name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
NonUnitalSubalgebra.topologicalClosure._proof_1 | Mathlib.Topology.Algebra.NonUnitalAlgebra | [
"Distrib.toAdd",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"TopologicalSpace",
"NonUnitalSemiring",
"NonUnitalNonAssocSemiring.toDistrib",
"IsSemitopologicalSemiring",
"ContinuousAdd",
"IsSemitopologicalSemiring.toContinuousAdd"
] | false |
UniqueFactorizationMonoid | Mathlib.RingTheory.UniqueFactorizationDomain.Defs | [
"CommMonoidWithZero",
"UniqueFactorizationMonoid.mk"
] | true |
Rep.instConcreteCategoryIntertwiningMapVρ._proof_4 | Mathlib.RepresentationTheory.Rep.Basic | [
"Monoid",
"Rep.V",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Rep.instCategory",
"Rep.hV1",
"Representation.IntertwiningMap.instFunLike",
"id",
"Rep",
"Rep.ρ",
"CategoryTheory.CategoryStruct.comp",
"Semiring",
"Eq.refl",
"Represe... | false |
Fin.decodeEmpty | Batteries.Data.Fin.Coding | [
"Fin.decodeEmpty.match_1",
"instOfNatNat",
"Empty",
"Nat",
"OfNat.ofNat",
"Fin"
] | true |
TrivSqZeroExt.inr_injective | Mathlib.Algebra.TrivSqZeroExt.Basic | [
"Function.LeftInverse.injective",
"TrivSqZeroExt.snd",
"TrivSqZeroExt.inr",
"TrivSqZeroExt",
"TrivSqZeroExt.snd_inr",
"Function.Injective",
"Zero"
] | true |
ClosedSubmodule.orthogonal_orthogonal_eq | Mathlib.Analysis.InnerProductSpace.Projection.Submodule | [
"Set.ext",
"InnerProductSpace.toNormedSpace",
"Submodule",
"SetLike.mem_coe._simp_1",
"Submodule.toAddSubmonoid",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Submodule.orthogonal_orthogonal",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddSubsemigr... | true |
HomologicalComplex.mapBifunctor₁₂.d₁ | Mathlib.Algebra.Homology.BifunctorAssociator | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"instHSMul",
"HomologicalComplex.mapBifunctor₁₂.ιOrZero",
"HMul.hMul",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.category",
"CategoryTheory.functorCategoryPr... | true |
SSet.skeletonOfMono_obj_eq_top | Mathlib.AlgebraicTopology.SimplicialSet.Skeleton | [
"Eq.mpr",
"SSet.Subcomplex.range",
"Lattice.toSemilatticeSup",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CompleteLattice.toLattice",
"congrArg",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category",
"SSet.skeleton",
"Preorder.toLE",
"CategoryTheory.Subfunct... | true |
CategoryTheory.GrothendieckTopology.mk.noConfusion | Mathlib.CategoryTheory.Sites.Grothendieck | [
"Lattice.toSemilatticeSup",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CompleteLattice.toLattice",
"HEq.refl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toBoundedOrder",
"id",
"CategoryTheory.Sieve.arrows",
"CategoryTheory.Sieve",
"CategoryT... | false |
IsUniformAddGroup.to_topologicalAddGroup | Mathlib.Topology.Algebra.IsUniformGroup.Defs | [
"AddGroup.toSubtractionMonoid",
"UniformSpace",
"NegZeroClass.toNeg",
"instUniformSpaceProd",
"ContinuousNeg.mk",
"AddMonoid.toAddZeroClass",
"uniformContinuous_add",
"uniformContinuous_neg",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"... | true |
Birkhoff_inequalities | Mathlib.Algebra.Order.Group.Unbundled.Abs | [
"Lattice",
"Lattice.toSemilatticeSup",
"abs",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"HSub.hSub",
"AddLeftMono",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"SemilatticeInf.toPartialOrder",
"AddZeroClass.toAddZero",
"SemilatticeSup.toMax",
"AddCommGroup",
"SemilatticeInf.to... | true |
AbsoluteValue.instSetoid | Mathlib.Analysis.AbsoluteValue.Equivalence | [
"PartialOrder",
"AbsoluteValue.instSetoid._proof_1",
"Setoid",
"Setoid.mk",
"Semiring",
"AbsoluteValue.IsEquiv",
"AbsoluteValue"
] | true |
BddLat.Hom.casesOn | Mathlib.Order.Category.BddLat | [
"BddLat.toLat",
"Lat.carrier",
"_private.Mathlib.Order.Category.BddLat.0.BddLat.Hom.mk",
"BddLat.Hom.rec",
"BoundedLatticeHom",
"BddLat",
"Lat.str",
"BddLat.Hom",
"BddLat.isBoundedOrder"
] | false |
