name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.TSyntax.ctorIdx | Init.Prelude | [
"Lean.TSyntax",
"Lean.SyntaxNodeKinds",
"Nat"
] | false |
_private.Mathlib.Algebra.Algebra.Subalgebra.Basic.0.Subalgebra.isDomain._proof_1 | Mathlib.Algebra.Algebra.Subalgebra.Basic | [
"Subalgebra.instSetLike",
"IsDomain",
"CommRing",
"Algebra",
"Membership.mem",
"Subtype",
"Subring.instIsDomainSubtypeMem",
"CommRing.toCommSemiring",
"Subalgebra.toSubring",
"Subalgebra",
"Ring.toSemiring",
"Ring",
"SetLike.instMembership",
"Subalgebra.toSemiring"
] | false |
AddEquiv.toMultiplicativeLeft._proof_7 | Mathlib.Algebra.Group.Equiv.TypeTags | [
"Equiv.right_inv",
"AddZeroClass.toAddZero",
"MulOne.toMul",
"MulEquiv.toEquiv",
"Equiv.toFun",
"Multiplicative",
"MulOneClass.toMulOne",
"AddZeroClass",
"Function.RightInverse",
"AddZero.toAdd",
"MulEquiv",
"MulOneClass",
"Multiplicative.mul",
"Equiv.invFun"
] | false |
String.Pos.Raw.instLTCiOfNatInt | Init.Data.String.OrderInstances | [
"_private.Init.Data.String.OrderInstances.0.String.Pos.Raw.instLTCiOfNatInt._simp_1",
"String.instLTRaw",
"Lean.Grind.ToInt.toInt",
"congrArg",
"Lean.Grind.ToInt.LT.mk",
"Lean.Grind.ToInt.LT",
"Int",
"String.Pos.Raw",
"iff_self",
"Int.instLTInt",
"Lean.Grind.IntInterval.ci",
"Iff",
"instOfNa... | true |
Std.DTreeMap.Internal.Impl.Const.get?_congr | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Ord",
"Std.instLawfulBEqOrd",
"congrArg",
"beqOfOrd",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.WF.ordered",
"Ordering",
"Ordering.eq",
"id",
"_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.Const.get?_congr._simp_1_1",
"Std.Internal.List.getValue?_congr",
... | true |
_private.Mathlib.Topology.Baire.LocallyCompactRegular.0.BaireSpace.of_t2Space_locallyCompactSpace._simp_2 | Mathlib.Topology.Baire.LocallyCompactRegular | [
"Set.mem_inter_iff",
"Membership.mem",
"Set.instInter",
"Inter.inter",
"And",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
Matrix.detp_smul_adjp | Mathlib.LinearAlgebra.Matrix.SemiringInverse | [
"Matrix.smul",
"NonAssocSemiring.toAddCommMonoidWithOne",
"MulOne.toOne",
"instHSMul",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Matrix.add",
"Semiring.toModule",
"instSMulOfMul",
"Matrix.detp_neg_one_one",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"AddMonoid.toAddSemigroup",
"Mat... | true |
Std.DHashMap.Internal.AssocList.foldrM | Std.Data.DHashMap.Internal.AssocList.Basic | [
"Std.DHashMap.Internal.AssocList.foldrM._f",
"Std.DHashMap.Internal.AssocList",
"Monad",
"Std.DHashMap.Internal.AssocList.brecOn"
] | true |
CategoryTheory.Limits.isCokernelEpiComp._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Kernels | [
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"congrArg",
"CategoryTheory.Limits.CokernelCofork",
"CategoryTheory.Limits.comp_zero",
"CategoryTheory.Limits.Co... | false |
_private.Mathlib.Analysis.CStarAlgebra.Multiplier.0.DoubleCentralizer.instCStarRing._simp_2 | Mathlib.Analysis.CStarAlgebra.Multiplier | [
"ContinuousLinearMap.sSup_unitClosedBall_eq_nnnorm",
"Real",
"SeminormedAddCommGroup",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"SeminormedAddGroup.toNNNorm",
"ContinuousLinearMap.funLike",
"NNNorm.nnnorm",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"RingHom",
"RingHomIs... | false |
CategoryTheory.Limits.isIsoZeroEquiv._proof_3 | Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"and_self",
"CategoryTheory.Limits.comp_zero",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"And",
"congr",
"True",
"eq_self",
"CategoryTheory.C... | false |
_private.Std.Time.Format.Basic.0.Std.Time.leftPad | Std.Time.Format.Basic | [
"String",
"HSub.hSub",
"String.pushn",
"instSubNat",
"instAppendString",
"instHAppendOfAppend",
"instHSub",
"Nat",
"String.length",
"Char",
"HAppend.hAppend"
] | true |
_private.Mathlib.LinearAlgebra.Matrix.FixedDetMatrices.0.FixedDetMatrices.reduce_mem_reps._simp_1_6 | Mathlib.LinearAlgebra.Matrix.FixedDetMatrices | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"AddMonoid.toAddZeroClass",
