name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Lsp.SymbolKind.interface.elim | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.SymbolKind.ctorIdx",
"Lean.Lsp.SymbolKind.ctorElim",
"PULift.up",
"Lean.Lsp.SymbolKind.interface",
"Nat",
"Eq.symm",
"Lean.Lsp.SymbolKind",
"Eq"
] | false |
ProfiniteAddGrp.hom_ext | Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic | [
"ProfiniteAddGrp.Hom.hom",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ContinuousAddMonoidHom",
"ProfiniteAddGrp",
"TotallyDisconnectedSpace",
"TopCat.str",
"ProfiniteAddGrp.addGroup",
"TopCat.carrier",
"AddGroup.toSubNegMonoid",
"CategoryTheory.Category.toCategoryStruct",
"TopCat... | true |
notMem_nonZeroDivisorsLeft_iff | Mathlib.Algebra.GroupWithZero.NonZeroDivisors | [
"Eq.mpr",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"setOf",
"Membership.mem",
"Exists",
"id",
"mem_nonZeroDivisorsLeft_iff._simp_1",
"Ne",
"Set.nonempty_def",
"MulZeroOneClass.toMulOneClass",
"funext",
"And",
"Iff",
"MonoidWithZero",
"Set.Nonempty",
"MonoidWithZero.toMulZeroO... | true |
Lean.RBNode.isSingleton | Lean.Data.RBMap | [
"Lean.RBColor",
"_private.Lean.Data.RBMap.0.Lean.RBNode.isSingleton.match_1",
"Lean.RBNode",
"Bool.true",
"Bool",
"Bool.false"
] | true |
Std.Iter.toArray_drop | Std.Data.Iterators.Lemmas.Combinators.Drop | [
"Eq.mpr",
"Std.Iter.toArray_toList",
"congrArg",
"Std.Iter.toList_drop",
"Std.Iterators.Finite",
"id",
"Id",
"Std.Iter.toArray",
"Array.extract",
"Std.Iterator",
"Std.Iter.drop",
"List.toArray",
"Array",
"List",
"Std.Iter",
"List.drop",
"Std.Iterators.Types.Drop",
"Std.Iter.toList"... | true |
Ideal.quotientInfToPiQuotient.eq_1 | Mathlib.RingTheory.Ideal.Quotient.Operations | [
"iInf",
"Semiring.toModule",
"Ideal.Quotient.mk",
"RingHom",
"Ideal.quotientInfToPiQuotient._proof_1",
"Ideal.IsTwoSided",
"Ideal.quotientInfToPiQuotient",
"Pi.ringHom",
"Ideal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"HasQuotient.Quotient",
"Pi.semiring",
"Ideal.Quotient.ring",
"Ide... | true |
_private.Batteries.Data.RBMap.Lemmas.0.Batteries.RBNode.balLeft.match_1.splitter._sparseCasesOn_3 | Batteries.Data.RBMap.Lemmas | [
"Batteries.RBNode",
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.hasNotBit",
"Batteries.RBNode.nil",
"instOfNatNat",
"Batteries.RBNode.ctorIdx",
"Nat.land",
"Batteries.RBNode.rec",
"Batteries.RBColor",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Batteries.RBNode.node"
] | false |
Lean.Elab.Term.Do.ToCodeBlock.Context.noConfusion | Lean.Elab.Do.Legacy | [
"Lean.Elab.Term.Do.ToCodeBlock.Context.casesOn",
"Lean.Syntax",
"Lean.Elab.Term.Do.VarSet",
"Lean.Elab.Term.Do.ToCodeBlock.Context.noConfusionType",
"Bool",
"Eq.ndrec",
"Eq.refl",
"Eq",
"Lean.Elab.Term.Do.ToCodeBlock.Context"
] | false |
minpoly.dvd_map_of_isScalarTower | Mathlib.FieldTheory.Minpoly.Field | [
"Eq.mpr",
"CommRing",
"Polynomial.aeval_map_algebraMap",
"Dvd.dvd",
"CommRing.toNonUnitalCommRing",
"Ring.toNonAssocRing",
"congrArg",
"CommSemiring.toSemiring",
"AlgHom",
"IsScalarTower",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra",
"semigroupDvd",
"Algebra",
"NonUnitalNonAssocSemir... | true |
Lean.Doc.Block.brecOn_2.eq | Lean.DocString.Types | [
"Lean.Doc.Block",