Std.Sat.AIG.BinaryRefVec.rhs_get_cast | Std.Sat.AIG.RefVec | [
"Std.Sat.AIG.RefVec.get",
"Std.Sat.AIG.Ref.cast",
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.Ref.mk",
"congrArg",
"Std.Sat.AIG.RefVec.get_cast",
"Std.Sat.AIG.BinaryRefVec.rhs",
"Std.Sat.AIG.Ref.cast_eq._proof_2",
"Std.Sat.AIG.BinaryRefVec",
"LE.le",
"instLENat",
"Std.Sat.AIG.Ref",
"Std.Sat.AIG",
"Na... | true |
FormalMultilinearSeries.le_radius_of_summable_norm | Mathlib.Analysis.Analytic.ConvergenceRadius | [
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real",
"ENNReal.ofNNReal",
"NormedSpace.toIsBoundedSMul",
"HMul.hMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"FormalMultilinearSeries",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedSp... | true |
Ordinal.veblenWith.match_1 | Mathlib.SetTheory.Ordinal.Veblen | [
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"Subtype.casesOn",
"Membership.mem",
"Subtype",
"Subtype.mk",
"Set.Iio",
"Set.instMembership",
"Ordinal",
"Set"
] | false |
gal_zero_isSolvable | Mathlib.FieldTheory.AbelRuffini | [
"IsSolvable",
"Polynomial.Gal",
"isSolvable_of_subsingleton",
"inferInstance",
"Polynomial.instGroupGal",
"Polynomial.Gal.uniqueGalZero",
"Field.toSemifield",
"Polynomial",
"Unique.instSubsingleton",
"Semifield.toDivisionSemiring",
"DivisionSemiring.toSemiring",
"Zero.toOfNat0",
"Polynomial.... | true |
Lean.Server.Test.Runner.logRpcResponse | Lean.Server.Test.Runner | [
"Pure.pure",
"Functor.discard",
"Lean.Server.Test.Runner.Client.NormalizeState",
"Lean.Json",
"Lean.Lsp.Ipc.IpcM",
"Monad.toApplicative",
"IO",
"ReaderT.instMonad",
"Lean.Server.Test.Runner.RunnerState",
"instMonadEIO",
"Id",
"IO.Process.Child",
"Applicative.toPure",
"Lean.Lsp.Ipc.ipcStdio... | true |
hnot_le_iff_codisjoint_right | Mathlib.Order.Heyting.Basic | [
"CoheytingAlgebra.toHNot",
"Eq.mpr",
"Codisjoint",
"Lattice.toSemilatticeSup",
"congrArg",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"CoheytingAlgebra.toOrderTop",
"SemilatticeSup.toMax",
"CoheytingAlgebra",
"id",
"codisjoint_iff_le_sup",
"LE... | true |
_private.Lean.Compiler.LCNF.ExtractClosed.0.Lean.Compiler.LCNF.Decl.extractClosed.match_1 | Lean.Compiler.LCNF.ExtractClosed | [
"Lean.Compiler.LCNF.Decl",
"Prod.mk",
"Lean.Compiler.LCNF.Purity.pure",
"Lean.Compiler.LCNF.ExtractClosed.State",
"Prod",
"Prod.casesOn"
] | false |
LinearMap.instModuleDomMulActOfSMulCommClass._proof_1 | Mathlib.Algebra.Module.LinearMap.Basic | [
"DomMulAct",
"instHSMul",
"LinearMap.ext",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"DomMulAct.instMonoidOfMulOpposite",
"LinearMap.instDistribMulActionDomMulActOfSMulCommClass",
"Distrib.toAdd",
"DistribSMul.toSMulZeroClass",
"LinearMa... | false |
Finite.Set.finite_replacement | Mathlib.Data.Set.Finite.Range | [
"Finite",
"setOf",
"Finite.Set.finite_range",
"Exists",
"Set.Elem",
"Eq"
] | true |
SSet.Subcomplex.Pairing.pairingCore._proof_3 | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.PairingCore | [
"SSet.S.simplex",
"Eq.mpr",
"SSet.S",
"Equiv.instEquivLike",
"SSet.Subcomplex.Pairing.isUniquelyCodimOneFace",
"congrArg",
"SSet.Subcomplex.Pairing.p",
"Membership.mem",
"SSet.N.ext_iff",
"SSet.Subcomplex.N",
"Set.Elem",
"id",
"Equiv",
"Subtype",
"SSet.Subcomplex.N.cast",
"SSet.Subcomp... | false |
convexOn_norm | Mathlib.Analysis.Normed.Module.Convex | [
"Norm.norm",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real.instLE",
"Real",
"instHSMul",
"Trans.trans",
"SeminormedAddCommGroup",
"instSMulOfMul",
"HMul.hMul",
"norm_smul",
"NormedSpace",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAd... | true |
_private.Mathlib.Probability.Kernel.RadonNikodym.0.ProbabilityTheory.Kernel.singularPart_compl_mutuallySingularSetSlice._simp_1_8 | Mathlib.Probability.Kernel.RadonNikodym | [
"AddGroup.toSubtractionMonoid",
"sub_eq_zero",
"HSub.hSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubNegMonoid.toSub",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"propext",