"AddLeftMono",
"le_neg",
"AddRightMono",
"AddZeroClass.toAddZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"LE.le",
"SubNegZeroMonoid.toNegZeroClass",
"LE",
"AddGroup",
"AddGroup.toSubNegMonoid",
"propext",
... | false |
_private.Mathlib.Tactic.Linter.Style.0.Mathlib.Linter.Style.longLine.longLineLinter | Mathlib.Tactic.Linter.Style | [
"Pure.pure",
"Lean.Linter.LinterOptions",
"Lean.TSyntax",
"Lean.MessageData",
"Inhabited.default",
"Lean.Name.mkNum",
"Lean.Syntax.Range.mk",
"Bool.not",
"Lean.FileMap.toPosition",
"instForInOfForIn'",
"IO.instMonadLiftSTRealWorldBaseIO",
"ReaderT",
"String",
"Lean.MonadLog.toMonadFileMap"... | true |
SemimoduleCat.Hom._sizeOf_1 | Mathlib.Algebra.Category.ModuleCat.Semi | [
"SemimoduleCat.isModule",
"SemimoduleCat.isAddCommMonoid",
"SemimoduleCat.Hom",
"instSizeOfDefault",
"SemimoduleCat",
"instOfNatNat",
"LinearMap",
"SemimoduleCat.carrier",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Semiring",
"instAddNat",
"LinearMap._sizeOf_inst",
"SizeOf",
"... | false |
UInt16.fromExpr | Lean.Meta.Tactic.Simp.BuiltinSimprocs.UInt | [
"Pure.pure",
"ReaderT",
"Lean.Meta.State",
"instMonadLiftT",
"Option.some",
"Lean.Meta.Simp.MethodsRef",
"ReaderT.instMonad",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"liftM",
"ReaderT.instMonadLift",
"Applicative.toPure",
"Option.none",
"UInt16.ofNat",
"Lean.Meta.Simp.SimpM",
... | true |
Std.Http.Chunk.ExtensionName.ctorIdx | Std.Internal.Http.Data.Chunk | [
"Nat",
"Std.Http.Chunk.ExtensionName"
] | false |
InfHom.id.eq_1 | Mathlib.Order.Hom.Lattice | [
"id",
"InfHom",
"Min",
"InfHom.id",
"InfHom.mk",
"InfHom.id._proof_1",
"Eq.refl",
"Eq"
] | true |
Action.instConcreteCategoryHomSubtypeV | Mathlib.CategoryTheory.Action.Basic | [
"Monoid",
"Action.instFunLikeHomSubtypeV",
"MonoidHom.instFunLike",
"Action.instConcreteCategoryHomSubtypeV._proof_3",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"CategoryTheory.ConcreteCategory.hom",
"Action.instConcreteCategoryHomSubtypeV._proof_... | true |
SemidirectProduct.inr_splitting | Mathlib.GroupTheory.GroupExtension.Defs | [
"GroupExtension.Splitting.mk",
"MonoidHom",
"Monoid.toMulOneClass",
"SemidirectProduct",
"GroupExtension.Splitting",
"MulAut.instGroup",
"Group",
"MulAut",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"SemidirectProduct.instGroup",
"SemidirectProduct.inr",
"Group.toDivInvMonoid",
"MulOneClass.... | true |
Equiv.ord_def | Mathlib.Logic.Equiv.Defs | [
"Equiv.instEquivLike",
"Ord",
"Equiv.ord",
"Ordering",
"Equiv",
"Ord.compare",
"Eq",
"DFunLike.coe",
"rfl",
"EquivLike.toFunLike"
] | true |
TensorAlgebra.GradedAlgebra.ι_apply._proof_1 | Mathlib.LinearAlgebra.TensorAlgebra.Grading | [
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"IsScalarTower.right",
"congrArg",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"Membership.mem",
"LinearMap.range",
"Algebra.toModule",
"Algebra.id",
"id",
"TensorAlgebra",
"instOfNatNat",
"LinearMap.mem_range_self",
"LinearMap",
... | false |
CategoryTheory.Functor.FullyFaithful.addGrpObj | Mathlib.CategoryTheory.Monoidal.Grp | [
"CategoryTheory.Functor",
"CategoryTheory.AddGrpObj.mk",
"CategoryTheory.Functor.FullyFaithful.addMonObj",
"CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory",
"CategoryTheory.CartesianMonoidalCategory",
"CategoryTheory.AddGrpObj.neg",
"CategoryTheory.AddGrpObj",
"CategoryTheory.Functor.... | true |
CartanMatrix.E₈ | Mathlib.Data.Matrix.Cartan | [
"Equiv.instEquivLike",
"Matrix",
"Matrix.of",
"Equiv",
"Int.instNegInt",
"instOfNatNat",
"Int",
"instOfNat",
"Nat",
"Matrix.vecEmpty",
"OfNat.ofNat",
"Fin",
"DFunLike.coe",
"Matrix.vecCons",
"Neg.neg",
"EquivLike.toFunLike"
] | true |
Mathlib.Tactic.Translate.Config.doc._default | Mathlib.Tactic.Translate.Core | [
"String",
"id",
"Option.none",
"Option"
] | false |
_private.Mathlib.Combinatorics.SetFamily.AhlswedeZhang.0.Finset.infs_aux | Mathlib.Combinatorics.SetFamily.AhlswedeZhang | [
"Eq.mpr",
"LowerSet.mem_inf_iff",
"Finset.coe_infs",