"Lean.Doc.Block.below_2",
"Array.casesOn",
"Lean.Doc.Block.brecOn_2.go",
"Lean.Doc.Block.below_6",
"Lean.Doc.DescItem",
"Lean.Doc.Block.below_7",
"Array",
"Lean.Doc.Block.brecOn_2",
"Lean.Doc.Block.below",
"List",
"Lean.Doc.Block.below_1",
"Eq.refl",
"Lean.Doc.ListItem",
... | true |
Set.fintypeImage2._proof_1 | Mathlib.Data.Finite.Prod | [
"Set.instSProd",
"SProd.sprod",
"congrArg",
"Set.image_prod",
"Set.Elem",
"id",
"Prod.fst",
"Fintype",
"Set.image2",
"Set.image",
"Prod",
"Eq.symm",
"Eq",
"Prod.snd",
"Set"
] | false |
Algebra.FiniteType.out | Mathlib.RingTheory.FiniteType | [
"Subalgebra.FG",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"Algebra.instCompleteLatticeSubalgebra",
"Algebra",
"Preorder.toLE",
"CompleteLattice.toBoundedOrder",
"Algebra.FiniteType",
"CommSemiring",
"OrderTop.toTop",
"BoundedOrder.toOrderTop",
"Semi... | true |
GradedMonoid.GMul.casesOn | Mathlib.Algebra.GradedMonoid | [
"GradedMonoid.GMul.mk",
"instHAdd",
"HAdd.hAdd",
"GradedMonoid.GMul.rec",
"GradedMonoid.GMul",
"Add"
] | false |
CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app_assoc | Mathlib.CategoryTheory.Triangulated.Opposite.OpOp | [
"CategoryTheory.Functor.op",
"CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso",
"CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app._auto_1",
"CategoryTheory.Functor",
"CategoryTheory.Pretriangulated.Opposite.UnopUnopCommShift.iso_inv_app",
"Opposite",
"CategoryTheory.Ca... | true |
CategoryTheory.MorphismProperty.TransfiniteCompositionOfShape._sizeOf_1 | Mathlib.CategoryTheory.MorphismProperty.TransfiniteComposition | [
"CategoryTheory.MorphismProperty",
"Preorder.toLT",
"Order.succ",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"LinearOrder",
"WellFoundedLT",
"PartialOrder.toPreorder",
"CategoryTheory.TransfiniteCompositionOfShape._sizeOf_inst",
"Preorder.toLE",
"OrderBot",
"SemilatticeInf.toParti... | false |
MeasureTheory.withDensityᵥ_toReal | Mathlib.MeasureTheory.VectorMeasure.WithDensity | [
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"MeasureTheory.Measure.withDensity",
"Real",
"MeasureTheory.Measure",
"MeasureTheory.Measure.withDensityᵥ",
"MeasurableSet",
"AEMeasurable",
"Real.instRCLike",
"congrArg",
"MeasureTheory.isFiniteMeasure_withDen... | true |
Lean.ErrorExplanation.mk.injEq | Lean.ErrorExplanation | [
"Eq.propIntro",
"String",
"Lean.injEq_helper",
"And",
"Eq.ndrec",
"Lean.DeclarationLocation",
"Eq.refl",
"Eq",
"Lean.ErrorExplanation.Metadata",
"Lean.ErrorExplanation.mk.inj",
"Lean.ErrorExplanation.mk",
"Option",
"Lean.ErrorExplanation"
] | true |
Ideal.fiberIsoOfBijectiveResidueField | Mathlib.RingTheory.Etale.QuasiFinite | [
"Ideal.fiberIsoOfBijectiveResidueField._proof_7",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"PrimeSpectrum.comapEquiv",
"Ideal.primesOver",
"AlgEquiv.symm",
"OreLocalization.instAlgebra",
"Ideal.R... | true |
EReal.add_iInf_le_iInf_add | Mathlib.Topology.Instances.EReal.Lemmas | [
"instInfSetEReal",
"iInf",
"CompletelyDistribLattice.toCompleteLattice",
"covariant_swap_add_of_covariant_add",
"add_le_add",
"PartialOrder.toPreorder",
"le_iInf",
"EReal",
"Preorder.toLE",
"LE.le",
"instAddCommMonoidEReal",
"instCompleteLinearOrderEReal",
"instHAdd",
"Pi.instAdd",