"Zero.toOfNat0",
"OfNat.ofNat",
"NegZeroClass.toZero",
"Eq"
] | false |
TopologicalSpace.OpenNhdsOf.instMax | Mathlib.Topology.Sets.Opens | [
"TopologicalSpace.OpenNhdsOf.toOpens",
"Lattice.toSemilatticeSup",
"Max.mk",
"TopologicalSpace.Opens.instCompleteLattice",
"TopologicalSpace.OpenNhdsOf",
"TopologicalSpace.Opens",
"TopologicalSpace.OpenNhdsOf.mk",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"Max",
"... | true |
AddGroupExtension.Equiv.Simps.symm_apply.eq_1 | Mathlib.GroupTheory.GroupExtension.Defs | [
"AddGroupExtension",
"AddGroupExtension.Equiv.Simps.symm_apply",
"AddGroupExtension.Equiv.instEquivLike",
"AddGroup",
"Eq.refl",
"AddGroupExtension.Equiv",
"Eq",
"DFunLike.coe",
"AddGroupExtension.Equiv.symm",
"EquivLike.toFunLike"
] | true |
Lean.Meta.Grind.Arith.Cutsat.LeCnstr.mk.sizeOf_spec | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Meta.Grind.Arith.Cutsat.LeCnstr._sizeOf_inst",
"instOfNatNat",
"Int.Linear.Poly._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Lean.Meta.Grind.Arith.Cutsat.LeCnstr",
"Nat",
"SizeOf.sizeOf",
"Lean.Meta.Grind.Arith.Cutsat.LeCnstr.mk",
"instAddNat",
"Eq.refl",
"Lean.Meta.Grind.Arith.Cutsat.LeCnst... | true |
ZeroHom.ctorIdx | Mathlib.Algebra.Group.Hom.Defs | [
"ZeroHom",
"Nat",
"Zero"
] | false |
Std.HashSet.Raw.any_eq_not_all_not | Std.Data.HashSet.RawLemmas | [
"Bool.not",
"Std.HashMap.Raw.any_eq_not_all_not",
"Std.HashSet.Raw.inner",
"Std.HashSet.Raw.WF",
"Unit",
"Std.HashSet.Raw.WF.out",
"Std.HashSet.Raw.all",
"Bool",
"Std.HashSet.Raw.any",
"Hashable",
"BEq",
"Eq",
"Std.HashSet.Raw"
] | true |
Std.DTreeMap.Internal.Cell.of | Std.Data.DTreeMap.Internal.Cell | [
"Std.DTreeMap.Internal.Cell.of._proof_1",
"Std.DTreeMap.Internal.Cell.ofEq",
"Ord",
"Ord.compare",
"Std.DTreeMap.Internal.Cell"
] | true |
Lean.Elab.Tactic.Do.Uses.casesOn | Lean.Elab.Tactic.Do.LetElim | [
"Lean.Elab.Tactic.Do.Uses.rec",
"Lean.Elab.Tactic.Do.Uses.one",
"Lean.Elab.Tactic.Do.Uses",
"Lean.Elab.Tactic.Do.Uses.zero",
"Lean.Elab.Tactic.Do.Uses.many"
] | false |
MeasureTheory.AddContent.mk.injEq | Mathlib.MeasureTheory.Measure.AddContent | [
"MeasureTheory.AddContent.mk.inj",
"ChainCompletePartialOrder.instOfCompleteLattice",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Eq.propIntro",
"Finset",
"Set.PairwiseDisjoint",
"AddMonoid.toAddZeroClass",
"Set.sUnion",
"Membership.mem",
"AddZeroClass.toAddZero",
"MeasureTheory.AddConte... | true |
PosNum.land._f | Mathlib.Data.Num.Bitwise | [
"PosNum.lor.match_1",
"PosNum.bit1",
"Num.bit1",
"PosNum.below",
"instOneNum",
"PosNum.bit0",
"Num",
"instZeroNum",
"Num.bit0",
"One.toOfNat1",
"Zero.toOfNat0",
"PosNum",
"OfNat.ofNat",
"PosNum.one"
] | false |
Filter.mem_comap._simp_1 | Mathlib.Order.Filter.Map | [
"Filter.instMembership",
"Membership.mem",
"Exists",
"HasSubset.Subset",
"Filter.mem_comap",
"And",
"Set.preimage",
"propext",
"Eq",
"Filter",
"Filter.comap",
"Set.instHasSubset",
"Set"
] | false |
Mathlib.Tactic.Push.initFn._@.Mathlib.Tactic.Push.609137422._hygCtx._hyg.4 | Mathlib.Tactic.Push | [
"Lean.Option",
"Lean.Name.mkStr5",
"IO",
"Lean.Option.Decl.mk",
"Lean.KVMap.instValueBool",
"Lean.Option.register",
"Bool",
"Lean.Name.mkStr2",
"Bool.false"
] | false |
_private.Lean.Meta.Tactic.Constructor.0.Lean.MVarId.existsIntro._sparseCasesOn_2 | Lean.Meta.Tactic.Constructor | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"List.rec",
"List.cons",
"Nat.land",
"List",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"List.ctorIdx",
"List.nil"
] | false |
Graded.equiv_symm_apply_coe | Mathlib.Data.FunLike.Graded | [
"SetLike",
"Equiv.instEquivLike",
"Membership.mem",
"Equiv",
"Subtype",
"EquivLike",
"Eq.refl",
"Equiv.symm",
"EquivLike.inv",
"GradedEquivLike",
"Subtype.val",
"Eq",
"DFunLike.coe",
"Graded.equiv",
"SetLike.instMembership",
"EquivLike.toFunLike"
] | true |
