name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
_private.Mathlib.CategoryTheory.ComposableArrows.Basic.0.CategoryTheory.ComposableArrows.Precomp.obj.match_1.eq_2 | Mathlib.CategoryTheory.ComposableArrows.Basic | [
"CategoryTheory.ComposableArrows.Precomp.obj.match_1",
"Fin.mk",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"Eq.refl",
"instLTNat",
"OfNat.ofNat",
"Fin",
"Nat.succ",
"Eq"
] | true |
_private.Std.Sync.Broadcast.0.Std.Bounded.rec | Std.Sync.Broadcast | [
"_private.Std.Sync.Broadcast.0.Std.Bounded",
"_private.Std.Sync.Broadcast.0.Std.Bounded.mk",
"Std.Mutex",
"_private.Std.Sync.Broadcast.0.Std.Bounded.State"
] | false |
EStateM.run_modify | Init.Control.Lawful.Instances | [
"modify",
"EStateM.Result",
"EStateM.run",
"EStateM.instMonadStateOf",
"PUnit",
"instMonadStateOfMonadStateOf",
"EStateM",
"PUnit.unit",
"EStateM.Result.ok",
"Eq",
"rfl"
] | true |
RingHom.algebraMap_toAlgebra | Mathlib.Algebra.Algebra.Defs | [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"RingHom",
"CommSemiring",
"Semiring.toNonAssocSemiring",
"Eq",
"RingHom.toAlgebra",
"rfl"
] | true |
CategoryTheory.ShortComplex.isLimitπ₃MapConeLimitCone._proof_2 | Mathlib.Algebra.Homology.ShortComplex.Limits | [
"CategoryTheory.Limits.limit.π",
"Eq.mpr",
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.ShortComplex",
"CategoryTheory.Fun... | false |
not_subsingleton | Mathlib.Logic.Nontrivial.Defs | [
"Nontrivial",
"Subsingleton",
"not_nontrivial",
"Not"
] | true |
Std.ExtHashMap.getKeyD_insertManyIfNewUnit_list_of_not_mem_of_contains_eq_false | Std.Data.ExtHashMap.Lemmas | [
"Std.ExtDHashMap.Const.getKeyD_insertManyIfNewUnit_list_of_not_mem_of_contains_eq_false",
"instForInOfForIn'",
"List.contains",
"Std.ExtHashMap.inner",
"Membership.mem",
"inferInstance",
"Std.ExtHashMap.getKeyD",
"Std.ExtHashMap.insertManyIfNewUnit",
"Id",
"Membership",
"LawfulHashable",
"Std.... | true |
Module.Basis.det_inv | Mathlib.LinearAlgebra.Determinant | [
"AlternatingMap",
"Units.val",
"Eq.mpr",
"MulOne.toOne",
"CommRing",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Module.Basis.isUnit_det",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"MonoidHom",
"Monoid.toMulOneClass",
"congrArg",
"Co... | true |
optionProdEquiv._proof_2 | Mathlib.Logic.Equiv.Prod | [
"optionProdEquiv.match_3",
"Option.casesOn",
"Option.some",
"Sum.casesOn",
"Sum",
"id",
"Prod.mk",
"Prod.map",
"Sum.inl",
"Prod.fst",
"Option.none",
"Sum.inr",
"Prod",
"Eq",
"Prod.snd",
"rfl",
"Option"
] | false |
instContinuousNegMulOpposite | Mathlib.Topology.Algebra.Ring.Basic | [
"Homeomorph.isInducing",
"NonUnitalNonAssocRing",
"NegZeroClass.toNeg",
"MulOpposite.opHomeomorph",
"NonUnitalNonAssocRing.toAddCommGroup",
"MulOpposite",
"SubtractionMonoid.toSubNegZeroMonoid",
"MulOpposite.instNeg",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
... | true |
_private.Lean.Compiler.LCNF.Main.0.Lean.Compiler.LCNF.isValidMainType._sparseCasesOn_4 | Lean.Compiler.LCNF.Main | [
"Lean.Name.rec",
"Nat.ne_of_beq_eq_false",
"String",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Name.num",
"Lean.Name.ctorIdx",
"Lean.Name.str",
"Lean.Name.anonymous",
"Nat.land",
"Nat",
"Bool",
"Lean.Name",
"Eq.refl",
"OfNat.ofNat",
"Bool.false"
] | false |
_private.Mathlib.Data.Num.Prime.0.PosNum.minFacAux.match_1.eq_1 | Mathlib.Data.Num.Prime | [
"instOfNatNat",
"Nat",
"PosNum.minFacAux.match_1",
"Eq.refl",
"PosNum",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
Multiset.zero_add | Mathlib.Data.Multiset.AddSub | [
"Multiset",
"Quotient.inductionOn",
"Quotient.mk",
"List",
"instHAdd",
"HAdd.hAdd",
"Zero.toOfNat0",
"List.isSetoid",
"OfNat.ofNat",
"Eq",
"Multiset.instAdd",
"rfl",
"Multiset.instZero"
] | true |
finrank_of_isSplittingField_X_pow_sub_C | Mathlib.FieldTheory.KummerExtension | [
"Iff.mpr",
"Eq.mpr",
"Polynomial.C",
"IsGalois.card_aut_eq_finrank",
"Exists.choose_spec",
"Nat.instMulZeroClass",
"NeZero.mk",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"ZMod.commRing",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"... | true |
