name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Function.Injective.addGroupWithOne._proof_1 | Mathlib.Algebra.Ring.InjSurj | [
"AddGroup.toSubtractionMonoid",
"Int.cast",
"Eq.mpr",
"Int.cast_natCast",
"instHSMul",
"One",
"AddMonoid.toAddSemigroup",
"AddGroupWithOne.toAddGroup",
"congrArg",
"SMul",
"AddGroupWithOne.toAddMonoidWithOne",
"AddMonoid.toNSMul",
"IntCast",
"NatCast",
"id",
"Function.Injective.addMono... | false |
ProbabilityTheory.Kernel.compProd_eq_iff | Mathlib.Probability.Kernel.CompProdEqIff | [
"MeasureTheory.ae",
"ProbabilityTheory.IsFiniteKernel",
"MeasureTheory.Measure",
"MeasurableSpace.CountableOrCountablyGenerated",
"ProbabilityTheory.Kernel.instFunLike",
"Filter.EventuallyEq",
"ProbabilityTheory.Kernel.ae_eq_of_compProd_eq",
"MeasureTheory.Measure.compProd_congr",
"MeasurableSpace",... | true |
_private.Lean.Elab.PreDefinition.Structural.BRecOn.0.Lean.Elab.Structural.replaceRecApps.loop.match_12 | Lean.Elab.PreDefinition.Structural.BRecOn | [
"Unit.unit",
"Lean.Meta.MatcherApp",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Option"
] | false |
LightCondensed.discrete._proof_1 | Mathlib.Condensed.Discrete.Basic | [
"CompHausLike.instFinitaryExtensiveOfHasExplicitPullbacksOfInclusions",
"SecondCountableTopology",
"LightProfinite.instHasExplicitFiniteCoproductsAndTotallyDisconnectedSpaceCarrierSecondCountableTopology",
"TotallyDisconnectedSpace",
"LightProfinite.instHasExplicitPullbacksAndTotallyDisconnectedSpaceCarrier... | false |
PseudoMetric.noConfusion | Mathlib.Topology.MetricSpace.BundledFun | [
"HEq.refl",
"PseudoMetric",
"PseudoMetric.noConfusionType",
"LE.le",
"LE",
"instHAdd",
"HAdd.hAdd",
"eq_of_heq",
"Eq.ndrec",
"Zero.toOfNat0",
"HEq",
"OfNat.ofNat",
"Eq",
"Add",
"PseudoMetric.casesOn",
"Zero"
] | false |
NormedSpace.expSeries_sum_eq | Mathlib.Analysis.Normed.Algebra.Exponential | [
"Algebra.to_smulCommClass",
"instHSMul",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"Ring.toNonAssocRing",
"tsum_congr",
"DistribMulAction.toDistribSMul",
"IsSemitopologicalRing.toIsSemitopologicalSemiring",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithO... | true |
_private.Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity.0.chevalley_mvPolynomial_mvPolynomial._simp_1_5 | Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity | [
"SetLike",
"Membership.mem",
"SetLike.coe",
"SetLike.mem_coe",
"propext",
"Eq",
"Set.instMembership",
"SetLike.instMembership",
"Set"
] | false |
CommRingCat.casesOn | Mathlib.Algebra.Category.Ring.Basic | [
"CommRing",
"CommRingCat",
"CommRingCat.of",
"CommRingCat.rec"
] | false |
CategoryTheory.GrothendieckTopology.MayerVietorisSquare.mk'._proof_2 | Mathlib.CategoryTheory.Sites.MayerVietorisSquare | [
"Iff.mpr",
"CategoryTheory.Functor.op",
"Eq.mpr",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Square.op",
"CategoryTheory.Sheaf.isPullback_square_op_map_yoneda_presheafToSheaf_yoneda_iff",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.yon... | false |
AddEquiv.comp_right_injective | Mathlib.Algebra.Group.Equiv.Defs | [
"Function.LeftInverse.injective",
"AddEquivClass.instAddMonoidHomClass",
"AddMonoidHomClass.toAddMonoidHom",
"congrArg",
"AddMonoidHom.id",
"AddZeroClass.toAddZero",
"AddZeroClass",
"True",
"eq_self",
"AddEquiv.instAddEquivClass",
"of_eq_true",
"AddEquiv.coe_addMonoidHom_symm_comp_coe_addMonoi... | true |
BitVec.ofNat_or | Init.Data.BitVec.Lemmas | [
"instPowNat",
"instHOrOfOrOp",
"Nat.or_mod_two_pow",
"congrArg",
"BitVec.eq_of_toNat_eq",
"BitVec.instOrOp",
"BitVec",
"Nat.instMod",
"instHMod",
"instOfNatNat",
"BitVec.toNat",
"BitVec.ofNat",
"instNatPowNat",
"HOr.hOr",
"HMod.hMod",
"BitVec.toNat_ofNat",
"HPow.hPow",
"Nat",
"co... | true |
LinearEquiv.prodProdProdComm | Mathlib.LinearAlgebra.Prod | [