_private.Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap.0.Std.IterM.toList_filterMapWithPostcondition_filterMapWithPostcondition'.match_1.splitter | Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap | [
"Option.some",
"Option.none",
"Unit",
"_private.Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap.0.Std.IterM.toList_filterMapWithPostcondition_filterMapWithPostcondition'.match_1",
"Option"
] | true |
CategoryTheory.inhabitedLiftableCocone | Mathlib.CategoryTheory.Limits.Creates | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"CategoryTheory.idLiftsCocone",
"Inhabited",
"CategoryTheory.LiftableCocone",
"CategoryTheory.Category",
"Inhabited.mk"
] | true |
_private.Mathlib.Algebra.Homology.DerivedCategory.TStructure.0.DerivedCategory.TStructure.t._proof_6 | Mathlib.Algebra.Homology.DerivedCategory.TStructure | [
"False",
"Classical.byContradiction",
"eq_false_of_decide",
"Int.decLe",
"Int.not_le_eq",
"False.casesOn",
"Int",
"LE.le",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"Bool",
"Int.instAdd",
"Lean.Grind.intro_with_eq",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Not",
"Int.instLEInt",
"E... | false |
R1Space.specializes_or_disjoint_nhds | Mathlib.Topology.Separation.Basic | [
"Specializes",
"R1Space",
"Filter.instCompleteLatticeFilter",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"nhds",
"CompleteLattice.toBoundedOrder",
"TopologicalSpace",
"BoundedOrder.toOrderBot",
"Or",
"Filter",
"Filter.instPartialOrder"
] | true |
Aesop.Frontend.Feature.elab._unsafe_rec | Aesop.Frontend.RuleExpr | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Aesop.Frontend.Feature.priority",
"Bool.not",
"Aesop.Frontend.PhaseName.elab",
"Lean.identKind",
"Lean.Elab.Term.instMonadTermElabM",
"Lean.Syntax.getArgs",
"Lean.Meta... | false |
_private.Mathlib.CategoryTheory.Triangulated.TStructure.TruncLEGT.0.CategoryTheory.Triangulated.TStructure.isLE_truncLE_obj._proof_1_1 | Mathlib.CategoryTheory.Triangulated.TStructure.TruncLEGT | [
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"Int.Linear.norm_le",
"Int.Linear.le_unsat",
"Classical.byContradiction",
"Int.not_le_eq",
"Eq.mp",
"Lean.RArray.branch",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"Int.instNegInt",
"instOfNatNat",
"Int",
"LE.le",
"Int.Linear.Poly.num",
"... | false |
Set.self_mem_Iic | Mathlib.Order.Interval.Set.Basic | [
"instReflLe",
"Preorder.toLE",
"Std.le_refl._simp_1",
"Set.mem_Iic._simp_2",
"Membership.mem",
"LE.le",
"True",
"of_eq_true",
"Set.Iic",
"Set.instMembership",
"Preorder",
"Eq.trans",
"Set"
] | true |
Submonoid.center.commMonoid'.eq_1 | Mathlib.GroupTheory.Submonoid.Center | [
"Submonoid.center.commMonoid'._proof_6",
"MulOne.toOne",
"Semigroup.mk",
"Membership.mem",
"Submonoid.center.commMonoid'._proof_2",
"MulOne.toMul",
"Subtype",
"npowRecAuto",
"Submonoid.toMulOneClass",
"Submonoid.center.commMonoid'._proof_1",
"Monoid.mk",
"Submonoid.center.commMonoid'._proof_4"... | true |
SimpleGraph.IsFiveWheelLike.card_right | Mathlib.Combinatorics.SimpleGraph.FiveWheelLike | [
"Finset",
"SimpleGraph",
"Nat",
"SimpleGraph.IsFiveWheelLike.symm",
"SimpleGraph.IsFiveWheelLike",
"Finset.card",
"SimpleGraph.IsFiveWheelLike.card_left",
"Eq",
"DecidableEq"
] | true |
Lean.Elab.Term.instToStringArg.match_1 | Lean.Elab.App | [
"Lean.Syntax",
"Lean.Elab.Term.Arg.expr",
"Lean.Expr",
"Lean.Elab.Term.Arg.stx",
"Lean.Elab.Term.Arg",
"Lean.Elab.Term.Arg.casesOn"
] | false |
_private.Mathlib.GroupTheory.FreeGroup.Orbit.0.FreeGroup.startsWith_mk_mul._proof_1_10 | Mathlib.GroupTheory.FreeGroup.Orbit | [
"FreeGroup.toWord",
"Lean.Grind.Nat.lt_eq",
"instOfNatNat",
"LE.le",
"instLENat",
"Nat",
"LT.lt",
"Eq.substr",
"Bool",
"instLTNat",
"Prod",
"OfNat.ofNat",
"List.length",
"FreeGroup",
"DecidableEq"
] | false |
_private.Mathlib.Tactic.Explode.Pretty.0.Mathlib.Explode.rowToMessageData.match_1 | Mathlib.Tactic.Explode.Pretty | [
"Unit.unit",
"Mathlib.Explode.Status",
"Mathlib.Explode.Status.casesOn",
"Mathlib.Explode.Status.reg",
"Unit",