_private.Mathlib.Tactic.CategoryTheory.Bicategory.Datatypes.0.Mathlib.Tactic.Bicategory.Mor₂IsoOfExpr.match_1 | Mathlib.Tactic.CategoryTheory.Bicategory.Datatypes | [
"of_decide_eq_true",
"String",
"_private.Mathlib.Tactic.CategoryTheory.Bicategory.Datatypes.0.Mathlib.Tactic.Bicategory.srcExpr._sparseCasesOn_2",
"Array.getLit",
"Lean.Expr",
"id",
"Nat.hasNotBit",
"Prod.mk",
"instOfNatNat",
"Lean.Name.ctorIdx",
"dite",
"Lean.Name.str",
"List.toArray",
"L... | false |
RCLike.re_eq_norm_of_mul_conj | Mathlib.Analysis.RCLike.Basic | [
"Norm.norm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"SeminormedRing.toNorm",
"Real",
"RCLike.ofReal_re",
"RCLike.toNormedAlgebra",
"HMul.hMul",
"RCLike.mul_conj",
"AddMonoid.toAddSemigroup",
"Algebra.algebraMap",
"norm_pow",
"Real.instAddMonoid",
"congrArg",
"CommSemiring.toSem... | true |
_private.Init.Data.List.Attach.0.List.findSome?.match_1.eq_1 | Init.Data.List.Attach | [
"Option.some",
"List.findSome?.match_1",
"Option.none",
"Unit",
"Eq.refl",
"Eq",
"Option"
] | true |
CategoryTheory.Square.isPullback_iff | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Square | [
"CategoryTheory.Square.f₂₄",
"CategoryTheory.IsPullback.mk",
"CategoryTheory.Limits.WidePullbackShape.category",
"CategoryTheory.Square.X₂",
"CategoryTheory.Square",
"CategoryTheory.Square.f₁₃",
"CategoryTheory.Square.f₁₂",
"CategoryTheory.CommSq.mk",
"CategoryTheory.Square.pullbackCone",
"Categor... | true |
UInt64.toNat.eq_1 | Init.Data.UInt.Lemmas | [
"UInt64",
"instOfNatNat",
"BitVec.toNat",
"UInt64.toNat",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"UInt64.toBitVec"
] | true |
FreeMonoid.map_of | Mathlib.Algebra.FreeMonoid.Basic | [
"CancelMonoid.toRightCancelMonoid",
"FreeMonoid",
"MonoidHom.instFunLike",
"MonoidHom",
"Monoid.toMulOneClass",
"FreeMonoid.instCancelMonoid",
"MulOneClass.toMulOne",
"FreeMonoid.of",
"RightCancelMonoid.toMonoid",
"Eq",
"DFunLike.coe",
"FreeMonoid.map",
"rfl"
] | true |
_private.Mathlib.RingTheory.SimpleRing.Congr.0.isSimpleRing_iff_isTwoSided_imp._simp_1_2 | Mathlib.RingTheory.SimpleRing.Congr | [
"Nontrivial",
"OrderBot.toBot",
"IsSimpleOrder",
"Bot.bot",
"LE",
"And",
"isSimpleOrder_iff",
"OrderTop.toTop",
"BoundedOrder.toOrderTop",
"BoundedOrder.toOrderBot",
"propext",
"Or",
"Top.top",
"BoundedOrder",
"Eq"
] | false |
_private.Mathlib.Geometry.Manifold.Instances.Real.0.instIsManifoldIcc._simp_4 | Mathlib.Geometry.Manifold.Instances.Real | [
"AddMonoid.toAddZeroClass",
"AddRightStrictMono",
"HSub.hSub",
"AddZeroClass.toAddZero",
"SubNegMonoid.toSub",
"instHAdd",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"LT.lt",
"propext",
"AddZero.toAdd",
"SubNegMonoid.toAddMonoid",
"lt_sub_iff_add_lt",
"Eq",
"LT"
... | false |
piecewise_ae_eq_restrict | Mathlib.MeasureTheory.Measure.Restrict | [
"MeasureTheory.ae",
"Eq.mpr",
"Filter.EventuallyEq.filter_mono",
"MeasureTheory.Measure",
"MeasurableSet",
"congrArg",
"Set.EqOn.eventuallyEq",
"Filter.instCompleteLatticeFilter",
"Membership.mem",
"inf_le_right",
"CompleteLattice.toConditionallyCompleteLattice",
"MeasureTheory.Measure.restric... | true |
_private.Mathlib.Probability.Independence.Process.HasIndepIncrements.IsGaussianProcess.0.Finset.orderEmbOfFinWithBot._proof_1 | Mathlib.Probability.Independence.Process.HasIndepIncrements.IsGaussianProcess | [
"instNeZeroNatHAdd_1",
"Finset",
"Zero.ofOfNat0",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"Finset.card",
"instAddNat",
"NeZero",
"OfNat.ofNat"
] | false |
CategoryTheory.Pseudofunctor.Grothendieck.map_comp_forget | Mathlib.CategoryTheory.Bicategory.Grothendieck | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Pseudofunctor.Grothendieck.map",
"CategoryTheory.Pseudofunctor.Grothendieck.forget",
"CategoryTheory.locallyDiscreteBicategory",
"CategoryTheory.Pseudofunctor.Grothendieck",
"CategoryTheory.Functor.comp",... | true |
String.Pos.ofSliceTo_startPos | Init.Data.String.Basic | [
"congrArg",
"String.Slice.Pos.offset",
"String",
"String.startPos",
"String.Slice.startPos",
"String.Pos.Raw",
"_private.Init.Data.String.Basic.0.String.Pos.ofSliceTo_startPos._simp_1_1",
"String.Pos.offset_ofSliceTo",
