name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.Combinatorics.Additive.SmallTripling.0.Finset.small_alternating_pow_of_small_tripling._simp_1_6 | Mathlib.Combinatorics.Additive.SmallTripling | [
"IsEmpty",
"True",
"propext",
"Eq",
"IsEmpty.forall_iff"
] | false |
Complex.orthonormalBasisOneI | Mathlib.Analysis.InnerProductSpace.PiL2 | [
"instInnerProductSpaceRealComplex",
"Real",
"Complex.instNormedAddCommGroup",
"Real.instRCLike",
"instOfNatNat",
"Fin.fintype",
"Complex.basisOneI",
"Complex.orthonormalBasisOneI._proof_1",
"Nat",
"OrthonormalBasis",
"Complex",
"Module.Basis.toOrthonormalBasis",
"OfNat.ofNat",
"Fin"
] | true |
Pi.instOne.eq_1 | Mathlib.Algebra.Notation.Pi.Defs | [
"One",
"One.mk",
"Pi.instOne",
"One.toOfNat1",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
eventually_closure_subset_of_isOpen_of_omegaLimit_subset | Mathlib.Dynamics.OmegaLimit | [
"Filter.instMembership",
"omegaLimit",
"Set.subset_univ",
"Set.univ",
"Membership.mem",
"Exists",
"HasSubset.Subset",
"CompactSpace",
"TopologicalSpace",
"And",
"closure",
"isCompact_univ",
"Set.image2",
"eventually_closure_subset_of_isCompact_absorbing_of_isOpen_of_omegaLimit_subset'",
... | true |
Lean.Grind.CommRing.Poly.denote_mulConstC | Init.Grind.Ring.CommSolver | [
"cond",
"Lean.Grind.Semiring.one_mul",
"Int.cast",
"Eq.mpr",
"Lean.Grind.Ring.intCast_zero",
"Decidable.casesOn",
"instHSMul",
"Lean.Grind.Ring.zsmul_eq_intCast_mul",
"Lean.Grind.CommRing.Poly",
"HMul.hMul",
"Lean.Grind.CommRing.Poly.add",
"congrArg",
"Lean.Grind.AddCommMonoid.zero_add",
"... | true |
MeasureTheory.measureReal_abs_gt_le_integral_charFun | Mathlib.MeasureTheory.Measure.IntegralCharFun | [
"instInnerProductSpaceRealComplex",
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"Iff.mpr",
"AddGroup.toSubtractionMonoid",
"MeasurableSet.preimage",
"Set.ext",
"Real.instIsOrderedRing",
"Norm.norm",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"InnerProductS... | true |
Set.notMem_Iic | Mathlib.Order.Interval.Set.LinearOrder | [
"not_le",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"LinearOrder",
"PartialOrder.toPreorder",
"Membership.mem",
"DistribLattice.toLattice",
"Iff",
"LT.lt",
"Set.Iic",
"SemilatticeSup.toPartialOrder",
"Set.instMembership",
"Not",
"instDistribLatticeOfLinearOrder",
"Set"
] | true |
PrimeSpectrum.BasicConstructibleSetData.map_n | Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet | [
"CommSemiring.toSemiring",
"PrimeSpectrum.BasicConstructibleSetData",
"RingHom",
"CommSemiring",
"Nat",
"Eq.refl",
"PrimeSpectrum.BasicConstructibleSetData.n",
"Semiring.toNonAssocSemiring",
"Eq",
"PrimeSpectrum.BasicConstructibleSetData.map"
] | true |
_private.Init.Data.BitVec.Bitblast.0.BitVec.msb_smod._simp_1_7 | Init.Data.BitVec.Bitblast | [
"Int",
"LE.le",
"Int.instLTInt",
"LT.lt",
"propext",
"Int.not_lt",
"Eq",
"Not",
"Int.instLEInt"
] | false |
CategoryTheory.ShortComplex.HasHomology.mk' | Mathlib.Algebra.Homology.ShortComplex.Homology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.HasHomology",
"Nonempty.intro",
"CategoryTheory.ShortComplex.HasHomology.mk",
"CategoryTheory.ShortComplex.HomologyData",
"CategoryTheory.Category"
] | true |
Std.ExtDHashMap.Const.get_union_of_mem_right | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.inductionOn₂",
"Std.ExtDHashMap.contains",
"Std.ExtDHashMap.mk",
"LawfulHashable",
"Std.ExtDHashMap.union",
"Bool.true",
"Std.DHashMap.Const.get_union_of_mem_right",
"Std.ExtDHashMap.mem_union_of_right",
"EquivBEq",
"Std.ExtDHashMap",
"Bool",
"Std.ExtDHashMap.Const.get",
"Ha... | true |
riemannZeta_neg_two_mul_nat_add_one | Mathlib.NumberTheory.LSeries.RiemannZeta | [
"Real",
"HMul.hMul",
"riemannZeta",
"Nat.instAtLeastTwoHAddOfNat",
"Complex.instZero",
"AddCommGroup.toAddGroup",
"Complex.instMul",
"HurwitzZeta.hurwitzZetaEven_neg_two_mul_nat_add_one",
"SubtractionMonoid.toSubNegZeroMonoid",
"instOfNatNat",
"Complex.instNatCast",