"LinearEquiv.mk",
"Prod.instAdd",
"AddMonoid.toAddZeroClass",
"LinearEquiv.prodProdProdComm._proof_2",
"AddZeroClass.toAddZero",
"Prod.mk",
"Prod.fst",
"AddCommMonoid",
"LinearEquiv.prodProdProdComm._proof_3",
"RingHomInvPair.ids",
"LinearEquiv",
"LinearMap.mk",
"Semiring",
"LinearEquiv.pr... | true |
CategoryTheory.LocalizerMorphism.rec | Mathlib.CategoryTheory.Localization.LocalizerMorphism | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"CategoryTheory.MorphismProperty.inverseImage",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartia... | false |
_private.Mathlib.Algebra.CubicDiscriminant.0.Cubic.ext.match_1 | Mathlib.Algebra.CubicDiscriminant | [
"Cubic.casesOn",
"Cubic.mk",
"Cubic"
] | false |
_private.Lean.Meta.Tactic.Grind.EMatch.0.Lean.Meta.Grind.EMatch.withFreshNGen | Lean.Meta.Tactic.Grind.EMatch | [
"Lean.Meta.Grind.GrindM",
"Lean.Meta.Grind.EMatch.SearchState",
"Lean.Meta.Grind.Goal",
"Lean.Meta.Grind.State",
"ReaderT",
"Lean.Meta.State",
"Lean.Meta.Sym.Context",
"Lean.Name.mkStr3",
"ReaderT.instMonad",
"Lean.Meta.Grind.Context",
"tryFinally",
"Lean.Meta.Grind.EMatch.Context",
"Lean.Me... | true |
Lean.Lsp.instToJsonInitializeResult.toJson | Lean.Data.Lsp.InitShutdown | [
"Lean.Lsp.ServerInfo",
"Lean.Json",
"Lean.Json.mkObj",
"Lean.Json.opt",
"String",
"Lean.Lsp.InitializeResult",
"Lean.Lsp.InitializeResult.serverInfo?",
"Lean.ToJson.toJson",
"Lean.Lsp.ServerCapabilities",
"Prod.mk",
"List.cons",
"Lean.Lsp.instToJsonServerCapabilities",
"List",
"Prod",
"L... | true |
Polynomial.Bivariate.swap | Mathlib.Algebra.Polynomial.Bivariate | [
"Polynomial.C",
"CommSemiring.toSemiring",
"Polynomial.algebraOfAlgebra",
"RingHom",
"Algebra.id",
"Polynomial.aevalAeval",
"Polynomial",
"CommSemiring",
"RingHom.instFunLike",
"AlgEquiv",
"Polynomial.semiring",
"AlgEquiv.ofAlgHom",
"Polynomial.Bivariate.swap._proof_1",
"Polynomial.Bivaria... | true |
Std.HashMap.Raw.isEmpty_emptyWithCapacity | Std.Data.HashMap.RawLemmas | [
"Bool.true",
"Std.HashMap.Raw.isEmpty",
"Nat",
"Std.HashMap.Raw.emptyWithCapacity",
"Bool",
"Hashable",
"Std.DHashMap.Raw.isEmpty_emptyWithCapacity",
"BEq",
"Eq"
] | true |
Filter.HasBasis.disjoint_iff | Mathlib.Order.Filter.Bases.Basic | [
"not_iff_not",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"CompleteLattice.toLattice",
"Filter.HasBasis.inf_basis_neBot_iff",
"congrArg",
"Filter.NeBot",
"Filter.instCompleteLatticeFilter",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"Exists",
"Semilatti... | true |
Semiquot.get.congr_simp | Mathlib.Data.Semiquot | [
"Semiquot.IsPure",
"Eq.rec",
"Semiquot.get",
"Eq.ndrec",
"Eq.refl",
"Semiquot",
"Eq"
] | true |
CategoryTheory.Limits.IsColimit.nonempty_isColimit_iff_isIso_desc | Mathlib.CategoryTheory.Limits.IsLimit | [
"CategoryTheory.Limits.IsColimit.fac",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.IsIso",
"CategoryTheory.Limits.IsColimit.hom_ext",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.... | true |
ENNReal.mul_eq_right | Mathlib.Data.ENNReal.Operations | [
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"ENNReal.mul_left_inj",
"Eq.mp",
"Ne",
"ENNReal.instCommSemiring",
"MulZeroOneClass.toMulOneClass",
"instDistribOfSemiring",
"instMulZeroOneClassOfSemiring",
"Iff",
"Distrib.toMul",
"ENNReal",
"One.toOfNat1",
"Zero.toOfNat0",
"ENNReal... | true |
CategoryTheory.Mon.instHasZeroMorphisms | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.SemiCartesianMonoidalCategory",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.Mon.instZeroHom",
"CategoryTheory.Mon",
"CategoryTheory.Limits.HasZeroMorphisms.mk",
"CategoryTheory.Mon.instCategory",
"Category... | true |
Array.pmap_attachWith | Init.Data.Array.Attach | [
"Array.pmap",
"congrArg",
"Array.getElem_pmap",
"Array.size_pmap",