"HAdd... | true |
Real.fromBinary_surjective | Mathlib.Topology.MetricSpace.HausdorffAlexandroff | [
"Real",
"Pi.topologicalSpace",
"Real.instZero",
"Set.univ",
"instTopologicalSpaceBool",
"Homeomorph.piCongrRight",
"instDiscreteTopologyBool",
"Set.SurjOn",
"Function.comp",
"Nat.instCharZero",
"Set.Elem",
"_private.Mathlib.Topology.MetricSpace.HausdorffAlexandroff.0.Real.fromBinary_surjective... | true |
ULift.distrib | Mathlib.Algebra.Ring.ULift | [
"ULift.distrib._proof_4",
"ULift",
"ULift.add",
"Distrib.toAdd",
"ULift.mul",
"Distrib.toMul",
"Distrib",
"ULift.distrib._proof_3",
"Distrib.mk"
] | true |
Std.DHashMap.Raw.get?_union_of_not_mem_right | Std.Data.DHashMap.RawLemmas | [
"Std.DHashMap.Raw.WF",
"Std.DHashMap.Raw.instMembershipOfBEqOfHashable",
"Eq.mpr",
"Std.DHashMap.Internal.Raw₀.get?",
"Std.DHashMap.Internal.Raw₀.contains",
"Std.DHashMap.Internal.Raw₀.get?_union_of_contains_eq_false_right",
"instLawfulHashableOfLawfulBEq",
"congrArg",
"Std.DHashMap.Raw.contains_eq_... | true |
Lean.initFn._@.Lean.DocString.Links.3730308748._hygCtx._hyg.2 | Lean.DocString.Links | [
"Pure.pure",
"String.endsWith",
"Unit.unit",
"_private.Lean.DocString.Links.0.Lean.manualRoot.match_1",
"_private.Lean.DocString.Links.0.Lean.fallbackManualRoot",
"Monad.toApplicative",
"String",
"IO.getEnv",
"instMonadLiftT",
"IO",
"String.isEmpty",
"EIO",
"instDecidableEqBool",
"liftM",
... | false |
CategoryTheory.Monad.algebraEquivOfIsoMonads_unitIso | Mathlib.CategoryTheory.Monad.Algebra | [
"CategoryTheory.Monad.algebraEquivOfIsoMonads._proof_1",
"CategoryTheory.Monad",
"CategoryTheory.Functor",
"CategoryTheory.Equivalence.unitIso",
"CategoryTheory.Monad.algebraFunctorOfMonadHomEq",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.id",
"Category... | true |
_private.Mathlib.Analysis.Normed.Operator.Compact.0.IsCompactOperator.add.match_1_1 | Mathlib.Analysis.Normed.Operator.Compact | [
"Membership.mem",
"Set.instInter",
"Inter.inter",
"And.casesOn",
"Set.preimage",
"And.intro",
"Set.instMembership",
"Set"
] | false |
Set.Icc_union_Icc' | Mathlib.Order.Interval.Set.LinearOrder | [
"Lattice.toSemilatticeSup",
"_private.Mathlib.Order.Interval.Set.LinearOrder.0.Set.Icc_union_Icc'._proof_1_1",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"Set.instUnion",
"SemilatticeSup.toMax",
"DistribLattice.toLattice",
"SemilatticeInf.toMin",
... | true |
MonadWriter.mk.noConfusion | Mathlib.Control.Monad.Writer | [
"outParam",
"id",
"MonadWriter.mk",
"MonadWriter",
"heq_of_eq",
"PUnit",
"Eq.refl",
"HEq",
"Prod",
"Eq",
"MonadWriter.noConfusion"
] | false |
Ring.instDirectLimit._proof_16 | Mathlib.Algebra.Colimit.Ring | [
"Monoid.npow_zero._autoParam",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Ring.instOneDirectLimit",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"FreeCommRing",
"AddGroupWithOne.toAddGroup",
"CommSemiring.toSemiring",
"setOf",
"AddGroupWithOne.toAddMonoidWithOne",
"HSub.hSub... | false |
toIcoDiv_add_left' | Mathlib.Algebra.Order.ToIntervalMod | [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"PartialOrder.toPreorder",
"HSub.hSub",
"SemilatticeInf.toPartialOrder",
"AddCommGroup",
"DistribLattice.toLattice",
"id",
"toIcoDiv",
"SubtractionMonoid.toSubNegZeroMonoid",