"SubNegZeroMonoid.toNegZero... | true |
CategoryTheory.Limits.BinaryBicone.isLimitFstKernelFork._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | [
"CategoryTheory.Limits.BinaryBicone.fst",
"CategoryTheory.Category.assoc",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.Limits.BinaryBicone.toCone",
"CategoryTheory.Limits.BinaryFan.fst",
"CategoryTheory.Limits.BinaryBicone.inr_snd",
"CategoryTheory.CategoryStruc... | false |
Rat.cast_div | Mathlib.Data.Rat.Cast.CharZero | [
"RingHom.instRingHomClass",
"instHDiv",
"DivisionRing.toRatCast",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"DivisionSemiring.toGroupWithZero",
"RingHom",
"DivisionRing.toDivisionSemiring",
"DivisionRing.toDivInvMonoid",
"HDiv.hDiv",
"RingHomClass.toMonoidWithZeroHomClass",
"Rat.cast",
"D... | true |
Std.Http.Request.Builder.json | Std.Internal.Http.Data.Body.Full | [
"Std.Http.Request.Builder.header",
"Std.Http.Request.Builder",
"Std.Http.Request.Builder.fromBytes",
"String",
"Std.Http.Header.Name.contentType",
"Std.Http.Header.Value.ofString!",
"String.toUTF8",
"Std.Internal.IO.Async.Async",
"Std.Http.Body.Full",
"Std.Http.Request"
] | true |
Turing.TM0.Cfg | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"Inhabited",
"Turing.TM0.Cfg.mk"
] | true |
Homotopy.comp_hom | Mathlib.Algebra.Homology.Homotopy | [
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"Homotopy.hom",
"HomologicalComplex",
"Homotopy.comp",
"ComplexShape",
"CategoryTheory.Preadditive",
"instHAdd",
"HAdd.hAdd",
"CategoryTheory... | true |
_private.Mathlib.FieldTheory.AlgebraicClosure.0.algebraicClosure.isIntegralClosure._proof_1 | Mathlib.FieldTheory.AlgebraicClosure | [
"IsIntegralClosure",
"CommSemiring.toSemiring",
"IntermediateField",
"Algebra",
"Membership.mem",
"Field.toDivisionRing",
"Algebra.id",
"Subtype",
"IntermediateField.instSubfieldClass",
"CommRing.toNonAssocCommRing",
"Field.toSemifield",
"Field.toCommRing",
"IntermediateField.instAlgebraSubt... | false |
NumberField.instIsTotallyRealRat | Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex | [
"Eq.mpr",
"Rat.infinitePlace",
"congrArg",
"Rat",
"Rat.isReal_infinitePlace",
"NumberField.IsTotallyReal.mk",
"id",
"NumberField.IsTotallyReal",
"NumberField.InfinitePlace.IsReal",
"Rat.instField",
"NumberField.InfinitePlace",
"Subsingleton.elim",
"Eq",
"Rat.instSubsingletonInfinitePlace"
... | true |
addInvariantVectorField | Mathlib.Geometry.Manifold.GroupLieAlgebra | [
"AddGroup.toSubtractionMonoid",
"mfderiv",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"instAddCommGroupTangentSpace",
"ContinuousLinearMap.funLike",
"AddMonoid.toAddZeroClass",
"AddGroupLieAlgebra",
"NormedField.toField",
"AddZeroClass.toAddZero",
"instModuleTangentSpace",
"SubtractionMono... | true |
Lean.Meta.LazyDiscrTree.PartialMatch.mk.inj | Lean.Meta.LazyDiscrTree | [
"Lean.Expr",
"Array",
"Lean.Meta.LazyDiscrTree.PartialMatch",
"And",
"Lean.Meta.LazyDiscrTree.TrieIndex",
"Nat",
"Lean.Meta.LazyDiscrTree.PartialMatch.mk",
"And.intro",
"Lean.Meta.LazyDiscrTree.PartialMatch.mk.noConfusion",
"Eq"
] | true |
CategoryTheory.cokernelOpOp_hom | Mathlib.CategoryTheory.Abelian.Opposite | [
"CategoryTheory.Abelian.toPreadditive",
"Opposite",
"CategoryTheory.Limits.cokernel.desc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"CategoryTheory.Limits.cokernel",
"CategoryTheory.Abelian",
"CategoryTheory.Limits.kernel",
"CategoryTheory.cokernelOpUnop._proof_5",
... | true |
LucasLehmer.X.instAddCommGroup._proof_20 | Mathlib.NumberTheory.LucasLehmer | [
"LucasLehmer.X.instAddCommGroup._aux_17",
"ZMod.commRing",
"AddMonoid.toAddSemigroup",
"Add.mk",
"Prod.subNegMonoid._proof_3",
"AddMonoid.mk",
"AddCommGroup.toAddGroup",
"LucasLehmer.X.instAddCommGroup._aux_4",
"Int",
"LucasLehmer.X.instAddCommGroup._proof_10",
"AddSemigroup.mk",
"Nat.cast",
... | false |
BoundedContinuousFunction.C._proof_3 | Mathlib.Topology.ContinuousMap.Bounded.Normed | [