"Mathlib.Explode.Status.cintro",
"Mathlib.Explode.Status.lam",
"Mathlib.Explode.Status.sintro",
"Mathlib.Explode.Status.intro"
] | false |
WithBot.ofDual_le_iff | Mathlib.Order.WithBot | [
"OrderDual.instLE",
"OrderDual.toDual",
"False",
"WithBot.some",
"WithBot",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"WithBot.coe_le_coe._simp_2",
"WithTop.coe_le_coe._simp_1",
"congrArg",
"WithBot.instOrderBot",
"le_top._simp_2",
"WithTop.coe_ne_top._simp_1",
"WithTop.top_le_iff._simp_1... | true |
AlgebraicGeometry.Scheme.instIsOpenImmersionMapOfHomAwayAlgebraMap | Mathlib.AlgebraicGeometry.OpenImmersion | [
"AlgebraicGeometry.Spec",
"CommRing",
"Algebra.algebraMap",
"OreLocalization.instAlgebra",
"CommSemiring.toSemiring",
"AlgebraicGeometry.Scheme.isOpenImmersion_SpecMap_localizationAway",
"Localization.Away",
"CommRingCat.ofHom",
"AlgebraicGeometry.Spec.map",
"Algebra.id",
"CommRing.toCommSemirin... | true |
Matrix.adjugate_conjTranspose | Mathlib.LinearAlgebra.Matrix.Adjugate | [
"Eq.mpr",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"congrArg",
"Matrix",
"id",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"StarAddMonoid.toInvolutiveStar",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"StarRing.toStarAddMonoid",
"Ri... | true |
CategoryTheory.GradedNatTrans.naturality_assoc | Mathlib.CategoryTheory.Enriched.Basic | [
"CategoryTheory.HalfBraiding.β",
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.HalfBraiding",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.GradedNatTrans.app",
"Eq.mp",
"CategoryTheory.EnrichedFunctor",
"id",
"Sigma.f... | true |
Submodule.smithNormalFormOfLE._proof_7 | Mathlib.LinearAlgebra.FreeModule.PID | [
"Submodule",
"CommRing",
"instHSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Fin.castLE",
"Submodule.addCommMonoid",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"AddCommG... | false |
DyckWord.le_add_self | Mathlib.Combinatorics.Enumerative.DyckWord | [
"instAddDyckWord",
"Preorder.toLE",
"DyckWord",
"DyckWord.le_add_self._unary",
"DyckWord.instPreorder",
"LE.le",
"instHAdd",
"HAdd.hAdd"
] | true |
CategoryTheory.Bicategory.Adj.Bicategory.associator_hom_τl | Mathlib.CategoryTheory.Bicategory.Adjunction.Adj | [
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Bicategory.Adj.Hom.l",
"Quiver.Hom",
"CategoryTheory.Bicategory.toCategoryStruct",
"CategoryTheory.Bicategory.Adj.Hom₂.τl",
"CategoryTheory.Bicategory.Adj.obj",
"CategoryTheory.Bicategory.Adj.instCategoryHom",
"CategoryTheory.Bicategory",
"Ca... | true |
NonAssocRing.mk._flat_ctor | Mathlib.Algebra.Ring.Defs | [
"AddGroupWithOne.intCast_negSucc._autoParam",
"AddMonoidWithOne.natCast_zero._autoParam",
"NonAssocRing.mk",
"Mul.mk",
"One.mk",
"HMul.hMul",
"AddGroupWithOne.intCast_ofNat._autoParam",
"SubNegMonoid.mk",
"Add.mk",
"Neg.mk",
"AddMonoidWithOne.natCast_succ._autoParam",
"AddMonoid.nsmul_zero._au... | false |
upperSemicontinuousOn_iff_restrict._simp_1 | Mathlib.Topology.Semicontinuity.Defs | [
"Membership.mem",
"Set.Elem",
"UpperSemicontinuous",
"TopologicalSpace",
"propext",
"instTopologicalSpaceSubtype",
"Set.restrict",
"Eq",
"Set.instMembership",
"UpperSemicontinuousOn",
"upperSemicontinuousOn_iff_restrict",
"Preorder",
"Set"
] | false |
Lean.Parser.Command.grindPattern._regBuiltin.Lean.Parser.Command.GrindCnstr.guard.parenthesizer_105 | Lean.Meta.Tactic.Grind.Parser | [
"Lean.Name.mkStr5",
"IO",
"Lean.Parser.Command.GrindCnstr.guard.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"Lean.PrettyPrinter.parenthesizerAttribute",
"Unit",
"Lean.Name.mkStr6",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
_private.Init.Core.0.if_neg.match_1_1 | Init.Core | [
"Decidable.isTrue",
"Decidable.casesOn",
"Decidable",
"Decidable.isFalse",
"Not"
] | false |
NonUnitalStarSubalgebra.ofClass._proof_2 | Mathlib.Algebra.Star.NonUnitalSubalgebra | [
"SetLike",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddZero.toZero",
