BVExpr",
"Std.Tactic.BVDecide.BVPred"
] | false |
Topology.IsUpperSet.topology_eq_upperSetTopology | Mathlib.Topology.Order.UpperLowerSetTopology | [
"Topology.IsUpperSet",
"TopologicalSpace",
"Topology.upperSet",
"Eq",
"Preorder"
] | true |
_private.Init.Data.UInt.Lemmas.0.USize.pos_iff_ne_zero._simp_1_2 | Init.Data.UInt.Lemmas | [
"propext",
"Eq.comm",
"Eq"
] | false |
Vector.back? | Init.Data.Vector.Basic | [
"Vector",
"Array.back?",
"Nat",
"Vector.toArray",
"Option"
] | true |
Units.val_le_val._simp_2 | Mathlib.Algebra.Order.Monoid.Units | [
"Monoid",
"Units.val",
"Preorder.toLE",
"Units",
"Units.val_le_val",
"LE.le",
"propext",
"Units.instPreorder",
"Eq",
"Preorder"
] | false |
_private.Mathlib.Tactic.LinearCombinationPrime.0.Mathlib.Tactic.LinearCombinationPrime.expandLinearCombo.match_1 | Mathlib.Tactic.LinearCombinationPrime | [
"Mathlib.Tactic.LinearCombinationPrime.Expanded.const",
"Mathlib.Tactic.LinearCombinationPrime.Expanded",
"Lean.Syntax.Term",
"Mathlib.Tactic.LinearCombinationPrime.Expanded.proof",
"Mathlib.Tactic.LinearCombinationPrime.Expanded.casesOn"
] | false |
_private.Lean.Compiler.LCNF.ElimDeadBranches.0.Lean.Compiler.LCNF.UnreachableBranches.Value.merge._sparseCasesOn_1 | Lean.Compiler.LCNF.ElimDeadBranches | [
"Lean.Compiler.LCNF.UnreachableBranches.Value.bot",
"Nat.ne_of_beq_eq_false",
"Lean.Compiler.LCNF.UnreachableBranches.Value.top",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Array",
"Lean.Compiler.LCNF.UnreachableBranches.Value.choice",
"Nat.land",
"List",
"PUnit",
"Nat",
"Lean.Compi... | false |
_private.Lean.Compiler.LCNF.ExplicitRC.0.Lean.Compiler.LCNF.VarInfo.mk._flat_ctor | Lean.Compiler.LCNF.ExplicitRC | [
"_private.Lean.Compiler.LCNF.ExplicitRC.0.Lean.Compiler.LCNF.VarInfo.mk",
"Nat",
"Bool",
"_private.Lean.Compiler.LCNF.ExplicitRC.0.Lean.Compiler.LCNF.VarInfo"
] | false |
Int.le_emod_self_add_one_iff | Init.Data.Int.DivMod.Lemmas | [
"Eq.mpr",
"Int.instDiv",
"Dvd.dvd",
"instHDiv",
"HMul.hMul",
"congrArg",
"_private.Init.Data.Int.DivMod.Lemmas.0.Int.le_emod_self_add_one_iff._proof_1_3",
"Std.IsLinearPreorder.toIsPreorder",
"Int.one_dvd._simp_1",
"Std.instReflLeOfIsPreorder",
"HSub.hSub",
"_private.Init.Data.Int.DivMod.Lemma... | true |
CategoryTheory.MonoidalCategory.IsPushout.whiskerLeft_w | Mathlib.CategoryTheory.Monoidal.Limits.Shapes.Pullback | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.IsPushout",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"congr",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.co... | true |
Topology.instIsLowerSet | Mathlib.Topology.Order.UpperLowerSetTopology | [
"Topology.IsLowerSet",
"Topology.IsLowerSet.mk",
"TopologicalSpace",
"Topology.lowerSet",
"rfl",
"Preorder"
] | true |
StandardEtalePair.instCommRingRing._aux_8 | Mathlib.RingTheory.Etale.StandardEtale | [
"Polynomial.C",
"Polynomial.instOne",
"CommRing",
"Semiring.toModule",
"HMul.hMul",
"CommSemiring.toSemiring",
"HSub.hSub",
"StandardEtalePair.f",
"RingHom",
"Set.instSingletonSet",
"Insert.insert",
"Polynomial.ring",
"Polynomial",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"ins... | false |
_private.Mathlib.AlgebraicTopology.SimplicialSet.NerveNondegenerate.0.PartialOrder.mem_nerve_nonDegenerate_iff_strictMono._simp_1_1 | Mathlib.AlgebraicTopology.SimplicialSet.NerveNondegenerate | [
"Opposite",
"Fin.succ",
"CategoryTheory.ConcreteCategory.hom",
"PartialOrder.toPreorder",
"TypeCat.instFunLikeFun",
"Membership.mem",
"PartialOrder",
"Preorder.smallCategory",
"instOfNatNat",
"PartialOrder.mem_range_nerve_σ_iff",
"instHAdd",
"Fin.instPartialOrder",
"TypeCat.Fun",