"NormedRing.toRing",
"PseudoMetricSpace.toBornology",
"AddMonoid.toAddZeroClass",
"AddGroupWithOne.toAddMonoidWithOne",
"instBoundedAddOfLipschitzAdd",
"NormedRing.toNonUnitalNormedRing",
"AddZeroClass.toAddZero",
"BoundedAdd",
"SeminormedAddCommGroup.to_lipschitzAdd",
"NormedRing.toSeminormedRing... | false |
Set.mulIndicator_mul_compl_eq_piecewise | Mathlib.Algebra.Group.Indicator | [
"Iff.mpr",
"Eq.mpr",
"MulOne.toOne",
"Pi.mul_apply",
"Set.piecewise_eq_of_notMem",
"HMul.hMul",
"congrArg",
"Compl.compl",
"Set.mulIndicator",
"Set.mulIndicator_of_notMem",
"Membership.mem",
"id",
"MulOne.toMul",
"Set.piecewise_eq_of_mem",
"Set.instCompl",
"dite",
"funext",
"MulOne... | true |
CategoryTheory.ShortComplex.HasLeftHomology.casesOn | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex.LeftHomologyData",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.HasLeftHomology.rec",
"CategoryTheory.ShortComplex.HasLeftHomology",
"Nonempty",
"CategoryTheory.ShortComplex.HasLeftHomology.mk",
"CategoryTheory.Categ... | false |
IsLocalization.AtPrime.equivQuotientMapOfIsMaximal._proof_2 | Mathlib.RingTheory.Localization.AtPrime.Extension | [
"RingHom.instRingHomClass",
"CommRing",
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Ideal.map",
"Ideal",
"HasQuotient.Quotient",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"Ideal.Quotient.semiring",
"CommRing.toRing",
"Semiring.toNonAssocSemiring",
"Rin... | false |
CategoryTheory.Bicategory.InducedBicategory.bicategory._proof_8 | Mathlib.CategoryTheory.Bicategory.InducedBicategory | [
"Eq.mpr",
"CategoryTheory.Bicategory.InducedBicategory.categoryStruct",
"CategoryTheory.Bicategory.InducedBicategory.mkHom₂",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Bicategory.InducedBicategory.Hom₂.hom",
"_private.Mathlib.CategoryTheory.Bicategory.InducedB... | false |
instMulActionRay._proof_1 | Mathlib.LinearAlgebra.Ray | [
"instHSMul",
"Equiv.instEquivLike",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"IsStrictOrderedRing",
"Group",
"AddZeroClass.toAddZero",
"PartialOrder",
"Equiv",
"Subtype",
"DistribSMul.toSMulZeroClass",
"DivInvMonoid.toMonoid",
"Ne",
"AddCom... | false |
_private.Std.Data.DTreeMap.Internal.Operations.0.Std.DTreeMap.Internal.Impl.Const.alter._proof_46 | Std.Data.DTreeMap.Internal.Operations | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"Std.DTreeMap.In... | false |
Int.associated_iff | Mathlib.Algebra.GCDMonoid.Nat | [
"Eq.mpr",
"Int.natAbs_eq_natAbs_iff",
"congrArg",
"id",
"Int.instNegInt",
"Int",
"Int.instMonoid",
"Iff",
"Associated",
"Nat",
"Int.associated_iff_natAbs",
"Int.natAbs",
"propext",
"Or",
"Eq",
"Neg.neg"
] | true |
CategoryTheory.Oplax.StrongTrans.whiskerRight_naturality_comp_assoc | Mathlib.CategoryTheory.Bicategory.NaturalTransformation.Oplax | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Oplax.StrongTrans.naturality",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Oplax.StrongTrans",
"CategoryTheory.OplaxFunctor.mapComp",
"CategoryTheory.OplaxFunctor.toPrelaxFunctor",
"Eq.mp",
"CategoryTheory.Bic... | true |
Aesop.instInhabitedCompleteMatch.default | Aesop.Forward.Match.Types | [
"Inhabited.default",
"Aesop.CompleteMatch.mk",
"Aesop.Match",
"Array",
"Array.instInhabited",
"Aesop.CompleteMatch"
] | true |
Lean.Server.ServerTask.mk.inj | Lean.Server.ServerTask | [
"Task",
"Lean.Server.ServerTask.mk.noConfusion",
"Lean.Server.ServerTask.mk",
"Lean.Server.ServerTask",
"eq_of_heq",
"HEq",
"Eq"
] | true |
Finset.map_refl | Mathlib.Data.Finset.Image | [
"Eq.mpr",
"congrArg",
"Finset",
"Finset.ext",
"Finset.map",
"Membership.mem",
"Exists",
"exists_eq_right",
"id",
"Function.Embedding",
"And",
"Iff",
"Finset.instSetLike",
"congrFun'",
"Function.instFunLikeEmbedding",
"Function.Embedding.refl",
"Eq",
"DFunLike.coe",
"SetLike.instM... | true |
Alexandrov.projSup_map | Mathlib.Topology.Sheaves.Alexandrov | [