"congr",
"True",
"eq_self",
"String.offset_startPos",
"String.Pos",
"of... | true |
LinearMap.bijective_of_surjective_of_bijective_of_right_exact | Mathlib.Algebra.FiveLemma | [
"Function.Exact",
"CommRing",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"Exists",
"AddCommGroup",
"id",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"LinearMap",
... | true |
CategoryTheory.Abelian.LeftResolution.karoubi.π'._proof_3 | Mathlib.Algebra.Homology.LeftResolution.Reduced | [
"CategoryTheory.Idempotents.Karoubi.Hom.f",
"CategoryTheory.Abelian.LeftResolution.karoubi.F",
"CategoryTheory.Functor",
"CategoryTheory.Idempotents.Karoubi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"sub_zero",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Abelian.... | false |
CompletePartialOrder.mk.noConfusion | Mathlib.Order.CompletePartialOrder | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"DirectedOn",
"OrderBot",
"PartialOrder",
"id",
"CompletePartialOrder.noConfusion",
"SupSet",
"LE.le",
"heq_of_eq",
"IsLUB",
"Eq.refl",
"HEq",
"Eq",
"SupSet.sSup",
"CompletePartialOrder.mk",
"CompletePartialOrder",
"Set"
] | false |
Submonoid.instSMulCommClassSubtypeMem_1 | Mathlib.Algebra.Group.Submonoid.MulAction | [
"SetLike",
"SMul",
"Membership.mem",
"Subtype",
"Submonoid.instSMulSubtypeMem",
"SMulCommClass.smul_comm",
"SMulCommClass.mk",
"Subtype.val",
"SetLike.instMembership",
"SMulCommClass"
] | true |
FreeLieAlgebra.Rel.brecOn | Mathlib.Algebra.Lie.Free | [
"FreeLieAlgebra.Rel.below",
"CommRing",
"FreeNonUnitalNonAssocAlgebra",
"CommSemiring.toSemiring",
"FreeLieAlgebra.Rel.below.leibniz_lie",
"FreeLieAlgebra.Rel.below.smul",
"FreeLieAlgebra.Rel.below.lie_self",
"FreeLieAlgebra.Rel.below.add_right",
"CommRing.toCommSemiring",
"FreeLieAlgebra.Rel.belo... | true |
Real.exp_strictMono | Mathlib.Analysis.Complex.Exponential | [
"Iff.mpr",
"Real.instIsOrderedRing",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"MulOne.toOne",
"Real.partialOrder",
"Real",
"Preorder.toLT",
"Mathlib.Tactic.Ring.Common.neg_add",
"HM... | true |
CompleteBooleanAlgebra.toCompleteDistribLattice | Mathlib.Order.CompleteBooleanAlgebra | [
"BiheytingAlgebra",
"CompleteDistribLattice",
"CompleteDistribLattice.mk",
"CompleteBooleanAlgebra",
"CompleteBooleanAlgebra.toCompleteDistribLattice._proof_5",
"BooleanAlgebra.toBiheytingAlgebra",
"CompleteBooleanAlgebra.toSDiff",
"CompleteBooleanAlgebra.toCompleteDistribLattice._proof_4",
"Complet... | true |
RingEquiv.piUnique | Mathlib.Algebra.Ring.Equiv | [
"Inhabited.default",
"Unique",
"Equiv",
"Distrib.toAdd",
"RingEquiv.piUnique._proof_2",
"Pi.instAdd",
"Distrib.toMul",
"Equiv.piUnique",
"RingEquiv.piUnique._proof_1",
"NonUnitalNonAssocSemiring.toDistrib",
"Pi.instMul",
"RingEquiv.mk",
"Unique.instInhabited",
"RingEquiv",
"NonUnitalNonA... | true |
CategoryTheory.Square.kernelFork | Mathlib.Algebra.Homology.Square | [
"NegZeroClass.toNeg",
"CategoryTheory.Square.f₂₄",
"CategoryTheory.Limits.KernelFork.ofι",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.biprod.desc",
"CategoryTheory.Limits.KernelFork",
"CategoryTheory.Square.kernelFork._proof_1",
"CategoryTheory.Square.X₂",
"Cate... | true |
_private.Batteries.Data.String.Lemmas.0.String.Pos.Raw.extract.go₁.match_1.splitter | Batteries.Data.String.Lemmas | [
"String.Pos.Raw",
"List.cons",
"List",
"List.casesOn",
"Char",
"List.nil"
] | true |
Units.inv_le_one._simp_1 | Mathlib.Algebra.Order.Monoid.Unbundled.Units | [
"Monoid",
"Units.val",
"MulOne.toOne",
"Monoid.toMulOneClass",
"Units.inv_le_one",
"Units",
"MulLeftMono",
"MulOne.toMul",
"LE.le",
"LE",
"MulOneClass.toMulOne",
"Inv.inv",
"propext",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"Units.instInv"
] | false |
Finset.noncommProd_mul_distrib | Mathlib.Data.Finset.NoncommProd | [
"Iff.mpr",
"Monoid",
"Eq.mpr",
"Commute.mul_mul_mul_comm",
"MulOne.toOne",
"Semigroup.toMul",
"Pi.mul_apply",
"HMul.hMul",
"Finset.mem_cons_of_mem",
"Function.onFun",
"Monoid.toMulOneClass",
"Finset.cons",
"congrArg",
"Finset",
"Commute",
"Set.Pairwise.mono",
"Function.comp",
"Memb... | true |