"Int",
"SubNegZeroMonoid.to... | true |
Int8.toNatClampNeg_lt | Init.Data.SInt.Lemmas | [
"Iff.mpr",
"instPowNat",
"of_decide_eq_true",
"Int8.toInt_lt",
"Int.toNat_lt'",
"Int8",
"Int8.toInt",
"id",
"instOfNatNat",
"Int",
"Nat.cast",
"instNatPowNat",
"Int.instLTInt",
"Bool.true",
"HPow.hPow",
"Int8.toNatClampNeg",
"Nat",
"LT.lt",
"Bool",
"Nat.decLt",
"Eq.refl",
"... | true |
_private.Lean.Meta.ForEachExpr.0.Lean.Meta.forEachExpr'.visit | Lean.Meta.ForEachExpr | [
"Inhabited.default",
"instInhabitedOfMonad",
"Lean.Expr.instBEq",
"instInhabitedPUnit",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.MonadCacheT",
"MonadLiftT",
"Lean.MonadCacheT.instMonad",
"Unit",
"MonadControlT",
"ST",
"Bool",
"Lean.Expr.instHashable",
"Monad",
"STWorld"
... | true |
_private.Init.Data.Nat.Lemmas.0.Nat.one_mod_eq_one.match_1_1 | Init.Data.Nat.Lemmas | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.mu'_apply_self | Mathlib.Combinatorics.Enumerative.IncidenceAlgebra | [
"NegZeroClass.toNeg",
"One",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"_private.Mathlib.Combinatorics.Enumerative.IncidenceAlgebra.0.IncidenceAlgebra.mu'",
"Preorder.toLE",
"AddCommGroup",
"SubtractionMonoid.toSubNegZeroMonoid",
"ite_cond_eq_true",
"SubNegZeroMonoid.toNegZeroClass",
"Subtract... | true |
MeasureTheory.Egorov.notConvergentSeqLTIndex | Mathlib.MeasureTheory.Function.Egorov | [
"MeasureTheory.ae",
"Real",
"MeasureTheory.Measure",
"HMul.hMul",
"MeasurableSet",
"Real.instZero",
"ENNReal.ofReal",
"Real.instInv",
"Filter.Eventually",
"PartialOrder.toPreorder",
"Measurable",
"Real.instLT",
"ENNReal.measurableSpace",
"Preorder.toLE",
"Membership.mem",
"nhds",
"Me... | true |
Lean.Meta.MVarRenaming.map | Lean.Meta.Match.MVarRenaming | [
"Lean.MVarIdMap",
"Lean.MVarId",
"Lean.Meta.MVarRenaming"
] | true |
SemidirectProduct.inr | Mathlib.GroupTheory.SemidirectProduct | [
"MulOne.toOne",
"SemidirectProduct.inr._proof_2",
"InvOneClass.toOne",
"DivInvOneMonoid.toInvOneClass",
"MonoidHom",
"Monoid.toMulOneClass",
"SemidirectProduct",
"OneHom.mk",
"MulAut.instGroup",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"MulAut",
"MulOne.toMul"... | true |
GroupSeminorm.coe_sSup_apply' | Mathlib.Analysis.Normed.Group.Seminorm | [
"Set.ext",
"Eq.mpr",
"Real",
"GroupSeminorm.instSupSet",
"Iff.of_eq",
"congrArg",
"iSup",
"Set.mem_image._simp_1",
"PartialOrder.toPreorder",
"Group",
"Preorder.toLE",
"Membership.mem",
"Exists",
"Real.instSupSet",
"Eq.rec",
"Set.Elem",
"id",
"Subtype",
"GroupSeminorm",
"SupSet... | true |
Algebra.IsPushout.cancelBaseChangeAux.congr_simp | Mathlib.RingTheory.IsTensorProduct | [
"IsScalarTower.to_smulCommClass'",
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"Algebra.IsPushout",
"TensorProduct.addCommMonoid",
"AddMo... | true |
_private.Lean.Server.GoTo.0.Lean.Server.getInstanceProjectionArg?.reduceToProjection?._sparseCasesOn_6 | Lean.Server.GoTo | [
"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 |
Array.merge.go._unary | Batteries.Data.Array.Merge | [
"Array.instAppend",
"Array.push",
"InvImage",
"Array.toSubarray",
"HSub.hSub",
"WellFounded.Nat.fix",
"Subarray.copy",
"GE.ge",
"PSigma.casesOn",
"instDecidableEqBool",
"instSubNat",