"CategoryTheory.ObjectProperty.FullSubcategory.mk",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instCompleteLattice",
"TopologicalSpace.Opens.instPartialOrder",
"iSup",
"Quiver.Hom.op",
"Topology.IsUpperSet",
"PartialOrder.toPreo... | true |
FirstOrder.Language.Embedding.mk.injEq | Mathlib.ModelTheory.Basic | [
"Eq.propIntro",
"FirstOrder.Language.Embedding.mk",
"FirstOrder.Language.Embedding.mk.inj",
"Function.comp",
"FirstOrder.Language.Structure.RelMap",
"FirstOrder.Language.Embedding",
"autoParam",
"Function.Embedding",
"FirstOrder.Language.Embedding.map_rel'._autoParam",
"FirstOrder.Language.Structu... | true |
FunctionField.RingOfIntegers.instFintypeClassGroupSubtypeMemSubalgebraPolynomialRingOfIntegers | Mathlib.NumberTheory.ClassNumber.FunctionField | [
"FunctionField.RingOfIntegers.instFintypeClassGroupSubtypeMemSubalgebraPolynomialRingOfIntegers._proof_3",
"Subalgebra.instSetLike",
"FunctionField.RingOfIntegers.instFintypeClassGroupSubtypeMemSubalgebraPolynomialRingOfIntegers._proof_2",
"instSMulOfMul",
"IsScalarTower.right",
"FunctionField.ringOfInteg... | true |
CategoryTheory.Subfunctor.Subpresheaf.preimage_comp | Mathlib.CategoryTheory.Subfunctor.Image | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Subfunctor.preimage_comp",
"CategoryTheory.Functor.category",
"CategoryTheory.Subfunctor",
"CategoryTheory.types",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"Ca... | true |
Fin.add._proof_3 | Init.Data.Fin.Basic | [
"_private.Init.Data.Fin.Basic.0.Fin.mlt",
"Nat.instMod",
"instHMod",
"instHAdd",
"HMod.hMod",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"instLTNat"
] | false |
Batteries.PairingHeapImp.Heap.WF.nil | Batteries.Data.PairingHeap | [
"Batteries.PairingHeapImp.Heap.WF",
"Batteries.PairingHeapImp.Heap.WF.nil",
"Bool",
"Batteries.PairingHeapImp.Heap.nil"
] | true |
MeasureTheory.VectorMeasure.map_zero | Mathlib.MeasureTheory.VectorMeasure.Basic | [
"Eq.mpr",
"MeasurableSet",
"congrArg",
"MeasureTheory.VectorMeasure.mk",
"MeasureTheory.VectorMeasure.ext",
"AddMonoid.toAddZeroClass",
"MeasureTheory.VectorMeasure.measureOf'",
"Measurable",
"Classical.propDecidable",
"MeasureTheory.VectorMeasure.zero_apply",
"AddZeroClass.toAddZero",
"id",
... | true |
Cardinal.mk_ord_toType | Mathlib.SetTheory.Ordinal.Basic | [
"Cardinal",
"congrArg",
"Cardinal.mk",
"Cardinal.ord",
"Ordinal.card",
"True",
"Cardinal.card_ord",
"Cardinal.mk_toType",
"eq_self",
"of_eq_true",
"congrFun'",
"Ordinal.ToType",
"Eq",
"Eq.trans"
] | true |
Set.EqOn.comp_left | Mathlib.Data.Set.Function | [
"Function.comp",
"Membership.mem",
"Set.EqOn",
"congr_arg",
"Set.instMembership",
"Set"
] | true |
Ideal.fg_of_isUnit | Mathlib.RingTheory.FractionalIdeal.Operations | [
"Eq.mpr",
"FractionalIdeal.fg_of_isUnit",
"CommRing",
"FractionalIdeal.coeIdeal_fg",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"Algebra.algebraMap",
"congrArg",
"CommSemiring.toSemiring",
"IsUnit",
"Algebra",
"RingHom",
"Algebra.toModule",
"id",
"No... | true |
AlgebraicTopology.DoldKan.QInfty_f | Mathlib.AlgebraicTopology.DoldKan.PInfty | [
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"Nat.instAddCancelCommMonoid",
"AlgebraicTopology.DoldKan.Q",
"AlgebraicTopology.AlternatingFaceMapComplex.obj",
"C... | true |
List.Pairwise.pwFilter | Mathlib.Data.List.Pairwise | [
"Iff.mpr",
"List.Pairwise",
"DecidableRel",
"List.pwFilter_eq_self",
"List",
"List.pwFilter",
"Eq"
] | true |
CategoryTheory.Functor.curry₃_obj_map_app_app | Mathlib.CategoryTheory.Functor.CurryingThree | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"Prod.mk",
"CategoryTheory.Equivalence.functor",
"CategoryTheory.Functor.map",
"Prod.fst",
"CategoryTheory.prod.associativity",
"CategoryTheory... | true |
SpecialLinearGroup.congr_linearEquiv_symm | Mathlib.LinearAlgebra.SpecialLinearGroup | [
"LinearEquiv.symm",
"CommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"SpecialLinearGroup",
"AddCommGroup",
"SpecialLinearGroup.instMul",