"Array.instMembership",
"Array.pmap_attachWith._proof_1",
"Membership.mem",
"Array.size_attachWith",
"Exists",
"Eq.rec",
"Subtype",
"Subtype.mk",
"Array",
"GetElem.getElem",
"Array.instGetElemNatLtSize",
"Array.ext",
... | true |
IntermediateField.fixingSubgroupEquiv._proof_2 | Mathlib.FieldTheory.Galois.Basic | [
"IntermediateField.isScalarTower_mid'",
"RingEquiv.toEquiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"CommRing.toNonUnitalCommRing",
"IntermediateField",
"AlgEquiv.commutes",
"Algebra",
"Membership.mem",
"Field.toDivisionRing",
"Algebra.toModule",
"IntermediateField.f... | false |
isUpperSet_iff_Ioi_subset | Mathlib.Order.UpperLower.Basic | [
"Set.Ioi",
"Preorder.toLT",
"congrArg",
"PartialOrder.toPreorder",
"IsUpperSet",
"Preorder.toLE",
"Membership.mem",
"forall_comm",
"Set.mem_Ioi._simp_1",
"PartialOrder",
"HasSubset.Subset",
"iff_self",
"Iff",
"implies_congr",
"_private.Mathlib.Order.UpperLower.Basic.0.isUpperSet_iff_Ioi_... | true |
ULift.isIsometricSMul | Mathlib.Topology.MetricSpace.IsometricSMul | [
"SMul",
"ULift",
"IsIsometricSMul",
"PseudoEMetricSpace",
"IsIsometricSMul.isometry_smul",
"ULift.smulLeft",
"IsIsometricSMul.mk",
"ULift.down"
] | true |
Composition.recOnSingleAppend | Mathlib.Combinatorics.Enumerative.Composition | [
"Composition.recOnSingleAppend._unary",
"instOfNatNat",
"Composition",
"Composition.single",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Nat.succ_pos",
"PSigma.mk",
"instAddNat",
"Composition.ones",
"OfNat.ofNat",
"Composition.append"
] | true |
_private.Mathlib.Data.Seq.Basic.0.Stream'.Seq.drop.match_1.splitter | Mathlib.Data.Seq.Basic | [
"instOfNatNat",
"Unit",
"Nat",
"Stream'.Seq.drop.match_1",
"OfNat.ofNat",
"Nat.succ"
] | true |
_private.Mathlib.Data.Finset.Option.0.Option.mem_toFinset._simp_1_1 | Mathlib.Data.Finset.Option | [
"eq_comm",
"propext",
"Eq"
] | false |
Std.Internal.IO.Async.EAsync.instMonadLiftBaseAsync | Std.Internal.Async.Basic | [
"Std.Internal.IO.Async.BaseAsync.mk",
"Except.ok",
"Std.Internal.IO.Async.EAsync",
"Std.Internal.IO.Async.BaseAsync.map",
"Task.Priority.default",
"MonadLift",
"Std.Internal.IO.Async.BaseAsync",
"MonadLift.mk",
"Except",
"Bool.false"
] | true |
ContinuousOn.continuous_of_mulTSupport_subset | Mathlib.Topology.Algebra.Support | [
"Continuous",
"One",
"IsOpen.continuousOn_iff",
"ContinuousAt",
"Membership.mem",
"HasSubset.Subset",
"TopologicalSpace",
"Iff.mp",
"ContinuousOn",
"IsOpen",
"mulTSupport",
"Set.instMembership",
"continuous_of_mulTSupport",
"Set.instHasSubset",
"Set"
] | true |
Lean.Expr.getUsedConstantsAsSet | Lean.Util.FoldConsts | [
"Lean.NameSet",
"Lean.Expr",
"Lean.NameSet.insert",
"Lean.NameSet.instEmptyCollection",
"Lean.Name",
"Lean.Expr.foldConsts",
"EmptyCollection.emptyCollection"
] | true |
_private.Mathlib.CategoryTheory.Localization.Monoidal.Braided.0.CategoryTheory.Localization.Monoidal.instIsLocalizationLocalizedMonoidalToMonoidalCategory_1._proof_1 | Mathlib.CategoryTheory.Localization.Monoidal.Braided | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.MorphismProperty.IsMonoidal",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Localization.instCategoryLocalizedMonoidal",
"CategoryTheory.Iso",
"CategoryTheory.Localization.Monoidal.toMonoidalCategory",
"CategoryTheory.Fu... | false |
MulAction.isBlock_top | Mathlib.GroupTheory.GroupAction.Blocks | [
"instHSMul",
"ChainCompletePartialOrder.instOfCompleteLattice",
"MulAction.IsBlock",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"Monoid.toMulOneClass",
"Equiv.forall_congr_left",
"Subgroup.mul",
"Group",
"Disjoint",
"Membership.mem",
"Subgroup.instMulAction",
"MulOne.toMul",
"Subtype... | true |
_private.Mathlib.Tactic.Linter.Style.0.Mathlib.Linter.Style.setOption.isSetOption._sparseCasesOn_1 | Mathlib.Tactic.Linter.Style | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