_private.Mathlib.Algebra.ContinuedFractions.Translations.0.GenContFract.contsAux.match_3.splitter | Mathlib.Algebra.ContinuedFractions.Translations | [
"instOfNatNat",
"GenContFract.contsAux.match_3",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ"
] | true |
LinearOrder.supClosed._simp_1 | Mathlib.Order.SupClosed | [
"Lattice.toSemilatticeSup",
"LinearOrder",
"DistribLattice.toLattice",
"SupClosed",
"True",
"eq_true",
"LinearOrder.supClosed",
"Eq",
"instDistribLatticeOfLinearOrder",
"Set"
] | false |
ESeminormedCommMonoid.mk.noConfusion | Mathlib.Analysis.Normed.Group.Defs | [
"ESeminormedMonoid",
"Semigroup.toMul",
"HMul.hMul",
"HEq.refl",
"ESeminormedCommMonoid.noConfusion",
"id",
"ESeminormedCommMonoid",
"ESeminormedMonoid.toMonoid",
"TopologicalSpace",
"heq_of_eq",
"ESeminormedCommMonoid.mk",
"Monoid.toSemigroup",
"Eq.refl",
"HEq",
"Eq",
"instHMul"
] | false |
Lean.getLibDir | Lean.Util.Path | [
"Pure.pure",
"Unit.unit",
"instHDiv",
"Monad.toApplicative",
"IO",
"HDiv.hDiv",
"instDecidableEqBool",
"instMonadEIO",
"Applicative.toPure",
"Bool.true",
"Unit",
"Lean.Internal.isStage0",
"System.FilePath.mk",
"Bool",
"PUnit.unit",
"IO.Error",
"System.FilePath.instDiv",
"Eq",
"Sy... | true |
Algebra.norm_natCast | Mathlib.RingTheory.Norm.Defs | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"CommRing",
"MonoidHom.instFunLike",
"Algebra.algebraMap",
"Ring.toNonAssocRing",
"MonoidHom",
"congrArg",
"CommSemiring.toSemiring",
"AddGroupWithOne.toAddMonoidWithOne",
"Algebra",
"RingHom",
"Algebra.toModu... | true |
Lean.Grind.CommRing.SPolResult.k₂._default | Lean.Meta.Tactic.Grind.Arith.CommRing.Poly | [
"id",
"Int",
"instOfNat",
"OfNat.ofNat"
] | false |
instTransLtAntisymmRelLe | Mathlib.Order.Antisymmetrization | [
"Preorder.toLT",
"Preorder.toLE",
"LE.le",
"Trans",
"LT.lt",
"AntisymmRel",
"Trans.mk",
"Preorder",
"lt_of_lt_of_antisymmRel"
] | true |
Con.lift._proof_1 | Mathlib.GroupTheory.Congruence.Hom | [
"Eq.mpr",
"MonoidHom.instMonoidHomClass",
"MulOne.toOne",
"MonoidHom.instFunLike",
"MonoidHom",
"congrArg",
"id",
"MulOne.toMul",
"Con.instLE",
"Con.mulOneClass",
"LE.le",
"Con.Quotient",
"MulOneClass.toMulOne",
"Con.ker",
"Con.liftOn",
"MonoidHom.map_one",
"MonoidHomClass.toMulHomCl... | false |
_private.Mathlib.Analysis.InnerProductSpace.Laplacian.0.ContDiffAt.laplacian_sub._simp_1_1 | Mathlib.Analysis.InnerProductSpace.Laplacian | [
"Finset",
"HSub.hSub",
"SubtractionMonoid.toSubNegMonoid",
"SubtractionCommMonoid.toSubtractionMonoid",
"SubtractionCommMonoid.toAddCommMonoid",
"SubNegMonoid.toSub",
"instHSub",
"Finset.sum_sub_distrib",
"SubtractionCommMonoid",
"Eq.symm",
"Eq",
"Finset.sum"
] | false |
_private.Mathlib.Order.Bounds.Basic.0.lt_isLUB_iff._simp_1_1 | Mathlib.Order.Bounds.Basic | [
"not_le",
"Preorder.toLT",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"LT.lt",
"propext",
"Eq.symm",
"LinearOrder.toPartialOrder",
"Eq",
"Not"
] | false |
Submonoid.bot_prod_bot | Mathlib.Algebra.Group.Submonoid.Operations | [
"MulOne.toOne",
"congrArg",
"and_self",
"Prod.instMulOneClass",
"Set.instSingletonSet",
"Set.singleton_eq_singleton_iff._simp_1",
"Prod.mk",
"Bot.bot",
"Prod.mk_eq_one._simp_2",
"SetLike.coe_injective",
"Set.singleton_prod_singleton",
"MulOneClass.toMulOne",
"And",
"SetLike.coe",
"congr"... | true |
Lean.Parser.Term.typeAscription._regBuiltin.Lean.Parser.Term.typeAscription.formatter_13 | Lean.Parser.Term | [
"Lean.PrettyPrinter.Formatter",
"Lean.Parser.Term.typeAscription.formatter",
"Lean.Name.mkStr5",
"IO",
"Unit",
"Lean.PrettyPrinter.formatterAttribute",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
nnnorm_commutator_units_sub_one_le | Mathlib.Analysis.Normed.Ring.Basic | [
"Units.val",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"SeminormedAddGroup.toNNNorm",
"NNNorm.nnnorm",
"PartialOrder.toPreorder",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub",
"Preorder.toLE",
"SeminormedRing.toRin... | true |
_private.Mathlib.LinearAlgebra.LinearIndependent.Lemmas.0.exists_linearIndependent'._simp_1_2 | Mathlib.LinearAlgebra.LinearIndependent.Lemmas | [
"Subtype",
"Subtype.ext_iff",
"propext",