"HAdd.hAd... | false |
Nat.iSup_le_succ | Mathlib.Data.Nat.Lattice | [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Iff.of_eq",
"congrArg",
"iSup",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"id",
"instOfNatNat",
"LE.le",
"instLENat",
"funext",
"instHAdd",
"HAdd.hAdd",
"Max.max",
"iSup_congr_Prop",
"Nat",
"congr",
"LT.lt",
... | true |
ContinuousMap.compMonoidHom'._proof_1 | Mathlib.Topology.ContinuousMap.Algebra | [
"MulOne.toOne",
"ContinuousMap",
"ContinuousMap.comp",
"ContinuousMap.instOne",
"TopologicalSpace",
"MulOneClass.toMulOne",
"ContinuousMap.one_comp",
"One.toOfNat1",
"MulOneClass",
"OfNat.ofNat",
"Eq"
] | false |
CategoryTheory.Pseudofunctor.ObjectProperty.ι | Mathlib.CategoryTheory.Bicategory.Functor.Cat.ObjectProperty | [
"CategoryTheory.Pseudofunctor.ObjectProperty.prop",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ObjectProperty.ι",
"CategoryTheory.Pseudofunctor.ObjectProperty.ι._proof_6",
"CategoryTheory.Pseudofunctor.ObjectProperty.IsClosedUnderMapObj",
"CategoryTheory.Cat.str",
"Categor... | true |
Order.exists_series_of_le_coheight | Mathlib.Order.KrullDimension | [
"RelSeries.reverse",
"Preorder.toLT",
"Order.exists_series_of_le_height",
"RelSeries.last",
"ENat.instNatCast",
"setOf",
"FiniteDimensionalOrder.match_1",
"Exists",
"id",
"RelSeries.length",
"LE.le",
"Nat.cast",
"instLEENat",
"And.casesOn",
"And",
"Exists.casesOn",
"LTSeries",
"Nat... | true |
Mathlib.Tactic.Bicategory.evalWhiskerRight_cons_of_of | Mathlib.Tactic.CategoryTheory.Bicategory.Normalize | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Bicategory.comp_whiskerRight",
"CategoryTheory.Bicategory.whiskerRight",
"id",
"CategoryTheory.Iso",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory",
"congr",
"True",
"eq_self",
"Cat... | true |
MeasureTheory.tendsto_of_uncrossing_lt_top | Mathlib.Probability.Martingale.Convergence | [
"Iff.mpr",
"NormedCommRing.toSeminormedCommRing",
"Real.partialOrder",
"Real.instLE",
"Real",
"ENNReal.ofNNReal",
"Preorder.toLT",
"Real.instArchimedean",
"Real.lattice",
"DivisionRing.toRatCast",
"Filter.liminf",
"MeasureTheory.not_frequently_of_upcrossings_lt_top",
"MulZeroClass.toMul",
... | true |
Mathlib.Tactic.RingNF.RingMode.recOn | Mathlib.Tactic.Ring.RingNF | [
"Mathlib.Tactic.RingNF.RingMode.raw",
"Mathlib.Tactic.RingNF.RingMode.rec",
"Mathlib.Tactic.RingNF.RingMode.SOP",
"Mathlib.Tactic.RingNF.RingMode"
] | false |
Algebra.Generators.toExtendScalars._proof_2 | Mathlib.RingTheory.Extension.Generators | [
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"MvPolynomial.aeval_X",
"MvPolynomial.aeval",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"IsScalarTower",
"AlgHom.funLike",
"AddMonoidAlgebra.algebra",
"Finsupp.instAddMonoid",
"MvPolynomial.X",
... | false |
Polynomial.natDegree_pow_X_add_C | Mathlib.Algebra.Polynomial.Monic | [
"Nontrivial",
"Eq.mpr",
"Polynomial.C",
"MulOne.toOne",
"HMul.hMul",
"Polynomial.Monic.natDegree_pow",
"congrArg",
"Nat.instMulOneClass",
"RingHom",
"Polynomial.natDegree_X_add_C",
"Polynomial.monic_X_add_C",
"id",
"MulOne.toMul",
"instMulNat",
"instOfNatNat",
"Polynomial.instAdd",
"... | true |
Substring.Raw.ValidFor.isEmpty | Batteries.Data.String.Lemmas | [
"Substring.Raw.isEmpty",
"congrArg",
"String.utf8Len",
"Substring.Raw.bsize",
"Substring.Raw.ValidFor",
"Substring.Raw.ValidFor.bsize",
"instOfNatNat",
"String.utf8Len_eq_zero._simp_1",
"_private.Batteries.Data.String.Lemmas.0.Substring.Raw.ValidFor.isEmpty.match_1_1",
"instBEqOfDecidableEq",
"S... | true |
_private.Std.Data.Iterators.Lemmas.Combinators.Zip.0.Std.Iter.step_intermediateZip.match_1.eq_2 | Std.Data.Iterators.Lemmas.Combinators.Zip | [