Subgroup.range_zpowersHom | Mathlib.Algebra.Group.Subgroup.ZPowers.Lemmas | [
"Multiplicative.group",
"MonoidHom.range",
"Equiv.instEquivLike",
"MonoidHom",
"Monoid.toMulOneClass",
"AddMonoid.toAddZeroClass",
"Group",
"Multiplicative.mulOneClass",
"Equiv",
"DivInvMonoid.toMonoid",
"Subgroup",
"Int",
"Int.instAddMonoid",
"Group.toDivInvMonoid",
"Multiplicative",
... | true |
Lean.Lsp.Ipc.writeRequest | Lean.Data.Lsp.Ipc | [
"IO.FS.Stream.writeLspRequest",
"Lean.Lsp.Ipc.IpcM",
"ReaderT",
"instMonadLiftT",
"IO",
"ReaderT.instMonad",
"EIO",
"liftM",
"instMonadEIO",
"ReaderT.instMonadLift",
"IO.Process.Child",
"Lean.Lsp.Ipc.ipcStdioConfig",
"Unit",
"Lean.Lsp.Ipc.stdin",
"Monad.toBind",
"Lean.ToJson",
"Bind.... | true |
CategoryTheory.SimplicialObject.Splitting.nondegComplex | Mathlib.AlgebraicTopology.DoldKan.SplitSimplicialObject | [
"CategoryTheory.SimplicialObject.Splitting.N",
"ChainComplex",
"Nat.instOne",
"CategoryTheory.SimplicialObject.Splitting.d._proof_1",
"AddRightCancelSemigroup.toAddSemigroup",
"CategoryTheory.SimplicialObject.Splitting",
"AddCancelMonoid.toAddRightCancelMonoid",
"CategoryTheory.SimplicialObject.Splitt... | true |
Lean.Expr.forallInfo | Lean.Expr | [
"_private.Lean.Expr.0.Lean.Expr.forallName.match_1",
"Lean.Expr",
"Lean.Expr.forallE",
"Bool.true",
"Bool",
"Lean.Name",
"Lean.BinderInfo",
"Eq",
"Lean.Expr.isForall"
] | true |
_private.Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex.0.SSet.Subcomplex.Pairing.RankFunction.range_homOfLE_app_union_range_b_app._simp_1_3 | Mathlib.AlgebraicTopology.SimplicialSet.AnodyneExtensions.RelativeCellComplex | [
"Set.mem_iUnion",
"Membership.mem",
"Exists",
"propext",
"Eq",
"Set.instMembership",
"Set.iUnion",
"Set"
] | false |
Ordinal.instOrderTopology | Mathlib.SetTheory.Ordinal.Topology | [
"OrderTopology",
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"OrderTopology.mk",
"TopologicalSpace",
"rfl",
"Ordinal",
"Ordinal.instTopologicalSpace"
] | true |
Add.mk | Init.Prelude | [
"Add.mk",
"Add"
] | true |
FractionalIdeal.extendedHom_eq_zero_iff | Mathlib.RingTheory.FractionalIdeal.Extended | [
"FractionalIdeal.extendedHom._proof_2",
"IsDomain",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"IsFractionRing",
"Module.IsTorsionFree",
"Algebra",
"RingHom",
"nonZeroDivisors",
"Algebra.toModu... | true |
RootPairing.restrictScalars'._proof_13 | Mathlib.LinearAlgebra.RootSystem.BaseChange | [
"Set.mem_range_self",
"Submodule",
"AddCommGroup.toAddCommMonoid",
"Membership.mem",
"AddCommGroup",
"Field.toSemifield",
"Field.toCommRing",
"Function.Embedding",
"Semifield.toDivisionSemiring",
"RootPairing.root",
"SetLike.coe",
"Submodule.setLike",
"Submodule.span",
"DivisionSemiring.to... | false |
Equiv.Set.union._proof_2 | Mathlib.Logic.Equiv.Set | [
"False",
"Set.disjoint_left",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"BiheytingAlgebra.toHeytingAlgebra",
"BiheytingAlgebra.toCoheytingAlgebra",
"Set.instDistribLattice",
"BooleanAlgebra.toBiheyting... | false |
InfHom.id | Mathlib.Order.Hom.Lattice | [
"id",
"InfHom",
"Min",
"InfHom.mk",
"InfHom.id._proof_1"
] | true |
FreeMagma.traverse_pure' | Mathlib.Algebra.Free | [
"Pure.pure",
"Monad.toApplicative",
"Function.comp",
"FreeMagma.instTraversable",
"Applicative.toPure",
"Applicative",
"Traversable.traverse",
"Applicative.toFunctor",
"FreeMagma.instMonad",
"Eq",
"Functor.map",
"rfl",
"FreeMagma"
] | true |
_private.Mathlib.Tactic.NormNum.IsSquare.0.Mathlib.Meta.NormNum.evalIsSquareRat.match_91 | Mathlib.Tactic.NormNum.IsSquare | [
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Mathlib.Meta.NormNum.BoolResult",
"Qq.Quoted",
"Lean.Level.zero",
"Qq.Quoted.unsafeMk",
"Bool",
"Lean.Expr.app",
"Sigma.mk",