"Subtype.val",
"Eq"
] | false |
MeasureTheory.MeasurePreserving.aestronglyMeasurable_comp_iff | Mathlib.MeasureTheory.Function.StronglyMeasurable.Lemmas | [
"MeasureTheory.MeasurePreserving",
"Eq.mpr",
"MeasureTheory.Measure",
"MeasurableEmbedding.aestronglyMeasurable_map_iff",
"congrArg",
"Iff.rfl",
"Function.comp",
"id",
"MeasureTheory.MeasurePreserving.map_eq",
"MeasurableSpace",
"TopologicalSpace",
"Iff",
"MeasureTheory.Measure.map",
"prop... | true |
MonoidAlgebra.nonAssocRing._proof_1 | Mathlib.Algebra.MonoidAlgebra.Defs | [
"Int.cast",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Int.cast_natCast",
"MulOne.toOne",
"congrArg",
"AddGroupWithOne.toAddMonoidWithOne",
"AddMonoidWithOne.toNatCast",
"Int",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"AddGroupWithOne.toIntCast",
"Nat.cast",
"MonoidAlgebra.nonAssocSemiring"... | false |
OrderIso.toCompleteLatticeHom._proof_1 | Mathlib.Order.Hom.CompleteLattice | [
"sInfHomClass.map_sInf",
"PartialOrder.toPreorder",
"Preorder.toLE",
"OrderIso",
"OrderIso.instEquivLike",
"OrderIso.instOrderIsoClass",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"instFunLikeOrderIso",
"Set.image",
"CompleteSemilatticeInf.toInfSet",
"... | false |
DividedPowers.IsDPMorphism | Mathlib.RingTheory.DividedPowers.DPMorphism | [
"CommSemiring.toSemiring",
"RingHom",
"Ideal",
"CommSemiring",
"DividedPowers.IsDPMorphism.mk",
"Semiring.toNonAssocSemiring",
"DividedPowers"
] | true |
ProbabilityTheory.Kernel.IsSFiniteKernel.finset_sum | Mathlib.Probability.Kernel.Defs | [
"Finset",
"ProbabilityTheory.Kernel.instAddCommMonoid",
"ProbabilityTheory.IsSFiniteKernel",
"Membership.mem",
"MeasurableSpace",
"Finset.instSetLike",
"ProbabilityTheory.Kernel.IsSFiniteKernel.finsetSum",
"SetLike.instMembership",
"Finset.sum",
"ProbabilityTheory.Kernel"
] | true |
mellin_hasDerivAt_of_isBigO_rpow | Mathlib.Analysis.MellinTransform | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"MeasureTheory.ae",
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Iff.mpr",
"IsModuleTopology.toContinuousSMul",
"sub_pos",
"NormedCommRing.toNormedRing",
"add_mul",
"AddGroup.toSubtractionMonoid",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCo... | true |
AddOpposite.instIsOrderedAddMonoid | Mathlib.Algebra.Order.Group.Opposite | [
"Eq.mpr",
"IsOrderedMonoid._proof_1._to_additive_1",
"AddOpposite.instAddCommMonoid",
"AddOpposite.instPreorder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"AddOpposite",
"PartialOrder",
"id",
"add_le_add_right",
"LE.le",
"AddCommMono... | true |
String.Slice.Pattern.Model.split_endPos | Init.Data.String.Lemmas.Pattern.Split.Basic | [
"dite_cond_eq_true",
"String.Slice.Subslice",
"String.Slice.subslice_endPos",
"congrArg",
"_private.Init.Data.String.Lemmas.Pattern.Split.Basic.0.String.Slice.Pattern.Model.split.match_1",
"_private.Init.Data.String.Lemmas.Pattern.Split.Basic.0.String.Slice.Pattern.Model.split._proof_3",
"Option.some",
... | true |
KaehlerDifferential.endEquivAuxEquiv._proof_3 | Mathlib.RingTheory.Kaehler.Basic | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"instSMulOfMul",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Algebra.TensorProduct.instCommRing",
"IsScalarTower",
"Algebra",
"Algebra.toSMul",
"Algebra.toModule",
"Algebra.id",
"KaehlerDiffer... | false |
Orientation.inner_rotation_pi_div_two_left_smul | Mathlib.Geometry.Euclidean.Angle.Oriented.Rotation | [
"LinearIsometryEquiv.instEquivLike",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"Orientation",
"Real.partialOrder",
"Real",
"instHSMul",
"instHDiv",
"Real.pi",
"HMul.hMul",
"Real.Angle.coe",
"MulZeroClass.toMul",
"Inner.inner",
"Real.instZero",
"Real.instRCLike",
"congrArg",
"Distr... | true |
_private.Lean.Elab.Tactic.NormCast.0.Lean.Elab.Tactic.NormCast.splittingProcedure._sparseCasesOn_9 | Lean.Elab.Tactic.NormCast | [
"Nat.ne_of_beq_eq_false",
"Lean.Expr.const",
"Lean.Expr.letE",
"Lean.Expr.mvar",
"Nat.shiftRight",
"Lean.MVarId",
"Lean.Expr",
"Lean.FVarId",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Expr.sort",
"Lean.Expr.bvar",
"Lean.Level",
"Lean.Literal",