"Std.Iter.step_intermediateZip.match_1",
"Std.IterStep",
"Std.IterStep.skip",
"Id",
"Std.Iterator",
"Subtype.mk",
"Std.Iter",
"Std.IterStep.yield",
"Std.Iter.IsPlausibleStep",
"Std.IterStep.done",
"Eq.refl",
"Eq",
"Std.Iter.Step"
] | true |
Batteries.instOrientedCmpCompareOnOfOrientedOrd | Batteries.Classes.Deprecated | [
"Ord",
"Batteries.OrientedCmp.symm",
"Batteries.OrientedCmp.mk",
"Ord.compare",
"compareOn",
"Batteries.OrientedOrd",
"Batteries.OrientedCmp"
] | true |
PFun.prodMap_id_id | Mathlib.Data.PFun | [
"Part",
"Eq.mpr",
"Part.mk",
"PFun",
"Iff.of_eq",
"congrArg",
"and_self",
"Part.some",
"exists_const._simp_1",
"instInhabitedTrue",
"Membership.mem",
"Exists",
"PFun.id",
"id",
"Part.instMembership",
"Prod.mk",
"Part.mem_mk_iff._simp_1",
"Part.get",
"Prod.fst",
"funext",
"And... | true |
ModularForm.mk.noConfusion | Mathlib.NumberTheory.ModularForms.Basic | [
"SlashInvariantForm",
"ModularForm",
"OnePoint.IsBoundedAt",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"Real",
"chartedSpaceSelf",
"Complex.instNormedAddCommGroup",
"SlashInvariantForm.toFun",
"Matrix",
"UpperHalfPlane.instChartedSpaceComplex",
"instDecidableEqF... | false |
Fin.foldr_congr | Init.Data.Fin.Fold | [
"Eq.rec",
"Fin.foldr",
"Fin.cast",
"Nat",
"Eq.refl",
"Eq.symm",
"Fin",
"Eq"
] | true |
topologicalGroup_of_lieGroup | Mathlib.Geometry.Manifold.Algebra.LieGroup | [
"ContinuousInv.mk",
"DivInvOneMonoid.toInvOneClass",
"NormedSpace",
"ContMDiff.continuous",
"Monoid.toMulOneClass",
"Group",
"IsTopologicalGroup.mk",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"continuousMul_of_contMDiffMul",
"Group... | true |
_private.Mathlib.Data.Finset.Prod.0.Finset.subset_product_image_fst._simp_1_1 | Mathlib.Data.Finset.Prod | [
"Finset.mem_image",
"Finset",
"Membership.mem",
"Exists",
"And",
"Finset.instSetLike",
"propext",
"Eq",
"Finset.image",
"SetLike.instMembership",
"DecidableEq"
] | false |
Finset.prod_bij' | Mathlib.Algebra.BigOperators.Group.Finset.Defs | [
"Eq.mpr",
"congrArg",
"Finset",
"Membership.mem",
"Exists",
"Eq.rec",
"id",
"Finset.prod",
"Finset.instSetLike",
"True",
"eq_self",
"Exists.intro",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"congrFun'",
"Eq.symm",
"Eq",
"CommMonoid",
"SetLike.instMembership",
"Finset.prod_bij",
... | true |
Lean.Lsp.DependencyBuildMode._sizeOf_inst | Lean.Data.Lsp.Extra | [
"Lean.Lsp.DependencyBuildMode._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Lean.Lsp.DependencyBuildMode"
] | false |
CategoryTheory.Limits.Trident.ι | Mathlib.CategoryTheory.Limits.Shapes.WideEqualizers | [
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelFamily",
"CategoryTheory.Limits.Trident",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.parallelFamily",
"CategoryTheory.Limits.Cone.pt"... | true |
_private.Init.Data.BitVec.Lemmas.0.BitVec.toInt_mul_toInt_lt_neg_two_pow_iff._proof_1_8 | Init.Data.BitVec.Lemmas | [
"instPowNat",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Lean.Omega.Int.le_of_not_lt",
"HMul.hMul",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.In... | false |
AlgebraicGeometry.Scheme.OpenCover.finiteSubcover_X | Mathlib.AlgebraicGeometry.Cover.Open | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"CategoryTheory.PreZeroHypercover.f",
"AlgebraicGeometry.Scheme.OpenCover.finiteSubcover",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
"TopCat.instCat... | true |
Lean.RBNode.leaf | Lean.Data.RBMap | [
"Lean.RBNode",
"Lean.RBNode.leaf"
] | true |
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