"SpecialLinearGroup.congr_linearEquiv",
"CommRing.toCommSemiring",
"RingHomInvPair.ids",
"LinearEquiv",
"MulEquiv",
"Module",
"MulE... | true |
_private.Mathlib.Order.OrderIsoNat.0.exists_increasing_or_nonincreasing_subseq'._proof_1_5 | Mathlib.Order.OrderIsoNat | [
"Int.Linear.eq_of_core",
"Int.Linear.not_eq_norm_expr",
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"Int.Linear.norm_le",
"Int.Linear.Expr.eq_of_norm_eq",
"congrArg",
"Int.Linear.le_norm_expr",
"Int.Linear.le_unsat",
"Int.Linear.le_neg",
"Int.Linear.eq_norm",
"Classical.byContradiction",
"HS... | false |
Lean.Meta.Hypothesis.noConfusion | Lean.Meta.Tactic.Assert | [
"Lean.LocalDeclKind",
"Lean.Meta.Hypothesis.noConfusionType",
"Lean.Expr",
"Lean.Meta.Hypothesis",
"Lean.Meta.Hypothesis.casesOn",
"Eq.ndrec",
"Lean.Name",
"Eq.refl",
"Lean.BinderInfo",
"Eq"
] | false |
SetRel.comp_eq_self | Mathlib.Data.Rel | [
"SetRel",
"SetRel.left_subset_comp",
"subset_antisymm",
"Set.instAntisymmSubset",
"SetRel.comp",
"SetRel.comp_subset_self",
"SetRel.IsTrans",
"SetRel.IsRefl",
"Prod",
"Eq",
"Set.instHasSubset"
] | true |
AffineMap.comp_lineMap | Mathlib.LinearAlgebra.AffineSpace.AffineMap | [
"AffineMap.ext",
"Semiring.toModule",
"AffineMap.instFunLike",
"AddGroupWithOne.toAddGroup",
"AddCommGroup.toAddCommMonoid",
"AffineMap.apply_lineMap",
"AffineMap.lineMap",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"addGroupIsAddTorsor",
"AffineMap",
"Ring.toAddCommGroup",
"AddTorsor",
"M... | true |
fixedPoints.completeLattice | Mathlib.Order.FixedPoints | [
"fixedPoints.instSemilatticeInfElemFixedPointsCoeOrderHom",
"OrderHom.prevFixed",
"ChainCompletePartialOrder.instOfCompleteLattice",
"fixedPoints.completeLattice._proof_3",
"fixedPoints.instSemilatticeSupElemFixedPointsCoeOrderHom",
"fixedPoints.completeLattice._proof_1",
"fixedPoints.completeLattice._p... | true |
EMetric.diam_pair | Mathlib.Topology.EMetricSpace.Diam | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Set.instSingletonSet",
"Insert.insert",
"PseudoEMetricSpace",
"Metric.ediam",
"Metric.ediam_pair",
"Set.instInsert",
"WeakPseudoEMetricSpace.toEDist",
"PseudoEMetricSpace.toUniformSpace",
"ENNReal",
"EDist.edist",
"Singleton.singleton",
"Unifor... | true |
_private.Init.Data.UInt.Lemmas.0.UInt16.lt_or_lt_of_ne._simp_1_2 | Init.Data.UInt.Lemmas | [
"UInt16",
"Nat",
"propext",
"UInt16.toNat_inj",
"UInt16.toNat",
"Eq.symm",
"Eq"
] | false |
Lean.PersistentHashMap.IsEntriesNode.mk | Lean.Data.PersistentHashMap | [
"Lean.PersistentHashMap.Entry",
"Lean.PersistentHashMap.Node",
"Lean.PersistentHashMap.Node.entries",
"Array",
"Lean.PersistentHashMap.IsEntriesNode.mk",
"Lean.PersistentHashMap.IsEntriesNode"
] | true |
Lean.Meta.Grind.Arith.CollectDecVars.State.mk | Lean.Meta.Tactic.Grind.Arith.Util | [
"UInt64",
"Std.HashSet",
"instBEqOfDecidableEq",
"Lean.Meta.Grind.Arith.CollectDecVars.State",
"instDecidableEqUInt64",
"Lean.Meta.Grind.Arith.CollectDecVars.State.mk",
"Lean.FVarIdSet",
"instHashableUInt64"
] | true |
CategoryTheory.isCommAddMonObj_iff_isAddCommutative | Mathlib.CategoryTheory.Monoidal.Cartesian.Mon | [
"CategoryTheory.AddMonObj.add_eq_add",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Hom.addMonoid",
"AddMonoid.toAddZeroClass",
"CategoryTheory.CartesianMonoidalCategory.braiding_hom_fst",
"CategoryTheory.AddMonObj.comp_add",
"AddZeroClass.toAddZero",
"Catego... | true |
_private.Batteries.Data.String.Lemmas.0.String.Pos.Raw.extract.match_1.eq_1 | Batteries.Data.String.Lemmas | [
"String",
"String.Pos.Raw",
"Eq.refl",
"String.Pos.Raw.extract.match_1",
"Eq"
] | true |
DeltaGenerated.noConfusion | Mathlib.Topology.Category.DeltaGenerated | [
"autoParam",
"TopCat.str",
"DeltaGenerated.casesOn",
"TopCat.carrier",
"DeltaGenerated",
"DeltaGenerated.deltaGenerated._autoParam",
"Eq.ndrec",
"Eq.refl",
"DeltaGeneratedSpace",
"TopCat",
"Eq",
"DeltaGenerated.noConfusionType"
] | false |