"Lean.Expr.mdata",
"Lean.Expr.fvar",
"Lean.... | false |
IsMoritaEquivalent.cond | Mathlib.RingTheory.Morita.Basic | [
"MoritaEquivalence",
"Algebra",
"CommSemiring",
"Nonempty",
"IsMoritaEquivalent",
"Ring.toSemiring",
"Ring"
] | true |
ContinuousLinearMap.toSpanSingletonCLE | Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toSpanSingletonLE",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"ContinuousLinearEquiv.mk",
"ContinuousSMul",
"ContinuousLinearMap.toSpanSingletonCLE._proof_5",
... | true |
_private.Mathlib.Order.Interval.Set.Disjoint.0.iUnion_Ici_eq_Ici_iInf._simp_1_1 | Mathlib.Order.Interval.Set.Disjoint | [
"Set.mem_range",
"Membership.mem",
"Exists",
"propext",
"Set.range",
"Eq",
"Set.instMembership",
"Set"
] | false |
Topology.IsCoinducing.casesOn | Mathlib.Topology.Defs.Induced | [
"Topology.IsCoinducing.mk",
"Topology.IsCoinducing",
"TopologicalSpace.coinduced",
"TopologicalSpace",
"Topology.IsCoinducing.rec",
"Eq"
] | false |
_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.comm_ring_aux₁._proof_13 | Mathlib.RingTheory.WittVector.Basic | [
"Int.cast",
"Nat.instMulZeroClass",
"Nat.Prime",
"_private.Mathlib.RingTheory.WittVector.Basic.0.WittVector.ghostFun",
"AddMonoidAlgebra.commRing",
"Pi.instIntCast",
"Rat",
"Rat.commSemiring",
"Fact",
"Int",
"AddGroupWithOne.toIntCast",
"Finsupp.instAddCommMonoid",
"_private.Mathlib.RingTheo... | false |
_private.Lean.Meta.Basic.0.Lean.Meta.forallMetaTelescopeReducingAux.process | Lean.Meta.Basic | [
"Inhabited.default",
"Lean.Expr",
"Lean.Meta.MetaM",
"Array",
"Lean.Meta.instInhabitedMetaM",
"Nat",
"Bool",
"Lean.MetavarKind",
"Prod",
"Lean.BinderInfo",
"Option"
] | true |
_private.Mathlib.CategoryTheory.Category.Basic.0.CategoryTheory.Category.mk'._proof_3 | Mathlib.CategoryTheory.Category.Basic | [
"False",
"eq_false",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Classical.byContradiction",
"CategoryTheory.CategoryStruct.id",
"Eq.mp",
"id",
"True",
"CategoryTheory.CategoryStruct.comp",
"eq_true",
"Eq.refl",
"CategoryTheory.CategoryStruct",
"Eq.symm",
"Eq",
"Not",
"E... | false |
Lean.Expr.relevantConstantsAsSet | Lean.LibrarySuggestions.Basic | [
"Pure.pure",
"Lean.NameSet",
"Lean.Meta.State",
"Lean.Expr.foldRelevantConstants",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Applicative.toPure",
"Lean.Core.CoreM",
"Lean.NameSet.insert",
"StateRefT'",
"StateRefT'.instMonad",
"Lean.NameSet.instEmptyCollection",
"Lean.Name",
"Lean.... | true |
Std.Roo.Sliceable | Init.Data.Slice.Notation | [
"outParam",
"Std.Roo.Sliceable.mk"
] | true |
Monoid.coprodCon | Mathlib.GroupTheory.Coprod.Basic | [
"MulOne.toOne",
"CancelMonoid.toRightCancelMonoid",
"FreeMonoid",
"Con.instInfSet",
"HMul.hMul",
"Monoid.toMulOneClass",
"FreeMonoid.instCancelMonoid",
"setOf",
"Sum",
"MulOne.toMul",
"Sum.inl",
"MulOneClass.toMulOne",
"And",
"Sum.inr",
"FreeMonoid.of",
"One.toOfNat1",
"Con",
"Righ... | true |
RingEquiv.sofLeftInverse'._proof_1 | Mathlib.RingTheory.NonUnitalSubsemiring.Basic | [
"Function.LeftInverse",
"RingEquiv.sofLeftInverse'._proof_3",
"NonUnitalRingHom.srange",
"NonUnitalRingHom.mem_srange",
"RingEquiv.sofLeftInverse'.match_1",
"Membership.mem",
"Exists",
"NonUnitalSubsemiringClass.subtype",
"Subtype",
"NonUnitalSubsemiring.instNonUnitalSubsemiringClass",
"NonUnita... | false |
CategoryTheory.Arrow.arrow_mk_eqToHom_comp | Mathlib.CategoryTheory.Comma.Arrow | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom",
"CategoryTheory.Arrow.left",
"CategoryTheory.Arrow.hom",
"CategoryTheory.Category.comp_id",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"of_eq_true",
"CategoryTheory.Category.toCategorySt... | true |
Lean.Elab.Tactic.BVDecide.Frontend.BVDecideConfig.noConfusion | Std.Tactic.BVDecide.Syntax | [
"Lean.Elab.Tactic.BVDecide.Frontend.SolverMode",
"Lean.Elab.Tactic.BVDecide.Frontend.BVDecideConfig.casesOn",
"Nat",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Lean.Elab.Tactic.BVDecide.Frontend.BVDecideConfig.noConfusionType",
"Lean.Elab.Tactic.BVDecide.Frontend.BVDecideConfig"
] | false |