"lowerClosure_infs",
"LowerSet.instMin",
"congrArg",
"Finset",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"id",
"HasInfs.infs",
"DistribLattic... | true |
NonAssocRing.toAddCommGroupWithOne | Mathlib.Algebra.Ring.Defs | [
"AddCommGroupWithOne",
"NonAssocRing.intCast_negSucc",
"NonUnitalNonAssocRing.toAddCommGroup",
"NonAssocRing.intCast_ofNat",
"AddCommGroupWithOne.mk",
"NonAssocRing",
"NonAssocRing.natCast_succ",
"NonAssocRing.toNonUnitalNonAssocRing",
"NonAssocRing.toIntCast",
"NonAssocRing.natCast_zero",
"NonA... | true |
ContDiffWithinAt.contDiffBump | Mathlib.Analysis.Calculus.BumpFunction.Basic | [
"ContDiffWithinAt.sub",
"NormedCommRing.toNormedRing",
"Set.instSProd",
"prod_mem_nhds",
"Ioi_mem_nhds",
"instClosedIicTopology",
"ContDiffBumpBase.smooth",
"Real",
"Set.Ioi",
"instHSMul",
"Prod.normedSpace",
"instHDiv",
"NormedSpace.toIsBoundedSMul",
"RCLike.toNormedAlgebra",
"Real.latt... | true |
WithCStarModule.norm_apply_le_norm | Mathlib.Analysis.CStarAlgebra.Module.Constructions | [
"Finset.mem_univ",
"Norm.norm",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonUnitalNormedRing.toNorm",
"Real.instLE",
"Real",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"Finset.univ",
"abs_le_of_sq_le_sq'",
"Inner.inner",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Finset",
"SMul",
"Normed... | true |
Nat.xor_right_injective | Batteries.Data.Nat.Bitwise.Lemmas | [
"Eq.mpr",
"Nat.instXorOp",
"congrArg",
"id",
"Nat.xor_xor_cancel_left",
"Nat",
"True",
"HXor.hXor",
"eq_self",
"of_eq_true",
"congrFun'",
"Function.Injective",
"Eq.symm",
"Eq",
"instHXorOfXorOp",
"Eq.trans"
] | true |
TopologicalSpace.le_def | Mathlib.Topology.Order | [
"Prop.le",
"Iff.rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"Pi.hasLe",
"TopologicalSpace",
"Iff",
"TopologicalSpace.instPartialOrder",
"IsOpen",
"Set"
] | true |
_private.Lean.Elab.Inductive.0.Lean.Elab.Command.elabCtors.match_7 | Lean.Elab.Inductive | [
"Option.ctorIdx",
"Option.some",
"Lean.FVarId",
"Nat.hasNotBit",
"_private.Lean.Elab.Inductive.0.Lean.Elab.Command.inductiveSyntaxToView._sparseCasesOn_1",
"Option"
] | false |
ValuationSubring.one_mem | Mathlib.RingTheory.Valuation.ValuationSubring | [
"AddGroupWithOne.toAddMonoidWithOne",
"Membership.mem",
"Field.toDivisionRing",
"DivisionRing.toRing",
"CommRing.toNonAssocCommRing",
"Field.toCommRing",
"AddMonoidWithOne.toOne",
"One.toOfNat1",
"ValuationSubring.instSetLike",
"OfNat.ofNat",
"Field",
"ValuationSubring.toSubring",
"Ring.toAd... | true |
TrivSqZeroExt.instAlgebra._proof_2 | Mathlib.Algebra.TrivSqZeroExt.Basic | [
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"MulOpposite",
"Algebra.toSMul",
"AddZeroClass.toAddZero",
"Algebra.id",
"DistribSMul.toSMulZeroClass",
"IsScalarTower.op_right",
"IsScalarTower.left",
"AddCommMonoid",
"CommSemiring",
... | false |
Lean.Elab.Command.InductiveElabStep3.finalize | Lean.Elab.MutualInductive | [
"Lean.Elab.Command.InductiveElabStep3",
"Unit",
"Lean.Elab.Term.TermElabM"
] | true |
CategoryTheory.PullbackShift.adjunction | Mathlib.CategoryTheory.Shift.Pullback | [
"CategoryTheory.Functor",
"CategoryTheory.PullbackShift.adjunction._proof_3",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Adjunction.unit",
"CategoryTheory.Functor.id",
"AddZeroClass.toAddZero",
"CategoryTheory.Adjunction.counit",
"... | true |
MeasureTheory.SimpleFunc.ofIsEmpty._proof_1 | Mathlib.MeasureTheory.Function.SimpleFunc | [
"Finite",
"IsEmpty.instSubsingleton",
"IsEmpty",
"Finite.of_subsingleton"
] | false |
Turing.TM0.Machine.map_step | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Eq.mpr",
"Turing.TM0.step",
"Turing.TM0.Stmt.map",
"Turing.Tape",
"Turing.TM0.Cfg.q",
"congrArg",
"Option.casesOn",
"Option.some",
"Membership.mem",
"id",
"Prod.mk",
"Prod.map",
"Turing.Tape.map",
"Turing.TM0.Machine.map.match_1",
"Turing.TM0.Cfg.map",
"Turing.TM0.step.match_1",
"Pr... | true |
CategoryTheory.NatTrans.CommShift.verticalComposition | Mathlib.CategoryTheory.Shift.CommShift | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.NatTrans.CommShift.whiskerRight",