"Sigma.casesOn",
"Lean.Name.mkStr1",
"Sigma",
"List.nil"
] | false |
PartialEquiv.IsImage.preimage_eq | Mathlib.Logic.Equiv.PartialEquiv | [
"PartialEquiv",
"PartialEquiv.IsImage.iff_preimage_eq",
"Set.instInter",
"Inter.inter",
"Set.preimage",
"Iff.mp",
"PartialEquiv.source",
"PartialEquiv.IsImage",
"PartialEquiv.toFun",
"Eq",
"Set"
] | true |
CategoryTheory.MonoidalCategory.Arrow.PullbackHom.isTerminalIso_hom_right | Mathlib.CategoryTheory.Monoidal.PushoutProduct | [
"CategoryTheory.Limits.IsTerminal.from",
"CategoryTheory.Functor",
"CategoryTheory.Functor.PullbackObjObj.π",
"CategoryTheory.Comma.right",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.Arrow.PullbackHom.isTerminalIso._proof_2",
"CategoryTheory.... | true |
ExceptCpsT.runK_bind_lift | Init.Control.ExceptCps | [
"ExceptCpsT.runK",
"ExceptCpsT.instMonad",
"ExceptCpsT.lift",
"Monad.toBind",
"Bind.bind",
"ExceptCpsT",
"Monad",
"Eq",
"rfl"
] | true |
Std.Time.Year.instOfNatOffset | Std.Time.Date.Unit.Year | [
"Int.ofNat",
"Std.Time.Year.Offset",
"Nat",
"OfNat.mk",
"OfNat"
] | true |
Lean.Grind.CommRing.Poly.add.noConfusion | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.noConfusion",
"Lean.Grind.CommRing.Poly.add",
"id",
"Int",
"Eq",
"Lean.Grind.CommRing.Mon"
] | false |
Module.ofMinimalAxioms._proof_2 | Mathlib.Algebra.Module.MinimalAxioms | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"AddMonoidHom.map_zero",
"instHSMul",
"AddCommGroup.toAddCommMonoid",
"SMul",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Distrib.toAdd",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"instDistribOfSe... | false |
_private.Std.Data.ExtDHashMap.Basic.0.Std.ExtDHashMap.modify._proof_1 | Std.Data.ExtDHashMap.Basic | [
"Std.DHashMap.Equiv",
"LawfulBEq",
"Std.ExtDHashMap.mk",
"Std.DHashMap.modify",
"Std.DHashMap.Equiv.modify",
"Std.ExtDHashMap",
"Hashable",
"Std.ExtDHashMap.sound",
"BEq",
"Eq",
"Std.DHashMap"
] | false |
Primrec.nat_rec' | Mathlib.Computability.Primrec.Basic | [
"Primcodable.ofDenumerable",
"Nat.rec",
"Prod.mk",
"Primcodable.prod",
"Primrec",
"Nat",
"Primcodable",
"Denumerable.nat",
"Primrec.nat_rec",
"Prod",
"Primrec₂.comp",
"Primrec.id",
"Primrec₂"
] | true |
Complex.«term_×ℂ_» | Mathlib.Data.Complex.Basic | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
_private.Mathlib.Tactic.DeriveEncodable.0.Mathlib.Deriving.Encodable.mkToSMatch.mkAlts.match_1 | Mathlib.Tactic.DeriveEncodable | [
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"_private.Mathlib.Tactic.DeriveEncodable.0.Mathlib.Deriving.Encodable.mkToSMatch.mkAlts._sparseCasesOn_1",
"Lean.Name",
"Option"
] | false |
Lean.Meta.arrowDomainsN | Lean.Meta.InferType | [
"Pure.pure",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"instForInOfForIn'",
"instMonadControlTOfPure",
"Lean.Expr.instBEq",
"String",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.MessageData.instAppend",
"Array.in... | true |
Batteries.RBNode.ctorElimType | Batteries.Data.RBMap.Basic | [
"cond",
"Batteries.RBNode",
"Nat.ble",
"Batteries.RBNode.nil",
"PULift",
"Batteries.RBColor",
"Nat",
"Batteries.RBNode.node"
] | false |
Std.HashSet.Equiv.mk._flat_ctor | Std.Data.HashSet.Basic | [
"Std.HashSet",
"Std.HashSet.Equiv.mk",
"Unit",
"Std.HashSet.inner",
"Std.HashMap.Equiv",
"Std.HashSet.Equiv",
"Hashable",
"BEq"
] | false |
Lean.Compiler.CSimp.Entry.noConfusion | Lean.Compiler.CSimpAttr | [
"Lean.Compiler.CSimp.Entry.noConfusionType",
"Lean.Compiler.CSimp.Entry.casesOn",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Eq",
"Lean.Compiler.CSimp.Entry"
] | false |
Array.find?_filterMap | Init.Data.Array.Find | [
"congrArg",
"Option.any",
"List.find?",
"Option.bind",
"Array.casesOn",
"instOfNatNat",
"Array.filterMap_congr",
"List.toArray",
"Array",
"List.find?_filterMap",
"List",