_private.Init.Data.BitVec.Bootstrap.0.BitVec.getElem_cons._simp_1_4 | Init.Data.BitVec.Bootstrap | [
"Nat.le_refl",
"LE.le",
"instLENat",
"Nat",
"True",
"eq_true",
"Eq"
] | false |
_private.Mathlib.Algebra.Homology.SpectralObject.SpectralSequence.0.CategoryTheory.Abelian.SpectralObject.SpectralSequence.HomologyData.isIso_mapFourδ₄Toδ₃'._proof_5 | Mathlib.Algebra.Homology.SpectralObject.SpectralSequence | [
"Lean.RArray.leaf",
"False",
"HMul.hMul",
"congrArg",
"Classical.byContradiction",
"Eq.mp",
"Lean.RArray.branch",
"Int.Linear.Expr.add",
"id",
"Lean.RArray",
"Int.instNegInt",
"instOfNatNat",
"Int",
"Int.Linear.Poly.num",
"autoParam",
"Int.instMul",
"Int.Linear.Poly.add",
"Int.Line... | false |
Std.FactoryInstances.instLawfulOrderLeftLeaningMaxOfOrd | Init.Data.Order.PackageFactories | [
"Std.LawfulOrderOrd",
"Std.FactoryInstances.instMaxOfOrd",
"False",
"instDecidableTrue",
"Ord",
"congrArg",
"_private.Init.Data.Order.PackageFactories.0.Std.LinearPreorderPackage.ofOrd._simp_7",
"Bool.false_eq_true",
"instDecidableEqBool",
"LE.le",
"ite_cond_eq_true",
"Ord.compare",
"LE",
... | true |
_private.Std.Time.DateTime.PlainDateTime.0.Std.Time.PlainDateTime.ofTimestampAssumingUTC._proof_8 | Std.Time.DateTime.PlainDateTime | [
"of_decide_eq_true",
"Int.decLe",
"id",
"Int.instNegInt",
"Int",
"LE.le",
"Bool.true",
"instHAdd",
"instOfNat",
"HAdd.hAdd",
"Bool",
"Int.instAdd",
"Eq.refl",
"OfNat.ofNat",
"Decidable.decide",
"Eq",
"Neg.neg",
"Int.instLEInt"
] | false |
_private.Mathlib.Tactic.Ring.Common.0.Mathlib.Tactic.Ring.Common.isAtomOrDerivable._sparseCasesOn_1 | Mathlib.Tactic.Ring.Common | [
"Lean.Name.rec",
"Nat.ne_of_beq_eq_false",
"String",
"Nat.shiftRight",
"Nat.hasNotBit",
"instOfNatNat",
"Lean.Name.num",
"Lean.Name.ctorIdx",
"Lean.Name.str",
"Lean.Name.anonymous",
"Nat.land",
"Nat",
"Bool",
"Lean.Name",
"Eq.refl",
"OfNat.ofNat",
"Bool.false"
] | false |
Filter.EventuallyEq.inf | Mathlib.Order.Filter.Basic | [
"Pi.instMinForall_mathlib",
"Filter.EventuallyEq",
"Filter.EventuallyEq.comp₂",
"Min",
"Filter",
"Min.min"
] | true |
Std.instStreamSubarray | Init.Data.Stream | [
"Subarray",
"Std.Slice.internalRepresentation",
"Option.some",
"Std.Slice.Internal.SubarrayData.stop_le_array_size",
"Std.Slice.Internal.SubarrayData.mk",
"Prod.mk",
"instOfNatNat",
"LE.le",
"Subarray.stop",
"instLENat",
"Std.Stream.mk",
"dite",
"Array",
"GetElem.getElem",
"Option.none",... | true |
_private.Mathlib.Data.List.GetD.0.List.getD_surjective_iff._simp_1_4 | Mathlib.Data.List.GetD | [
"exists_or",
"Exists",
"propext",
"Or",
"Eq"
] | false |
_private.Mathlib.Data.Finset.Lattice.Lemmas.0.Finset.singleton_inter_of_notMem._simp_1_2 | Mathlib.Data.Finset.Lattice.Lemmas | [
"Finset.mem_singleton",
"Finset",
"Membership.mem",
"Finset.instSetLike",
"propext",
"Finset.instSingleton",
"Singleton.singleton",
"Eq",
"SetLike.instMembership"
] | false |
Std.DTreeMap.Internal.Impl.minEntry.eq_def | Std.Data.DTreeMap.Internal.Queries | [
"Std.DTreeMap.Internal.Impl.minEntry.match_1",
"namedPattern",
"Std.DTreeMap.Internal.Impl.inner",
"id",
"Std.DTreeMap.Internal.Impl.minEntry._unary.eq_def",
"Std.DTreeMap.Internal.Impl.leaf",
"Std.DTreeMap.Internal.Impl.isEmpty",
"Std.DTreeMap.Internal.Impl.minEntry._proof_5",
"Nat",
"Std.DTreeMa... | true |
CategoryTheory.Idempotents.instIsIdempotentCompleteKaroubi | Mathlib.CategoryTheory.Idempotents.Karoubi | [
"Eq.mpr",
"CategoryTheory.Idempotents.Karoubi.Hom.f",
"CategoryTheory.IsIdempotentComplete",
"CategoryTheory.Idempotents.Karoubi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.IsIdempotentComplete.mk",
"congrArg",
"and_self",
"CategoryTheory.Idempotents.Karoubi.comp_p",
... | true |
HasFDerivWithinAt.fun_sum | Mathlib.Analysis.Calculus.FDeriv.Add | [
"Pure.pure",
"HasFDerivAtFilter.fun_sum",
"NormedSpace",
"SProd.sprod",
"AddCommGroup.toAddCommMonoid",
"Finset",
"nhdsWithin",
"NormedSpace.toModule",
"PseudoMetricSpace.toUniformSpace",
"ContinuousLinearMap.addCommMonoid",
"AddCommGroup.toAddGroup",
"Membership.mem",
"HasFDerivWithinAt",
... | true |
Order.enum | Mathlib.SetTheory.Cardinal.Cofinality.Enum | [
"Preorder.toLT",
"LinearOrder",