"CategoryTheory.NatTrans.CommShift.associator",
"CategoryTheory.Functor.comp",
"CategoryTheory.NatTrans.CommShift.comp",
"inferInstan... | true |
CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.casesOn | Mathlib.CategoryTheory.Monoidal.DayConvolution | [
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Functor.LeftExtension.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct._proof_2"... | false |
Lean.Json.instCoeArrayStructured | Lean.Data.Json.Basic | [
"Lean.Json",
"Coe.mk",
"Lean.Json.Structured",
"Array",
"Lean.Json.Structured.arr",
"Coe"
] | true |
groupCohomology.map_one_fst_of_isCocycle₂ | Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree | [
"Monoid",
"MulOne.toOne",
"instHSMul",
"HMul.hMul",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"Monoid.toMulOneClass",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddCancelCommMonoid",
"AddCommGroup",
"Eq.mp",
"MulOne.toMul",
"Prod.mk",
"one_smul",
"AddLeftCancelMonoid.t... | true |
_private.Mathlib.MeasureTheory.VectorMeasure.AddContent.0.MeasureTheory.VectorMeasure.exists_extension_of_isSetRing_of_le_measure_of_dense._simp_1_6 | Mathlib.MeasureTheory.VectorMeasure.AddContent | [
"MeasurableSet",
"Set.instUnion",
"MeasurableSpace",
"True",
"MeasurableSet.union",
"eq_true",
"Union.union",
"Eq",
"Set"
] | false |
Ordinal.iterate_veblen_lt_gamma_zero | Mathlib.SetTheory.Ordinal.Veblen | [
"Ordinal.veblen",
"Eq.mpr",
"Ordinal.instLinearOrder",
"Preorder.toLT",
"Ordinal.gamma_zero_eq_nfp",
"Ordinal.omega0",
"Ordinal.partialOrder",
"congrArg",
"instIsBotZeroClass",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"AddZero... | true |
GaloisCoinsertion.isAtom_of_image | Mathlib.Order.Atoms | [
"OrderDual.toDual",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderBot",
"Function.comp",
"PartialOrder",
"Equiv",
"IsAtom.dual",
"GaloisInsertion.isCoatom_of_image",
"OrderDual.instOrderTopOfOrderBot",
"GaloisCoinsertion.dual",
"IsAtom",
"Or... | true |
Mathlib.Tactic.Widget.StringDiagram.Kind.monoidal.sizeOf_spec | Mathlib.Tactic.Widget.StringDiagram | [
"Mathlib.Tactic.Widget.StringDiagram.Kind",
"instOfNatNat",
"Mathlib.Tactic.Widget.StringDiagram.Kind.monoidal",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Mathlib.Tactic.Widget.StringDiagram.Kind._sizeOf_inst"
] | true |
_private.Lean.Meta.Tactic.Contradiction.0.Lean.Meta.isGenDiseq | Lean.Meta.Tactic.Contradiction | [
"Lean.Expr",
"Bool",
"Lean.Meta.Simp.isEqnThmHypothesis"
] | true |
DifferentiableOn.sinh | Mathlib.Analysis.SpecialFunctions.Trigonometric.DerivHyp | [
"Real",
"Semiring.toModule",
"NormedSpace",
"Real.denselyNormedField",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField",
"Real.sinh",
"Real.instAddCommGroup",
"Field.toSemifield",
"Semifield.toDivisionSemiring",
"SeminormedAddCommGroup.toPse... | true |
Orientation.inner_smul_rotation_pi_div_two_smul_right | Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | [
"LinearIsometryEquiv.instEquivLike",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Orientation",
"Real.partialOrder",
"Real",
"instHSMul",
"instHDiv",
"Real.pi",
"Real.Angle.coe",
"Inner.inner",
"Real.instZero",
"Real.instRCLike",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommG... | true |
TopCat.Sheaf.interUnionPullbackCone._proof_3 | Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections | [
"TopologicalSpace.Opens.instCompleteLattice",
"PartialOrder.toPreorder",
"TopologicalSpace.Opens",
"Preorder.toLE",
"inf_le_right",
"SemilatticeInf.toPartialOrder",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeInf.toMin",
"LE.le",
"TopCat.str",
"TopCat.carrier",
"TopCat",
"C... | false |
Commute.zpow_right | Mathlib.Algebra.Group.Commute.Basic | [
"Monoid.toMulOneClass",
"DivInvMonoid.toZPow",
"Group",
"Commute",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Int",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"HPow.hPow",
"SemiconjBy.zpow_right",
"instHPow"
] | true |