"List.size_toArray",
"Array.filterMap",
"Nat",
"congr",
"True",
"eq_self",
"Bool",
"of_eq_true",
"Eq.ndrec",... | true |
Int32.toInt_le | Init.Data.SInt.Lemmas | [
"Int32.maxValue",
"Int.le_of_lt_add_one",
"Int",
"LE.le",
"Int32.toInt",
"Int32.toInt_lt",
"Int32",
"Int.instLEInt"
] | true |
Ordinal.blsub_congr | Mathlib.SetTheory.Ordinal.Family | [
"Preorder.toLT",
"Ordinal.partialOrder",
"PartialOrder.toPreorder",
"Eq.rec",
"LT.lt.trans_eq",
"Ordinal.blsub",
"LT.lt",
"Eq.refl",
"Eq.symm",
"Eq",
"Ordinal"
] | true |
IntermediateField.inf_relfinrank_right | Mathlib.FieldTheory.Relrank | [
"Nat.instMulZeroOneClass",
"Cardinal",
"congrArg",
"CommSemiring.toSemiring",
"IntermediateField",
"IntermediateField.relfinrank",
"IntermediateField.inf_relrank_right",
"Cardinal.commSemiring",
"Cardinal.toNat",
"MonoidWithZeroHom.funLike",
"Algebra",
"CompleteLattice.toConditionallyCompleteL... | true |
_private.Mathlib.Topology.UniformSpace.Cauchy.0.isCompact_iff_totallyBounded_isComplete.match_1_3 | Mathlib.Topology.UniformSpace.Cauchy | [
"UniformSpace",
"Membership.mem",
"Exists",
"And.casesOn",
"ClusterPt",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro",
"UniformSpace.toTopologicalSpace",
"Set.instMembership",
"Filter",
"Set"
] | false |
Topology.IsInducing.regularSpace | Mathlib.Topology.Separation.Regular | [
"Filter.instMembership",
"Eq.mpr",
"Topology.IsInducing.nhds_eq_comap",
"RegularSpace",
"congrArg",
"closed_nhds_basis",
"Membership.mem",
"nhds",
"id",
"Topology.IsInducing",
"RegularSpace.of_hasBasis",
"Filter.HasBasis.comap",
"IsClosed",
"TopologicalSpace",
"And",
"Filter.HasBasis",... | true |
AlgebraicGeometry.SpecMap_preimage_basicOpen | Mathlib.AlgebraicGeometry.Scheme | [
"AlgebraicGeometry.Spec",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"PrimeSpectrum.basicOpen",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat... | true |
_private.Mathlib.Order.Filter.Ultrafilter.Defs.0.Ultrafilter.exists_le.match_1_1 | Mathlib.Order.Filter.Ultrafilter.Defs | [
"Filter.instCompleteLatticeFilter",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Exists",
"CompleteLattice.toBoundedOrder",
"LE.le",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"BoundedOrder.toOrderBot",
"Exists.intro",
"IsAtom",
"Filter",
"Filter.instPartialOrder"
] | false |
TopModuleCat.ofCone._proof_1 | Mathlib.Algebra.Category.ModuleCat.Topology.Basic | [
"TopModuleCat.instCategory",
"CategoryTheory.Limits.Cone.π",
"TopModuleCat.instHasForget₂ContinuousLinearMapIdCarrierModuleCatLinearMap",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"TopModuleCat.fromInduced",
"ModuleCat.Hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Mo... | false |
Mathlib.Tactic.UnfoldBoundary.UnfoldEntry.cast | Mathlib.Tactic.Translate.UnfoldBoundary | [
"Lean.Name",
"Mathlib.Tactic.UnfoldBoundary.UnfoldEntry",
"Mathlib.Tactic.UnfoldBoundary.UnfoldEntry.cast"
] | true |
IsAdjoinRootMonic.powerBasis_basis | Mathlib.RingTheory.IsAdjoinRoot | [
"CommRing",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"PowerBasis.basis",
"NonAssocRing.toNonUnitalNonAssocRing",
"Polynomial",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Module.Basis",
"CommRing.toC... | true |
Rack.toEnvelGroup.mapAux._sunfold | Mathlib.Algebra.Quandle | [
"Quandle.toRack",
"ShelfHom",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"Rack.toShelf",
"Rack",
"Group",
"Group.toDivisionMonoid",
"Quandle.Conj.quandle",
"DivisionMonoid.toDivInvOneMonoid",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Quandl... | false |
emultiplicity_le_emultiplicity_of_dvd_right | Mathlib.RingTheory.Multiplicity | [
"Iff.mpr",
"Monoid",
"Dvd.dvd",
"semigroupDvd",
"emultiplicity_le_emultiplicity_iff",
"LE.le",
"instLEENat",
"Monoid.toPow",
"HPow.hPow",
"Nat",