"WellFoundedLT",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"SemilatticeInf.toPartialOrder",
"Set.Elem",
"DistribLattice.toLattice",
"Nonempty.some",
"OrderIso",
"_private.Mathlib.SetTheory.Cardinal.Cofinality.Enum.0.Order.enum._proof_1",
"R... | true |
IsAddIndecomposable.pairwise_sub_notMem_range | Mathlib.Algebra.Group.Irreducible.Indecomposable | [
"Eq.mpr",
"NegZeroClass.toNeg",
"False",
"neg_sub",
"eq_false",
"Iff.of_eq",
"Classical.not_not",
"congrArg",
"imp_false",
"AddMonoid.toAddZeroClass",
"setOf",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"AddCommGroup",
"HasSubset.S... | true |
CategoryTheory.GrothendieckTopology.uliftYoneda.eq_1 | Mathlib.CategoryTheory.Sites.Subcanonical | [
"CategoryTheory.sheafCompose",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.GrothendieckTopology.yoneda",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.GrothendieckTopology.Subcanonical",
"CategoryTheory.GrothendieckTopology.uliftYoneda",
"CategoryTheory.... | true |
disjoint_bot_right._simp_2 | Mathlib.Order.Disjoint | [
"disjoint_bot_right",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"OrderBot",
"PartialOrder",
"Bot.bot",
"True",
"eq_true",
"Eq"
] | false |
_private.Mathlib.Tactic.Positivity.Core.0.Mathlib.Meta.Positivity.OrderRel.toCtorIdx | Mathlib.Tactic.Positivity.Core | [
"_private.Mathlib.Tactic.Positivity.Core.0.Mathlib.Meta.Positivity.OrderRel",
"Nat",
"_private.Mathlib.Tactic.Positivity.Core.0.Mathlib.Meta.Positivity.OrderRel.ctorIdx"
] | false |
Lean.Parser.Command.checkAssertions._regBuiltin.Lean.Parser.Command.checkAssertions.parenthesizer_11 | Lean.Parser.Command | [
"Lean.Name.mkStr5",
"IO",
"Lean.Parser.Command.checkAssertions.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"Lean.PrettyPrinter.parenthesizerAttribute",
"Unit",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
CategoryTheory.Limits.BinaryBicone.retract_left | Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts | [
"CategoryTheory.Limits.BinaryBicone.fst",
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.BinaryBicone.inl",
"CategoryTheory.Limits.BinaryBicone.pt",
"CategoryTheory.Retract",
"CategoryTheory.Limits.BinaryBicone",
"CategoryTheory.Retract.mk",
"CategoryTheory.Limits.BinaryBicone.retrac... | true |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.tdiv_eq_ediv_of_nonneg.match_1_1 | Init.Data.Int.DivMod.Lemmas | [
"False",
"Int.ctorIdx",
"Int.NonNeg",
"HEq.refl",
"Int.NonNeg.casesOn",
"False.elim",
"HSub.hSub",
"Nat.shiftRight",
"noConfusion_of_Nat",
"Int.casesOn",
"Nat.hasNotBit",
"Int.ofNat",
"instOfNatNat",
"Int",
"LE.le",
"Nat.cast",
"Bool.true",
"Nat.land",
"absurd",
"instHSub",
"... | false |
WeierstrassCurve.Jacobian.addX_eq' | Mathlib.AlgebraicGeometry.EllipticCurve.Jacobian.Formula | [
"Mathlib.Tactic.Ring.Common.mul_pf_left",
"AddGroup.toSubtractionMonoid",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Mathlib.Tactic.Ring.Common.neg_mul",
"Mathlib.Meta.NormNum.isNat_add",
"CommRing",
"Mathlib.Meta.NormNum.inst... | true |
DistLat.hom_inv_apply | Mathlib.Order.Category.DistLat | [
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"DistLat.instConcreteCategoryLatticeHomCarrier",
"DistLat.str",
"DistribLattice.toLattice",
"CategoryTheory.Iso",
"DistLat.instCategory",
"LatticeHom",
"True",
"eq_self",
"of_eq_true",
"congrFun'",
"LatticeHom.instFunLike",
"CategoryTheory... | true |
_private.Batteries.Data.List.Count.0.List.idxToSigmaCount_sigmaCountToIdx._proof_1_73 | Batteries.Data.List.Count | [
"List.sigmaCountToIdx",
"_private.Batteries.Data.List.Count.0.List.idxToSigmaCount_sigmaCountToIdx._proof_1_72",
"Lean.Grind.CommRing.le_norm_expr",
"Lean.Grind.instOrderedRingInt",
"Lean.RArray.leaf",
"GetElem",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Int.Linear.norm_le",
"Lean.Grind.nested... | false |
Lean.Option.setIfNotSet | Lean.Data.Options | [
"Lean.Option",
"Lean.Option.set",
"instDecidableEqBool",
"Bool.true",
"Bool",
"Lean.KVMap.Value",
"Lean.Options",
"Lean.Option.name",
"Eq",
"Lean.Options.contains",
"ite"
] | true |
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