Std.Slice.iter | Std.Data.Iterators.Producers.Slice | [
"Std.ToIterator",
"Id",
"Std.Iter",
"Std.Slice.Internal.iter",
"Std.Slice"
] | true |
CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app | Mathlib.CategoryTheory.Triangulated.Opposite.OpOp | [
"_private.Mathlib.CategoryTheory.Triangulated.Opposite.OpOp.0.CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app._proof_1_1",
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Pretriangulated.Opposite.OpOpCommShift.iso_inv_app._proof_4",
"CategoryTheory.Cate... | true |
_private.Mathlib.Data.Part.0.Part.mem_right_unique.match_1_1 | Mathlib.Data.Part | [
"Part",
"Membership.mem",
"Part.instMembership",
"Part.get",
"Exists.casesOn",
"Exists.intro",
"Part.Dom",
"Eq"
] | false |
ZFSet.card_powerset | Mathlib.SetTheory.ZFC.Cardinal | [
"Eq.mpr",
"Cardinal.instPowCardinal",
"Cardinal",
"congrArg",
"ZFSet",
"Nat.instAtLeastTwoHAddOfNat",
"Set.powerset",
"Cardinal.lift",
"Cardinal.mk",
"Membership.mem",
"Eq.mp",
"Set.Elem",
"id",
"Subtype",
"HasSubset.Subset",
"instOfNatNat",
"ZFSet.mem_powerset._simp_1",
"Cardinal.... | true |
Std.Time.Second.instOrdOrdinal | Std.Time.Time.Unit.Second | [
"Ord",
"Std.Time.Second.Ordinal",
"Ord.mk",
"Std.Time.Second.instOrdOrdinal._aux_1",
"Bool"
] | true |
Finset.inter_assoc | Mathlib.Data.Finset.Lattice.Basic | [
"Finset",
"_private.Mathlib.Data.Finset.Lattice.Basic.0.Finset.inter_assoc._proof_1_1",
"Inter.inter",
"Finset.instInter",
"Eq",
"DecidableEq"
] | true |
Multiset.dedup_add | Mathlib.Data.Multiset.FinsetOps | [
"Multiset.dedup",
"List.dedup",
"Multiset",
"instBEqOfDecidableEq",
"Quot.induction_on₂",
"congr_arg",
"instHAppendOfAppend",
"List",
"instHAdd",
"Multiset.ofList",
"HAdd.hAdd",
"List.dedup_append",
"List.union",
"List.instAppend",
"List.isSetoid",
"Eq",
"Multiset.instAdd",
"HAppen... | true |
String.Slice.Pos.toReplaceEnd | Init.Data.String.Basic | [
"String.instLEPos_1",
"String.Slice",
"LE.le",
"String.Slice.Pos.sliceTo",
"String.Slice.Pos",
"String.Slice.sliceTo"
] | true |
_private.Mathlib.Analysis.Complex.Liouville.0.Complex.norm_iteratedDeriv_le_of_forall_mem_sphere_norm_le._simp_1_2 | Mathlib.Analysis.Complex.Liouville | [
"False",
"eq_false",
"instOfNatNat",
"Nat.factorial_ne_zero",
"Nat.factorial",
"Nat",
"OfNat.ofNat",
"Eq"
] | false |
BooleanAlgebra.ofRegular._proof_3 | Mathlib.Order.Heyting.Regular | [
"LT.mk",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"Compl.compl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Preorder.mk",
"Preorder.le_refl",
"SemilatticeInf.toMin",
"LE.le",
"Preorder.le_trans",
"SemilatticeInf.mk",
"Preorder.lt_iff_le_not_ge",
"PartialOrder.le_antisymm",
"General... | false |
Std.Iter.Partial.instForIn' | Init.Data.Iterators.Consumers.Loop | [
"Std.Iter.instForIn'",
"Std.Iter.Partial.it",
"Std.IteratorLoop",
"Membership.mem",
"ForIn'.mk",
"ForIn'.forIn'",
"Id",
"ForInStep",
"Std.Iterator",
"ForIn'",
"Std.Iter.IsPlausibleIndirectOutput",
"Std.Iter",
"Membership.mk",
"Monad",
"Std.Iter.Partial"
] | true |
ProbabilityTheory.Kernel.HasSubgaussianMGF.ae_eq_zero_of_hasSubgaussianMGF_zero_of_measurable | Mathlib.Probability.Moments.SubGaussian | [
"MeasureTheory.ae",
"Eq.mpr",
"Real",
"MeasureTheory.Measure",
"measurableSet_eq_fun",
"Real.instZero",
"congrArg",
"Filter.Eventually",
"EMetricSpace.metrizableSpace",
"Measurable",
"PseudoMetricSpace.toUniformSpace",
"ProbabilityTheory.Kernel.instFunLike",
"Filter.EventuallyEq",
"Filter.... | true |
Matrix.SpecialLinearGroup.row_ne_zero | Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup | [
"Nontrivial",
"Matrix.SpecialLinearGroup.det_ne_zero",
"CommRing",
"Matrix.SpecialLinearGroup",
"congrArg",
"CommSemiring.toSemiring",
"Matrix",
"AddGroupWithOne.toAddMonoidWithOne",
"Pi.instZero",
"Ne",
"AddMonoidWithOne.toOne",
"CommRing.toCommSemiring",
"Fintype",
"congrFun",
"True",
... | true |
CategoryTheory.ShortComplex.exact_and_mono_f_iff_f_is_kernel | Mathlib.Algebra.Homology.ShortComplex.Exact | [