"ENat",
"Monoid.toSemigroup",
"instHPow",
"emultiplicity",
"Dvd.dvd.trans"
] | true |
SymplecticGroup.instGroupSubtypeMatrixSumMemSubmonoidSymplecticGroup | Mathlib.LinearAlgebra.SymplecticGroup | [
"Monoid",
"Semigroup.toMul",
"CommRing",
"instFintypeSum",
"Inv",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"Matrix",
"instDecidableEqSum",
"DivInvMonoid.mk",
"Group",
"SymplecticGroup.instGroupSubtypeMatrixSumMemSubmonoidSymplecticGroup._proof_1",
"Membership.mem",
"SymplecticGro... | true |
_private.Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent.0.aux_summable_add | Mathlib.Analysis.SpecialFunctions.Trigonometric.Cotangent | [
"neg_add_rev",
"Int.instAddCommGroup",
"Iff.mpr",
"Int.cast",
"NormedCommRing.toSeminormedCommRing",
"Int.cast_natCast",
"summable_nat_add_iff",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"DivisionCommMonoid.toDivisionMonoid",
"AddMonoid.toAddSemigroup",
"congrArg",
"AddCo... | true |
CategoryTheory.Limits.DiagramOfCones.mkOfHasLimits._proof_6 | Mathlib.CategoryTheory.Limits.Fubini | [
"CategoryTheory.Limits.limMap_π",
"CategoryTheory.Limits.ConeMorphism.mk",
"CategoryTheory.Limits.limit.π",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cone",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limit... | false |
_private.Init.Data.UInt.Bitwise.0.UInt32.toUSize_not._simp_1_1 | Init.Data.UInt.Bitwise | [
"instModUSize",
"instHMod",
"UInt32.toUSize",
"HMod.hMod",
"USize.toUInt32",
"propext",
"UInt32.toUSize_eq_mod_4294967296_iff",
"UInt32",
"OfNat.ofNat",
"Eq",
"USize",
"USize.instOfNat"
] | false |
_private.Mathlib.CategoryTheory.NatIso.0.CategoryTheory.NatIso.cancel_natIso_hom_right_assoc._simp_1_2 | Mathlib.CategoryTheory.NatIso | [
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.cancel_mono",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.Category"
] | false |
Submonoid.LocalizationMap.eq_iff_eq | Mathlib.GroupTheory.MonoidLocalization.Basic | [
"HMul.hMul",
"Monoid.toMulOneClass",
"Membership.mem",
"Exists",
"Submonoid.LocalizationMap.eq_iff_exists",
"MulOne.toMul",
"Subtype",
"MulOneClass.toMulOne",
"Iff",
"CommMonoid.toMonoid",
"Submonoid.LocalizationMap",
"Submonoid.LocalizationMap.instFunLike",
"Iff.trans",
"Submonoid.instSet... | true |
_private.Init.Data.Range.Polymorphic.NatLemmas.0.Nat.map_add_toList_roc'._simp_1_1 | Init.Data.Range.Polymorphic.NatLemmas | [
"instHAdd",
"HAdd.hAdd",
"Nat",
"Nat.add_assoc",
"instAddNat",
"Eq.symm",
"Eq"
] | false |
Finset.map_ssubset_map._simp_1 | Mathlib.Data.Finset.Image | [
"Finset",
"HasSSubset.SSubset",
"Finset.map",
"Finset.map_ssubset_map",
"Function.Embedding",
"propext",
"Finset.instHasSSubset",
"Eq"
] | false |
_private.Mathlib.Algebra.Group.Int.Even.0.Int.instDecidablePredIsSquare._simp_1 | Mathlib.Algebra.Group.Int.Even | [
"eq_comm",
"propext",
"Eq"
] | false |
Padic.adicCompletionEquiv._proof_4 | Mathlib.NumberTheory.Padics.HeightOneSpectrum | [
"Int.instAddCommGroup",
"NormedCommRing.toNormedRing",
"IsIntegralClosure",
"Multiplicative.linearOrder",
"CommRing",
"Rat.HeightOneSpectrum.primesEquiv",
"NormedRing.toRing",
"Equiv.instEquivLike",
"AddGroupWithOne.toAddGroup",
"Int.instLinearOrder",
"IsFractionRing",
"Rat",
"IsDedekindDoma... | false |
List.take_eq_self_iff._simp_1 | Mathlib.Data.List.TakeDrop | [
"LE.le",
"instLENat",
"List",
"Nat",
"propext",
"List.take_eq_self_iff",
"Eq",
"List.take",
"List.length"
] | false |
_private.Aesop.Forward.Substitution.0.Aesop.Substitution.mergeCompatible._proof_1 | Aesop.Forward.Substitution | [
"Std.Legacy.Range.stop",
"Membership.mem",
"inferInstance",
"Lean.Expr",
"Aesop.Substitution",
"instOfNatNat",
"Membership",
"Std.Legacy.Range.mk",
"Nat",
"LT.lt",
"Std.Legacy.Range",
"Std.Legacy.instMembershipNatRange",
"Eq.refl",
"instLTNat",