"Zero.toOfNat0",
"AddCommMonoid.toAddMonoid",
"ZeroMemClass.zero_mem",
"NonUnitalSubsemiringClass",
"NonUnitalNonAssocSemiring",
"OfNat.ofNat",
"N... | false |
_private.Mathlib.Order.KrullDimension.0.Order.height_eq_krullDim_Iic._simp_1_3 | Mathlib.Order.KrullDimension | [
"ge_iff_le",
"GE.ge",
"LE.le",
"LE",
"propext",
"Eq"
] | false |
Subgroup.commutator_le_focalSubgroupOf | Mathlib.GroupTheory.Focal | [
"Eq.mpr",
"Subgroup.closure",
"congrArg",
"HEq.refl",
"PartialOrder.toPreorder",
"Bracket.bracket",
"setOf",
"Group",
"Preorder.toLE",
"Membership.mem",
"Subgroup.focalSubgroupOf",
"Exists",
"Eq.casesOn",
"id",
"Subtype",
"Subgroup",
"commutatorElement",
"LE.le",
"Subgroup.closur... | true |
instDecidableEqNzsNum | Mathlib.Data.Num.Bitwise | [
"instDecidableEqNzsNum.decEq",
"NzsNum",
"DecidableEq"
] | true |
_private.Mathlib.Analysis.SpecialFunctions.Pow.Real.0.Mathlib.Meta.NormNum.evalRPow.match_1 | Mathlib.Analysis.SpecialFunctions.Pow.Real | [
"Lean.Level.ctorIdx",
"Lean.Meta.MetaM",
"Nat.hasNotBit",
"Lean.Expr.sort",
"Lean.Level",
"Qq.Quoted",
"Lean.Level.zero",
"Mathlib.Meta.NormNum.Result",
"_private.Mathlib.Analysis.SpecialFunctions.Pow.Real.0.Mathlib.Meta.Positivity.evalRpowZero._sparseCasesOn_1",
"Lean.Level.succ",
"Lean.Level.i... | false |
tendsto_mul | Mathlib.Topology.Algebra.Monoid | [
"Continuous",
"HMul.hMul",
"ContinuousAt",
"instTopologicalSpaceProd",
"Mul",
"nhds",
"Prod.mk",
"ContinuousMul.continuous_mul",
"Prod.fst",
"TopologicalSpace",
"ContinuousMul",
"Filter.Tendsto",
"Iff.mp",
"Prod",
"Prod.snd",
"continuous_iff_continuousAt",
"instHMul"
] | true |
Lean.Compiler.LCNF.LambdaLifting.State.recOn | Lean.Compiler.LCNF.LambdaLifting | [
"Lean.Compiler.LCNF.LambdaLifting.State",
"Lean.Compiler.LCNF.Decl",
"Lean.Compiler.LCNF.Purity.pure",
"Array",
"Nat",
"Lean.Compiler.LCNF.LambdaLifting.State.mk",
"Lean.Compiler.LCNF.LambdaLifting.State.rec"
] | false |
CategoryTheory.Abelian.mono_inr_of_isColimit | Mathlib.CategoryTheory.Abelian.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Limits.colimit.isColimit",
"CategoryTheory.Abelian"... | true |
HomotopicalAlgebra.FibrantObject.HoCat.localizerMorphismResolution | Mathlib.AlgebraicTopology.ModelCategory.FibrantObjectHomotopy | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomotopicalAlgebra.FibrantObject.instCategoryWithWeakEquivalencesHoCat",
"CategoryTheory.Quotient.category",
"HomotopicalAlgebra.ModelCategory.categoryWithFibrations",
"HomotopicalAlgebra.FibrantObject",
"HomotopicalAlgebra.FibrantObject.homRel",
... | true |
Aesop.popGoal? | Aesop.Search.SearchM | [
"Pure.pure",
"Aesop.BaseM",
"Aesop.SearchM.State.iteration",
"Aesop.Queue.popGoal",
"_private.Aesop.Search.SearchM.0.Aesop.popGoal?.match_1",
"Lean.Core.instMonadLiftIOCoreM",
"IO.instMonadLiftSTRealWorldBaseIO",
"ReaderT",
"Aesop.SearchM.instMonad",
"Lean.Meta.State",
"instMonadLiftT",
"Monad... | true |
_private.Mathlib.Analysis.Complex.JensenFormula.0.norm_herglotzLogIntegrand_circleMap_le | Mathlib.Analysis.Complex.JensenFormula | [
"_private.Mathlib.Analysis.Complex.JensenFormula.0.norm_herglotzLogIntegrand_circleMap_le._proof_1_8",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"sub_le_sub_right",
"Iff.mpr",
"Real.instIsOrderedRing",
"Norm.norm",
"div_le_div₀",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"GroupWithZero.t... | true |
Algebra.SubmersivePresentation.ofHasCoeffs | Mathlib.RingTheory.Extension.Presentation.Core | [
"Algebra.SubmersivePresentation.mk",
"Algebra.Presentation.relationOfHasCoeffs",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"AddMonoidAlgebra.commRing",
"CommSemiring.toSemiring",
"Algebra.Presentation.ModelOfHasCoeffs",
"IsScalarTower",
"Algebra.SubmersivePresentation.instHa... | true |
Valuation.ltSubmodule_monotone | Mathlib.RingTheory.Valuation.Integers | [
"GroupWithZero.toMonoidWithZero",
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Submodule",