"CategoryTheory.ShortComplex.Exact.fIsKernel",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.HasHomology",
"CategoryTheory... | true |
CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.precomposeObjComp._proof_4 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | [
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.Hom.snd",
"CategoryTheory.Functor",
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.instCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
... | false |
_private.Lean.Syntax.0.Lean.Syntax.hasIdent.match_1 | Lean.Syntax | [
"Lean.Syntax.node",
"Lean.Syntax.ident",
"Lean.Syntax.ctorIdx",
"Lean.SourceInfo",
"Lean.Syntax",
"Nat.hasNotBit",
"Substring.Raw",
"Array",
"List",
"Lean.Syntax.Preresolved",
"_private.Lean.Syntax.0.Lean.Syntax.hasIdent._sparseCasesOn_1",
"Lean.Name",
"Lean.SyntaxNodeKind"
] | false |
Nucleus.coe_top | Mathlib.Order.Nucleus | [
"Nucleus",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"OrderTop",
"Nucleus.instTop",
"Nucleus.instFunLike",
"SemilatticeInf",
"OrderTop.toTop",
"Pi.instTopForall",
"Top.top",
"Eq",
"DFunLike.coe",
"rfl"
] | true |
Nat.choose._sunfold | Mathlib.Data.Nat.Choose.Basic | [
"Nat.choose.match_1",
"Nat.choose",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat"
] | false |
_private.Mathlib.RingTheory.HahnSeries.Summable.0.HahnSeries.instField._simp_9 | Mathlib.RingTheory.HahnSeries.Summable | [
"Int.cast",
"ZeroHom.funLike",
"HahnSeries.instIntCast",
"HahnSeries.single_zero_intCast",
"HahnSeries.single",
"IntCast",
"PartialOrder",
"HahnSeries.instZero",
"Int",
"ZeroHom",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq.symm",
"HahnSeries",
"Eq",
"DFunLike.coe",
"Zero"
] | false |
_private.Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape.0.CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_iff_of_equivalence._simp_1_1 | Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape | [
"Prop.le",
"CategoryTheory.ObjectProperty.IsClosedUnderLimitsOfShape",
"LE.le",
"Pi.hasLe",
"propext",
"CategoryTheory.ObjectProperty.limitsOfShape",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"CategoryTheory.ObjectProperty.isClosedUnderLimitsOfShape_iff",
"CategoryTheory.ObjectProperty",
... | false |
Lean.Grind.ToInt.Add | Init.Grind.ToInt | [
"outParam",
"Lean.Grind.ToInt.Add.mk",
"Lean.Grind.ToInt",
"Add",
"Lean.Grind.IntInterval"
] | true |
VAdd.comp.vadd.eq_1 | Mathlib.Algebra.Group.Action.Defs | [
"VAdd.comp.vadd",
"VAdd",
"HVAdd.hVAdd",
"instHVAdd",
"Eq.refl",
"Eq"
] | true |
upperHemicontinuousOn_iff_preimage_Iic | Mathlib.Topology.Semicontinuity.Hemicontinuity | [
"Filter.instMembership",
"congrArg",
"nhdsWithin",
"PartialOrder.toPreorder",
"Membership.mem",
"CompleteLattice.toConditionallyCompleteLattice",
"UpperHemicontinuousOn",
"iff_self",
"TopologicalSpace",
"UpperHemicontinuousWithinAt",
"Iff",
"Set.preimage",
"_private.Mathlib.Topology.Semicont... | true |
_private.Mathlib.Algebra.Module.ZLattice.Basic.0.ZSpan.fundamentalDomain_ae_parallelepiped._simp_1_5 | Mathlib.Algebra.Module.ZLattice.Basic | [
"Exists",
"propext",
"Classical.not_forall",
"Eq",
"Not"
] | false |
CategoryTheory.Comon.Hom.mk.injEq | Mathlib.CategoryTheory.Monoidal.Comon_ | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Eq.propIntro",
"CategoryTheory.IsComonHom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Comon.Hom",
"Eq.ndrec",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Comon.Hom.mk",
"CategoryTheory.Comon.Hom.mk.inj",... | true |
Ordinal.lt_omega0_opow_succ | Mathlib.SetTheory.Ordinal.Exponential | [
"le_refl",
"Ordinal.instLinearOrder",
"Ordinal.mulRightMono",
"Ordinal.instAddRightMono",
"Preorder.toLT",
"HMul.hMul",
"Order.succ",
"_private.Mathlib.SetTheory.Ordinal.Exponential.0.Ordinal.lt_omega0_opow_succ.match_1_1",
"Ordinal.omega0",
"Ordinal.partialOrder",
"MulZeroClass.toMul",
"instI... | true |