Filter.IsCobounded.mk | Mathlib.Order.Filter.IsBounded | [
"Filter.instMembership",
"trans",
"Filter.Eventually",
"setOf",
"Membership.mem",
"Exists",
"IsTrans",
"And",
"Filter.IsCobounded",
"Exists.intro",
"_private.Mathlib.Order.Filter.IsBounded.0.Filter.IsCobounded.mk.match_1_1",
"Set.instMembership",
"Filter",
"Set"
] | true |
SSet.stdSimplex.spineId | Mathlib.AlgebraicTopology.SimplicialSet.Path | [
"SSet.Path",
"Opposite",
"Equiv.instEquivLike",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"Equiv",
"SSet",
"SSet.stdSimplex",
"SimplexCategory.mk",
"Opposite.op",
"Nat",
"CategoryTheory.types",
"SimplexC... | true |
Polynomial.Nontrivial.of_polynomial_ne | Mathlib.Algebra.Polynomial.Basic | [
"Nontrivial",
"subsingleton_or_nontrivial",
"Or.resolve_left",
"Ne",
"Polynomial",
"Unique.instSubsingleton",
"Semiring",
"Subsingleton",
"Polynomial.unique",
"Subsingleton.elim"
] | true |
Subfield.instIsScalarTowerSubtypeMem | Mathlib.Algebra.Field.Subfield.Basic | [
"IsScalarTower",
"_private.Mathlib.Algebra.Field.Subfield.Basic.0.Subfield.instIsScalarTowerSubtypeMem._proof_1",
"SMul",
"Membership.mem",
"Subtype",
"Subfield.instSetLike",
"DivisionRing",
"Subfield",
"SetLike.instMembership",
"Subfield.instSMulSubtypeMem"
] | true |
CategoryTheory.Lax.LaxTrans.isoMk._proof_8 | Mathlib.CategoryTheory.Bicategory.Modification.Lax | [
"CategoryTheory.Lax.LaxTrans.Modification.app",
"CategoryTheory.Iso.inv_hom_id",
"CategoryTheory.Lax.LaxTrans.isoMk._proof_2",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Lax.LaxTrans.Hom.as",
"congrArg",
"CategoryTheory.Lax.LaxTrans.naturality",
"CategoryTheory.Lax.LaxTr... | false |
AlgebraicGeometry.Scheme.Hom.mem_smoothLocus | Mathlib.AlgebraicGeometry.Morphisms.Smooth | [
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"AlgebraicGeometry.Scheme",
"CommRingCat.Hom.hom",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CommRingCat",
... | true |
Complex.arg_exp_mul_I | Mathlib.Analysis.SpecialFunctions.Complex.Arg | [
"Complex.mul_im",
"Real",
"Preorder.toLT",
"Real.instArchimedean",
"Real.pi",
"HMul.hMul",
"Real.instZero",
"Real.instAddMonoid",
"congrArg",
"toIocMod.congr_simp",
"Complex.im",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Nat.instAtLeastTwoHAddOfNat",
"Complex.instMul",
"S... | true |
ContinuousMultilinearMap.smulRight | Mathlib.Topology.Algebra.Module.Multilinear.Basic | [
"Semiring.toModule",
"ContinuousSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"ContinuousMultilinearMap",
"AddZeroClass.toAddZero",
"MultilinearMap.smulRight",
"DistribSMul.toSMulZeroClass",
"ContinuousMultilinearMap.mk",
"MultilinearMap",
"Add... | true |
_private.Batteries.Data.Vector.Basic.0.Vector.scanlMFast.loop._unary._proof_3 | Batteries.Data.Vector.Basic | [
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"HAdd.hAdd",
"USize.toNat",
"Nat",
"LT.lt",
"Decidable.byContradiction",
"instAddNat",
"instLTNat",
"OfNat.ofNat",
"instAddUSize",
"Eq",
"_private.Batteries.Data.Vector.Basic.0.Vector.scanlMFast._proof_2",
"Not",
"Nat.decLe",
"USize... | false |
_private.Mathlib.Data.EReal.Operations.0.EReal.add_ne_top_iff_ne_top₂._simp_1_2 | Mathlib.Data.EReal.Operations | [
"False",
"Real",
"eq_false",
"EReal",
"instTopEReal",
"EReal.coe_ne_top",
"Top.top",
"Eq",
"Real.toEReal"
] | false |
List.prod_mul_prod_eq_prod_zipWith_mul_prod_drop | Mathlib.Algebra.BigOperators.Group.List.Basic | [
"List.brecOn",
"MulOne.toOne",
"List.zipWith",
"HMul.hMul",
"Monoid.toMulOneClass",
"List.prod_mul_prod_eq_prod_zipWith_mul_prod_drop._f",
"MulOne.toMul",
"List",
"MulOneClass.toMulOne",
"List.drop",
"CommMonoid.toMonoid",
"Eq",
"CommMonoid",
"List.length",
"List.prod",
"instHMul"
] | true |
Lean.ScopedEnvExtension.State.rec | Lean.ScopedEnvExtension | [
"Lean.NameSet",
"Lean.ScopedEnvExtension.State",
"Lean.ScopedEnvExtension.State.mk",
"Bool"
] | false |
Std.LawfulOrderMin.mk | Init.Data.Order.Classes | [
"Std.LawfulOrderMin",
"Std.LawfulOrderMin.mk",
"LE",
"Min",
"Std.MinEqOr",
"Std.LawfulOrderInf"
] | true |