"Membership.get_elem_helper",
"Aesop.Subs... | false |
Lean.Meta.Grind.AC.DiseqCnstr.brecOn.eq | Lean.Meta.Tactic.Grind.AC.Types | [
"Lean.Meta.Grind.AC.DiseqCnstr",
"Lean.Meta.Grind.AC.DiseqCnstrProof",
"Lean.Meta.Grind.AC.DiseqCnstr.brecOn.go",
"Lean.Meta.Grind.AC.DiseqCnstr.casesOn",
"Lean.Meta.Grind.AC.DiseqCnstr.below",
"Lean.Meta.Grind.AC.DiseqCnstr.brecOn",
"Lean.Meta.Grind.AC.DiseqCnstr.mk",
"Eq.refl",
"Lean.Meta.Grind.AC... | true |
Lean.Meta.Simp.Arith.Int.ToLinear.State._sizeOf_inst | Lean.Meta.Tactic.Simp.Arith.Int.Basic | [
"Lean.Meta.Simp.Arith.Int.ToLinear.State._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Lean.Meta.Simp.Arith.Int.ToLinear.State"
] | false |
InfHom.instSemilatticeInf._proof_3 | Mathlib.Order.Hom.Lattice | [
"Preorder.toLT",
"Iff.rfl",
"PartialOrder.toPreorder",
"SemilatticeInf.toPartialOrder",
"InfHom",
"SemilatticeInf.toMin",
"Min",
"SemilatticeInf",
"Iff",
"LT.lt",
"InfHom.instFunLike",
"Pi.instSemilatticeInf",
"DFunLike.coe"
] | false |
Module.Presentation.tautological.R | Mathlib.Algebra.Module.Presentation.Tautological | [
"Module.Presentation.tautological.R.add",
"Module.Presentation.tautological.R.smul"
] | true |
LowerAdjoint.instInhabitedId | Mathlib.Order.Closure | [
"id",
"Inhabited",
"LowerAdjoint",
"Preorder",
"Inhabited.mk",
"LowerAdjoint.id"
] | true |
FirstOrder.Language.Substructure.casesOn | Mathlib.ModelTheory.Substructures | [
"FirstOrder.Language.Substructure.rec",
"FirstOrder.Language.ClosedUnder",
"FirstOrder.Language.Substructure",
"FirstOrder.Language.Structure",
"Nat",
"FirstOrder.Language.Functions",
"FirstOrder.Language",
"FirstOrder.Language.Substructure.mk",
"Set"
] | false |
_private.Mathlib.RingTheory.Polynomial.IsIntegral.0.IsIntegral.coeff._simp_1_7 | Mathlib.RingTheory.Polynomial.IsIntegral | [
"Finset",
"Membership.mem",
"Finset.mem_range",
"Finset.range",
"Finset.instSetLike",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"Eq",
"SetLike.instMembership"
] | false |
CategoryTheory.HasExactColimitsOfShape.rec | Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.HasExactColimitsOfShape",
"CategoryTheory.Limits.PreservesFiniteLimits",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.Limits.colim",
"CategoryTheory.Functor.category",
"CategoryTheory.HasExactColimitsOfShape.mk",
"CategoryTheory.Category"
] | false |
NNReal.toReal_le | Mathlib.Data.NNReal.Basic | [
"Real.instLE",
"Real",
"congrArg",
"PartialOrder.toPreorder",
"Preorder.toLE",
"NNReal.coe_le_coe._simp_1",
"NNReal",
"LE.le",
"iff_self",
"NNReal.instPartialOrder",
"Iff",
"True",
"of_eq_true",
"NNReal.toReal",
"Eq.trans"
] | true |
CategoryTheory.Functor.IsRightDerivedFunctor.isLeftKanExtension | Mathlib.CategoryTheory.Functor.Derived.RightDerived | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.Functor.IsLeftKanExtension",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.IsRightDerivedFunctor",
"CategoryTheory.Functor.... | true |
BitVec.toNat_lt_iff_getLsbD_eq_false | Init.Data.BitVec.Lemmas | [
"instPowNat",
"False",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.toNat_lt_iff_getLsbD_eq_false._proof_1_5",
"_private.Init.Data.BitVec.Lemmas.0.BitVec.toNat_lt_iff_getLsbD_eq_false._proof_1_2",
"Bool.not_eq_false",
"congrArg",
"BitVec.getLsbD_of_ge",
"exists_const._simp_1",
"False.elim",
"Classic... | true |
Representation.Coinvariants.le_comap_ker | Mathlib.RepresentationTheory.Coinvariants | [
"Iff.mpr",
"Eq.mpr",
"Submodule",
"Representation.Coinvariants.ker",
"MonoidHom.instMonoidHomClass",
"SetLike.mem_coe._simp_1",
"CommRing",
"Representation",
"MonoidHom.instFunLike",
"HMul.hMul",
"map_sub",
"DivInvOneMonoid.toInvOneClass",
"SemilinearMapClass.distribMulActionSemiHomClass",
... | true |
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