Pi.default_apply | Mathlib.Logic.Unique | [
"Inhabited.default",
"Pi.instInhabited",
"Inhabited",
"Eq",
"rfl"
] | true |
ContinuousOrderHom.coe_id | Mathlib.Topology.Order.Hom.Basic | [
"id",
"ContinuousOrderHom.id",
"ContinuousOrderHom",
"TopologicalSpace",
"ContinuousOrderHom.instFunLike",
"Eq",
"DFunLike.coe",
"rfl",
"Preorder"
] | true |
instSemilatticeSupTropical | Mathlib.Algebra.Tropical.Lattice | [
"SemilatticeSup.mk",
"instSemilatticeSupTropical._proof_3",
"SemilatticeSup.toMax",
"PartialOrder",
"Tropical",
"instSemilatticeSupTropical._proof_1",
"Tropical.instPartialOrderTropical",
"Max.max",
"instSemilatticeSupTropical._proof_2",
"SemilatticeSup.toPartialOrder",
"Tropical.trop",
"Semil... | true |
Topology.RelCWComplex.cellFrontier.eq_1 | Mathlib.Topology.CWComplex.Classical.Basic | [
"Topology.RelCWComplex",
"Real",
"pseudoMetricSpacePi",
"Real.instZero",
"Topology.RelCWComplex.cellFrontier",
"Topology.RelCWComplex.map",
"Pi.instZero",
"Fin.fintype",
"Real.instOne",
"TopologicalSpace",
"Nat",
"Topology.RelCWComplex.cell",
"One.toOfNat1",
"Zero.toOfNat0",
"Eq.refl",
... | true |
Fin.encodeSubtype.match_3 | Batteries.Data.Fin.Coding | [
"instNeZeroNatHAdd_1",
"False",
"Fin.casesOn",
"Fin.ofNat._proof_1",
"HEq.refl",
"False.elim",
"Subtype.casesOn",
"noConfusion_of_Nat",
"Fin.mk",
"Fin.instOfNat",
"Subtype",
"instOfNatNat",
"Nat.le.step",
"Subtype.mk",
"instHAdd",
"HAdd.hAdd",
"Nat.le",
"Nat.instNeZeroSucc",
"Dec... | false |
CoxeterSystem.isReflection_conj_iff | Mathlib.GroupTheory.Coxeter.Inversion | [
"MulOne.toOne",
"Semigroup.toMul",
"inv_mul_cancel",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"Eq.mp",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"CoxeterSystem.IsReflection",
"D... | true |
_private.Mathlib.CategoryTheory.Monoidal.Comon_.0.CategoryTheory.Comon.instIsComonHomHom._proof_1 | Mathlib.CategoryTheory.Monoidal.Comon_ | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsComonHom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Comon.instCategory",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Comon.comon",
"CategoryTheory.Comon.Hom.isComonHom_hom",
"CategoryTheory.Comon",
... | false |
Int.units_eq_one_or | Mathlib.Algebra.Ring.Int.Units | [
"Units.val",
"Eq.mpr",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"congrArg",
"Int.isUnit_eq_one_or",
"_private.Mathlib.Algebra.Ring.Int.Units.0.Int.units_eq_one_or._simp_1_1",
"Units.instNeg",
"Units",
"id",
"Int",
"Units.instOne",
"Int.instMonoid",
"... | true |
Rat.mul._proof_1 | Init.Data.Rat.Basic | [
"Nat.gcd",
"Rat.num",
"Dvd.dvd",
"Rat",
"Rat.den",
"Rat.normalize.dvd_num",
"Int",
"Nat.cast",
"Int.instDvd",
"Nat",
"Int.natAbs",
"instNatCastInt",
"rfl"
] | false |
Submodule.FG.restrictScalars | Mathlib.RingTheory.Finiteness.Basic | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"Submodule.module._proof_1",
"instSMulOfMul",
"congrArg",
"DistribMulAction.toDistribSMul",
"IsScalarTower",
"Submodule.addCommMonoid",
"Submodule.restrictScalars",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.t... | true |
Lean.Elab.Term.initFn._@.Lean.Elab.MutualDef.772248409._hygCtx._hyg.4 | Lean.Elab.MutualDef | [
"Lean.Option",
"Lean.Name.mkStr5",
"IO",
"Lean.Option.Decl.mk",
"Bool.true",
"Lean.KVMap.instValueBool",
"Lean.Option.register",
"Bool",
"Lean.Name.mkStr2"
] | false |
_private.Lean.Meta.Tactic.Grind.Internalize.0.Lean.Meta.Grind.isCongruentCheck.go.match_1 | Lean.Meta.Tactic.Grind.Internalize | [
"_private.Lean.Meta.Tactic.Grind.Internalize.0.Lean.Meta.Grind.isCongruentCheck.go._sparseCasesOn_1",
"Lean.Expr",
"Nat.hasNotBit",
"Lean.Expr.app",
"Lean.Expr.ctorIdx"
] | false |
_private.Mathlib.Data.Finset.Union.0.Finset.mem_disjiUnion._simp_1_2 | Mathlib.Data.Finset.Union | [
"Membership.mem",
"Exists",
"Multiset",
"Multiset.instMembership",
"And",
"propext",
"Multiset.mem_bind",
"Eq",
"Multiset.bind"
] | false |
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