Array.Perm.pairwise | Init.Data.Array.Perm | [
"List.Pairwise",
"Array.Perm.pairwise_iff",
"Array.toList",
"Array",
"Array.Perm",
"Iff.mp"
] | true |
Algebra.tensorH1CotangentOfIsLocalization._proof_2 | Mathlib.RingTheory.Etale.Kaehler | [
"RingHom.instRingHomClass",
"CommRing",
"Algebra.Extension.commRing",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.Generators.self",
"RingHom",
"RingHomClass.toMonoidWithZeroHomClass",
"NonAssocSemiring.toMulZeroOneClass",
"MonoidWithZeroHomClass.toMonoidHomClass",
"Algebra.Extension.Ring",
... | false |
Int.le_floor_add | Mathlib.Algebra.Order.Floor.Ring | [
"Int.cast",
"Eq.mpr",
"AddMonoid.toAddSemigroup",
"Int.floor",
"Ring.toNonAssocRing",
"IsOrderedRing",
"congrArg",
"LinearOrder",
"covariant_swap_add_of_covariant_add",
"add_le_add",
"PartialOrder.toPreorder",
"AddGroupWithOne.toAddMonoidWithOne",
"Preorder.toLE",
"SemilatticeInf.toPartial... | true |
Std.Internal.List.containsKey_maxKey? | Std.Data.Internal.List.Associative | [
"Std.Internal.List.DistinctKeys",
"Ord",
"Std.TransOrd",
"Std.OrientedOrd.opposite",
"Std.TransOrd.opposite",
"Option.some",
"inferInstance",
"Ord.compare",
"Bool.true",
"List",
"Std.Internal.List.containsKey",
"Ord.opposite",
"Std.Internal.List.maxKey?",
"Bool",
"Std.LawfulBEqOrd",
"S... | true |
Lean.Language.SnapshotBundle.mk | Lean.Language.Basic | [
"Lean.Language.SyntaxGuarded",
"Lean.Language.SnapshotTask",
"IO.Promise",
"Lean.Language.SnapshotBundle",
"Lean.Language.SnapshotBundle.mk",
"Option"
] | true |
Std.IterM.TerminationMeasures.Productive.mk.injEq | Init.Data.Iterators.Basic | [
"Eq.propIntro",
"Std.IterM.TerminationMeasures.Productive.mk.inj",
"Std.Iterator",
"Std.IterM.TerminationMeasures.Productive",
"Eq.ndrec",
"Std.IterM.TerminationMeasures.Productive.mk",
"Eq.refl",
"Std.IterM",
"Eq"
] | true |
CategoryTheory.PreOneHypercover.cylinderX._proof_1 | Mathlib.CategoryTheory.Sites.Hypercover.Homotopy | [
"CategoryTheory.PreZeroHypercover.Hom.h₀",
"CategoryTheory.PreZeroHypercover.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.PreOneHypercover",
"CategoryTheory.PreOneHypercover.toPreZeroHypercover",
"CategoryTheory.PreZeroHypercover.Hom.w₀",
"CategoryTheory.Pr... | false |
ContinuousMultilinearMap.compContinuousLinearMap._proof_1 | Mathlib.Topology.Algebra.Module.Multilinear.Basic | [
"Continuous",
"Pi.topologicalSpace",
"Continuous.comp",
"LinearMap.instFunLike",
"ContinuousMultilinearMap",
"Function.comp",
"continuous_pi",
"ContinuousLinearMap.toLinearMap",
"LinearMap.toAddHom",
"LinearMap",
"AddCommMonoid",
"ContinuousLinearMap",
"TopologicalSpace",
"ContinuousMultil... | false |
CategoryTheory.Bicategory.prod._proof_22 | Mathlib.CategoryTheory.Bicategory.Product | [
"CategoryTheory.prod",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Prod.mkHom",
"CategoryTheory.Bicategory.rightUnitor",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Bicategory.whiskerRight",
"Prod.mk",
"CategoryTheory.Bicategory.toCategoryStruct",
... | false |
AddCon.list_sum | Mathlib.GroupTheory.Congruence.BigOperators | [
"AddCon.instFunLikeForallProp",
"AddCon",
"Eq.mpr",
"AddCon.add",
"List.map_cons",
"congrArg",
"List.Mem.tail",
"List.map",
"List.sum",
"Membership.mem",
"AddZeroClass.toAddZero",
"id",
"List.rec",
"List.cons",
"AddZero.toZero",
"List",
"instHAdd",
"AddZeroClass",
"List.instMembe... | true |
List.nil_eq_flatten_iff | Init.Data.List.Lemmas | [
"List.flatten_eq_nil_iff._simp_1",
"congrArg",
"Membership.mem",
"List.nil_eq._simp_1",
"iff_self",
"List",
"Iff",
"List.instMembership",
"True",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.trans",
"List.flatten",
"List.nil"
] | true |
_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPropagationsData.rec | Lean.Meta.Tactic.Grind.Types | [
"_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPropagationsData.eq",
"Lean.Meta.Grind.ParentSet",
"Lean.Expr",
"_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPropagationsData.nil",
"Nat",
"_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.PendingSolverPr... | false |