"Semiring.toModule",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"Valuation.ltAddSubgroup_monotone",
"PartialOrder.toPreorder",
"Monotone",
"LinearOrderedCommMonoidWithZero.toLinear... | true |
OrthonormalBasis.coe_equiv_euclideanSpace | Mathlib.Analysis.InnerProductSpace.PiL2 | [
"LinearIsometryEquiv.instEquivLike",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"instHSMul",
"fact_one_le_two_ennreal",
"Finset.univ",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Finset",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"AddCommGroup.t... | true |
SModEq.symm | Mathlib.LinearAlgebra.SModEq.Basic | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"Submodule.Quotient.mk",
"Submodule.hasQuotient",
"AddCommGroup",
"HasQuotient.Quotient",
"Module",
"Eq.symm",
"Ring.toSemiring",
"Ring",
"SModEq"
] | true |
_private.Mathlib.MeasureTheory.VectorMeasure.Basic.0.MeasureTheory.Measure.zero_le_toSignedMeasure._simp_1_1 | Mathlib.MeasureTheory.VectorMeasure.Basic | [
"Real.instLE",
"Real",
"MeasureTheory.Measure",
"Real.instZero",
"MeasureTheory.measureReal_nonneg",
"MeasureTheory.Measure.real",
"LE.le",
"MeasurableSpace",
"True",
"eq_true",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"Set"
] | false |
Units.add._proof_1 | Mathlib.Analysis.Normed.Ring.Units | [
"Norm.norm",
"Units.val",
"NegZeroClass.toNeg",
"Real",
"NormedRing.toRing",
"HMul.hMul",
"Real.instInv",
"HasSummableGeomSeries",
"Real.instLT",
"Units",
"Units.oneSub",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",... | false |
CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.mk.injEq | Mathlib.CategoryTheory.Localization.Predicate | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"Eq.propIntro",
"CategoryTheory.Functor.comp",
"CategoryTheory.MorphismProperty.IsInvertedBy",
"Eq.ndrec",
"CategoryTheory.Localization.StrictUniversalPropertyFixedTarget.mk",
"Eq.refl",
"CategoryTheory.Localization.StrictUniversalProperty... | true |
Bifunctor.snd | Mathlib.Control.Bifunctor | [
"id",
"Bifunctor.bimap",
"Bifunctor"
] | true |
Lean.mkAppRange | Lean.Expr | [
"_private.Lean.Expr.0.Lean.mkAppRangeAux",
"Lean.Expr",
"Array",
"Nat"
] | true |
Lean.Parser.Term.fun._regBuiltin.Lean.Parser.Term.fun_1 | Lean.Parser.Term | [
"IO",
"Lean.Parser.Term.fun",
"Unit",
"Lean.Parser.addBuiltinLeadingParser",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | false |
MeasureTheory.UniformIntegrable.memLp_of_ae_tendsto | Mathlib.MeasureTheory.Function.UniformIntegrable | [
"MeasureTheory.ae",
"MeasureTheory.UniformIntegrable.uniformIntegrable_of_ae_tendsto",
"MeasureTheory.Measure",
"Filter.NeBot",
"Filter.Eventually",
"setOf",
"MeasureTheory.UniformIntegrable",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"Exists",
"nhds",
"Set.Elem",
"SeminormedAddG... | true |
_private.Aesop.Builder.Forward.0.Aesop.RuleBuilder.getImmediatePremises._sparseCasesOn_1 | Aesop.Builder.Forward | [
"Nat.ne_of_beq_eq_false",
"Lean.BinderInfo.rec",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Nat.land",
"Lean.BinderInfo.ctorIdx",
"Nat",
"Bool",
"Lean.BinderInfo.instImplicit",
"Eq.refl",
"Lean.BinderInfo.default",
"Lean.BinderInfo",
"OfNat.ofNat",
"Bool.false",
"Lean.BinderIn... | false |
Set.infinite_of_injective_forall_mem | Mathlib.Data.Set.Finite.Basic | [
"Set.Infinite.mono",
"Set.infinite_range_of_injective",
"congrArg",
"Membership.mem",
"Eq.mp",
"HasSubset.Subset",
"propext",
"Infinite",
"Set.range",
"Function.Injective",
"Set.range_subset_iff",
"Eq.symm",
"Set.instMembership",
"Set.Infinite",
"Set.instHasSubset",
"Set"
] | true |
IntCast.rec | Init.Data.Int.Basic | [
"IntCast",
"Int",
"IntCast.mk"
] | false |
_private.Mathlib.Topology.Separation.Hausdorff.0.t2_iff_isClosed_diagonal._simp_1_4 | Mathlib.Topology.Separation.Hausdorff | [
"Prod.mk",
"propext",
"Prod.forall",
"Prod",
"Eq"
] | false |
QuadraticForm.radical_weightedSumSquares | Mathlib.LinearAlgebra.QuadraticForm.Radical | [