_private.Lean.Meta.DiscrTree.Main.0.Lean.Meta.DiscrTree.reduceUntilBadKey.step._unsafe_rec | Lean.Meta.DiscrTree.Main | [
"Pure.pure",
"Lean.Meta.State",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instDecidableEqBool",
"Lean.Meta.whnfCore",
"_private.Lean.Meta.DiscrTree.Main.0.Lean.Meta.DiscrTree.reduce.match_1",
"Applicative.toPure",
"Bool.true",
"Unit",
"Lean.Core.CoreM",
"Lean.Meta.instMonadMetaM",
"... | false |
Cardinal.mk_set_nat | Mathlib.SetTheory.Cardinal.Continuum | [
"Cardinal.instPowCardinal",
"Cardinal",
"congrArg",
"Nat.instAtLeastTwoHAddOfNat",
"Cardinal.mk",
"instOfNatNat",
"Cardinal.aleph0",
"Cardinal.mk_eq_aleph0",
"Cardinal.continuum",
"HPow.hPow",
"Nat.instNeZeroSucc",
"Nat",
"Cardinal.mk_set",
"True",
"eq_self",
"of_eq_true",
"congrFun'... | true |
Submodule.comap_equiv_self_of_inj_of_le.match_1 | Mathlib.Algebra.Module.Submodule.Equiv | [
"Submodule",
"Subtype.casesOn",
"Membership.mem",
"Subtype",
"LinearMap",
"AddCommMonoid",
"Subtype.mk",
"Submodule.comap",
"Submodule.setLike",
"Semiring",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"SetLike.instMembership"
] | false |
Std.DHashMap.Const.mem_ofList | Std.Data.DHashMap.Lemmas | [
"List.any_eq_true._simp_1",
"congrArg",
"List.map",
"_private.Std.Data.DHashMap.Lemmas.0.Std.DHashMap.Const.mem_ofList._simp_1_1",
"List.contains",
"List.contains_map",
"Prod.exists._simp_1",
"Membership.mem",
"Exists",
"exists_and_right._simp_1",
"Std.DHashMap.instMembership",
"Std.DHashMap.C... | true |
CategoryTheory.Localization.Preadditive.add.congr_simp | Mathlib.CategoryTheory.Localization.CalculusOfFractions.Preadditive | [
"CategoryTheory.MorphismProperty.HasLeftCalculusOfFractions",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Eq.rec",
"CategoryTheory.Iso",
"CategoryTheory.Preadditive",
"CategoryTheory.Functor.IsLocalization",
"CategoryTheory.... | true |
_private.Mathlib.Order.SupIndep.0.iSupIndep.of_coe_Iic_comp._simp_1_1 | Mathlib.Order.SupIndep | [
"iSup",
"PartialOrder.toPreorder",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"Set.Elem",
"Set.Iic.instCompleteLattice",
"Set.Iic.coe_iSup",
"ConditionallyCompletePartialOrderSup.toPartialOrder",
"Set.Iic",
"ConditionallyCompleteLattice.toConditionallyCompletePartialOrder"... | false |
LinearIndepOn.image_of_comp | Mathlib.LinearAlgebra.LinearIndependent.Basic | [
"Nontrivial",
"Iff.mpr",
"Equiv.instEquivLike",
"LinearIndepOn.of_subsingleton._simp_1",
"linearIndependent_equiv'",
"Function.comp",
"Membership.mem",
"Set.Elem",
"Set.injOn_iff_injective",
"LinearIndependent.injective",
"Equiv",
"AddCommMonoid",
"Equiv.Set.imageOfInjOn",
"LinearIndepende... | true |
CategoryTheory.Presieve.IsSheafFor.functorInclusion_comp_extend | Mathlib.CategoryTheory.Sites.IsSheafFor | [
"CategoryTheory.Functor",
"Exists.choose_spec",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Presieve.YonedaSheafCondition",
"ExistsUnique.exists",
"CategoryTheory.Presieve.IsSheafFor.extend",
"CategoryTheory.Presieve.IsSheafFor",
"CategoryTheory.Presieve.isS... | true |
CategoryTheory.MorphismProperty.IsStableUnderCobaseChange.hasOfPrecompProperty_epimorphisms | Mathlib.CategoryTheory.MorphismProperty.Limits | [
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.HasOfPrecompProperty",
"CategoryTheory.Category.assoc",
"CategoryTheory.Epi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.pushout.condition",
"CategoryTheory.MorphismPropert... | true |
LeanSearchClient.SearchResult.mk.noConfusion | LeanSearchClient.Syntax | [
"String",
"LeanSearchClient.SearchResult.noConfusion",
"id",
"LeanSearchClient.SearchResult.mk",
"Eq",
"LeanSearchClient.SearchResult",
"Option"
] | false |
Lean.Server.FileWorker.WorkerContext.modifyGetPartialHandler | Lean.Server.FileWorker | [
"Std.TreeMap.insert",
"IO.instMonadLiftSTRealWorldBaseIO",
"String",
"instMonadLiftT",
"ST.Ref.modifyGet",
"Lean.Server.FileWorker.PartialHandlerInfo",
"IO.RealWorld",
"Prod.mk",
"Lean.Server.FileWorker.WorkerContext.partialHandlersRef",