"Distrib.leftDistribClass",
"Eq.mpr",
"Pi.Function.module",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"False",
"Algebra.to_smulCommClass",
"instHSMul",
"IsDomain.to_noZeroDivisors",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Pi.addCommMonoid",
"HMul.... | true |
Std.Rxi.HasSize.rec | Init.Data.Range.Polymorphic.Basic | [
"Nat",
"Std.Rxi.HasSize",
"Std.Rxi.HasSize.mk"
] | false |
CategoryTheory.ShortComplex.RightHomologyMapData.mk | Mathlib.Algebra.Homology.ShortComplex.RightHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ShortComplex.RightHomologyData",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.RightHomologyMapData.commι._autoParam",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTh... | true |
AlgebraicGeometry.Scheme.affineOpenCoverOfSpanRangeEqTop._proof_3 | Mathlib.AlgebraicGeometry.Cover.Open | [
"Mathlib.Tactic.Push.not_exists._simp_1",
"Ideal.span_le",
"Eq.mpr",
"AlgebraicGeometry.Spec",
"Semiring.toModule",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"PrimeSpectrum.isPrime",
"congrArg",
"CommSemiring.toSemiring",
"CommRingCat",
"Classical.byContradiction",
... | false |
_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.Tree.term | Lean.Elab.Extra | [
"_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.Tree.term",
"Lean.Elab.InfoTree",
"Lean.Syntax",
"Lean.Expr",
"Lean.PersistentArray",
"_private.Lean.Elab.Extra.0.Lean.Elab.Term.Op.Tree"
] | true |
Submodule.starProjection_inj | Mathlib.Analysis.InnerProductSpace.Positive | [
"InnerProductSpace.toNormedSpace",
"Submodule",
"Submodule.starProjection",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"PartialOrder.toPreorder",
"PseudoMetricSpace.toUniformSpace",
"_private.Mathlib.Analysis.InnerProductSpace.Positive.0.Submodule.starProjection_inj._simp_1_... | true |
BiheytingHom.id_comp | Mathlib.Order.Heyting.Hom | [
"BiheytingAlgebra",
"BiheytingHom.comp",
"BiheytingHom.ext",
"BiheytingHom.id",
"BiheytingHom.instFunLike",
"BiheytingHom",
"Eq",
"DFunLike.coe",
"rfl"
] | true |
_private.Batteries.Data.String.Lemmas.0.String.foldlAux_of_valid.match_1_1 | Batteries.Data.String.Lemmas | [
"List.cons",
"List",
"List.casesOn",
"Char",
"List.nil"
] | false |
BoundedLatticeHom.toInfTopHom | Mathlib.Order.Hom.BoundedLattice | [
"Lattice",
"Lattice.toSemilatticeSup",
"SupHom.toFun",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"SemilatticeSup.toMax",
"LatticeHom.map_inf'",
"BoundedLatticeHom.map_top'",
"SemilatticeInf.toMin",
"InfTopHom.mk",
"OrderTop.toTop",
"BoundedLatticeHom",
"B... | true |
SSet.Edge.map_id | Mathlib.AlgebraicTopology.SimplicialSet.CompStruct | [
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.category",
"SSet.Truncated",
"TypeCat.instFunLikeFun",
"SSet.truncation",
"instOfNatNat",
"SSet",
"LE.le",
"instLENat",
"CategoryTheory.Functor.map",
"SSet.Tru... | true |
_private.Std.Data.String.ToNat.0.noRepetition_iff | Std.Data.String.ToNat | [
"_private.Std.Data.String.ToNat.0.NoRepetition.mk",
"_private.Std.Data.String.ToNat.0.NoRepetition",
"List.cons",
"List.IsInfix",
"List",
"Iff",
"Iff.intro",
"_private.Std.Data.String.ToNat.0.noRepetition_iff.match_1_1",
"Not",
"List.nil"
] | true |
Convexity.convexCombPair_one | Mathlib.Geometry.Convex.ConvexSpace.Defs | [
"Finsupp.instAddZeroClass",
"NonAssocSemiring.toAddCommMonoidWithOne",
"congrArg",
"Convexity.ConvexSpace",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"Preorder.toLE",
"Convexity.StdSimplex.duple",
"Convexity.StdSimplex.mk.congr_simp",
"AddZeroClass.toAddZero",... | true |
GroupExtension.Equiv.ofMonoidHom._proof_6 | Mathlib.GroupTheory.GroupExtension.Basic | [
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"Group",
"MonoidHom.comp",
"DivInvMonoid.toMonoid",
"GroupExtension.rightHom",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"Eq",
"DFunLike.coe",
"GroupExtension"
] | false |
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