"Id.run",
"_private.Lean.Server.FileWorker.0.Lean.Server.F... | true |
GaloisCoinsertion.monotoneIntro._proof_1 | Mathlib.Order.GaloisConnection.Defs | [
"Monotone",
"ge_of_eq",
"Preorder.toLE",
"LE.le",
"GaloisConnection.monotone_intro",
"Eq",
"Preorder",
"GaloisConnection"
] | false |
List.allM._f | Init.Data.List.Control | [
"Pure.pure",
"Monad.toApplicative",
"Applicative.toPure",
"_private.Init.Data.List.Control.0.List.mapA.match_1",
"List.cons",
"_private.Init.Data.List.Control.0.List.anyM.match_1",
"Bool.true",
"List",
"Unit",
"Bool",
"List.below",
"Monad.toBind",
"Bind.bind",
"Monad",
"Bool.false",
"L... | false |
ContinuousMap.HomotopyRel.symm_bijective | Mathlib.Topology.Homotopy.Basic | [
"Iff.mpr",
"Function.LeftInverse",
"ContinuousMap.HomotopyRel.symm",
"ContinuousMap.HomotopyRel",
"ContinuousMap",
"Exists",
"Function.bijective_iff_has_inverse",
"TopologicalSpace",
"And",
"And.intro",
"Function.RightInverse",
"Exists.intro",
"Function.Bijective",
"ContinuousMap.HomotopyR... | true |
isDedekindRing_iff | Mathlib.RingTheory.DedekindDomain.Basic | [
"Iff.mpr",
"IsDedekindRing.toIsIntegralClosure",
"CommRing",
"Algebra.algebraMap",
"_private.Mathlib.RingTheory.DedekindDomain.Basic.0.isDedekindRing_iff.match_1_1",
"CommSemiring.toSemiring",
"IsFractionRing",
"Algebra",
"RingHom",
"Exists",
"inferInstance",
"IsNoetherianRing",
"And",
"Is... | true |
_private.Std.Data.DTreeMap.Internal.Model.0.Std.DTreeMap.Internal.Impl.some_getEntryLE_eq_getEntryLE?._simp_1_9 | Std.Data.DTreeMap.Internal.Model | [
"Option.getD",
"Option.some",
"Option.or",
"Option.or_some",
"Eq.symm",
"Eq",
"Option"
] | false |
Complex.equivRealProd | Mathlib.Data.Complex.Basic | [
"Complex.equivRealProd._proof_2",
"Real",
"Complex.im",
"Equiv.mk",
"Equiv",
"Prod.mk",
"Prod.fst",
"Complex.re",
"Complex",
"Prod",
"Complex.equivRealProd._proof_1",
"Prod.snd",
"Complex.mk"
] | true |
IsLocalization.AtPrime.mk'_mem_maximal_iff | Mathlib.RingTheory.Localization.AtPrime.Basic | [
"not_iff_not",
"Eq.mpr",
"_private.Mathlib.RingTheory.Localization.AtPrime.Basic.0.IsLocalization.AtPrime.mk'_mem_maximal_iff._simp_1_3",
"_private.Mathlib.RingTheory.Localization.AtPrime.Basic.0.IsLocalization.AtPrime.mk'_mem_maximal_iff._simp_1_1",
"Semiring.toModule",
"congrArg",
"CommSemiring.toSemi... | true |
CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct.recOn | Mathlib.CategoryTheory.Monoidal.DayConvolution | [
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.Functor.LeftExtension.mk",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory.LawfulDayConvolutionMonoidalCategoryStruct._proof_2"... | false |
Lean.PrettyPrinter.parenthesizeTerm | Lean.PrettyPrinter.Parenthesizer | [
"Lean.Syntax",
"Lean.Core.CoreM",
"Lean.PrettyPrinter.parenthesizeCategory",
"Lean.Name.mkStr1"
] | true |
ENNReal.ofReal_rpow_of_pos | Mathlib.Analysis.SpecialFunctions.Pow.NNReal | [
"Eq.mpr",
"Real.instPow",
"Real.toNNReal_eq_zero._simp_1",
"Real.instLE",
"Real",
"ENNReal.ofNNReal",
"Preorder.toLT",
"Real.instZero",
"ENNReal.ofReal",
"congrArg",
"ENNReal.instPowReal",
"ENNReal.coe_inj",
"PartialOrder.toPreorder",
"Real.instLT",
"id",
"LT.lt.le",
"NNReal",
"LE.... | true |
Lean.Parser.suppressInsideQuot | Lean.Parser.Basic | [
"Lean.Parser.Parser",
"Lean.Parser.CacheableParserContext.mk",
"instDecidableEqBool",
"Lean.Parser.CacheableParserContext.prec",
"Lean.Parser.adaptCacheableContext",
"instOfNatNat",
"instBEqOfDecidableEq",
"Bool.true",
"BEq.beq",
"Nat",
"Bool",
"Lean.Parser.CacheableParserContext.forbiddenTk?"... | true |
Path.Homotopic.equivalence | Mathlib.Topology.Homotopy.Path | [
"Path.Homotopic.trans",
"Path.Homotopic.symm",
"Equivalence",
"Path.Homotopic.refl",
"TopologicalSpace",
"Path",
"Equivalence.mk",
"Path.Homotopic"
] | true |
Lean.Elab.Term.LetIdDeclView.recOn | Lean.Elab.Binders | [
"Lean.Elab.Term.LetIdDeclView.rec",
"Lean.Syntax",
"Array",
"Lean.Elab.Term.LetIdDeclView.mk",
"Lean.Elab.Term.LetIdDeclView"
] | false |
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