"instOfNatNat",
"Array.merge._proof_2",
"instLENat",
"dite",
"Array",
"GetElem.getElem",
"Bool.true... | false |
RingSeminormClass.mk._flat_ctor | Mathlib.Algebra.Order.Hom.Basic | [
"AddGroup.toSubtractionMonoid",
"NonUnitalNonAssocRing",
"SubmultiplicativeHomClass.mk",
"NegZeroClass.toNeg",
"RingSeminormClass.mk",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"outParam",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup",
"PartialOrder.toPreorder",
"Preorder.t... | false |
_private.Init.Data.Fin.Basic.0.Fin.exists_iff.match_1_1 | Init.Data.Fin.Basic | [
"Fin.casesOn",
"Exists",
"Fin.mk",
"Exists.casesOn",
"Nat",
"LT.lt",
"Exists.intro",
"instLTNat",
"Fin"
] | false |
LieModule.Cohomology.twoCocycle.eq_1 | Mathlib.Algebra.Lie.Cochain | [
"LieAlgebra.toModule",
"Submodule",
"CommRing",
"LieRing.toAddCommGroup",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instSMulCommClass",
"Submodule.addCommMonoid",
"LinearMap.ker",
"LieModule.Cohomology.d₂₃._proof_1",
"Membership.mem... | true |
Convex.norm_image_sub_le_of_norm_fderiv_le | Mathlib.Analysis.Calculus.MeanValue | [
"Norm.norm",
"Real.partialOrder",
"Real.instLE",
"Real",
"HMul.hMul",
"NormedSpace",
"HasFDerivAt.hasFDerivWithinAt",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Convex.norm_image_sub_le_of_norm_hasFDerivWithin_le",
"DifferentiableAt",
"NormedSpace.toModule",
"AddMonoi... | true |
Std.DTreeMap.Internal.Impl.applyPartition_eq_apply_toListModel | Std.Data.DTreeMap.Internal.WF.Lemmas | [
"Ordering.gt",
"Std.DTreeMap.Internal.List.findCell",
"Eq.mpr",
"instDecidableEqOrdering",
"Std.DTreeMap.Internal.Impl.applyPartition",
"Std.DTreeMap.Internal.List.findCell_inner",
"instLawfulBEq",
"Std.DTreeMap.Internal.Impl.applyPartition_eq_apply_toListModel._proof_1",
"List.Pairwise",
"Ord",
... | true |
Lean.Elab.Do.InferControlInfo.ofSeq | Lean.Elab.Do.InferControlInfo | [
"Lean.TSyntax",
"Inhabited.default",
"Lean.Elab.Term.instInhabitedTermElabM",
"List.cons",
"Lean.Elab.Do.ControlInfo",
"Lean.Elab.Term.TermElabM",
"Lean.SyntaxNodeKind",
"Lean.Name.mkStr4",
"List.nil"
] | true |
Mathlib.Tactic.Order.OrderType.lin.sizeOf_spec | Mathlib.Tactic.Order.Preprocessing | [
"Mathlib.Tactic.Order.OrderType",
"instOfNatNat",
"Mathlib.Tactic.Order.OrderType._sizeOf_inst",
"Nat",
"Mathlib.Tactic.Order.OrderType.lin",
"SizeOf.sizeOf",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
_private.Init.Data.Nat.Control.0.Nat.forM.loop._unsafe_rec | Init.Data.Nat.Control | [
"Pure.pure",
"Unit.unit",
"Monad.toApplicative",
"Nat.le_of_succ_le",
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"Applicative.toPure",
"instHAdd",
"Unit",
"instHSub",
"_private.Init.Data.Nat.Control.0.Nat.forM.loop.match_1",
"HAdd.hAdd",
"PUnit",
"Nat",
"LT.lt... | false |
SymAlg.instCommMagmaOfInvertibleOfNat | Mathlib.Algebra.Symmetrized | [
"SymAlg.instCommMagmaOfInvertibleOfNat._proof_1",
"Ring.toNonAssocRing",
"CommMagma.mk",
"Nat.instAtLeastTwoHAddOfNat",
"AddGroupWithOne.toAddMonoidWithOne",
"SymAlg.instMulOfAddOfInvertibleOfNat",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"AddMonoidWithOne.toNatCast",
... | true |
LeanSearchClient.instReprSearchResult | LeanSearchClient.Syntax | [
"LeanSearchClient.instReprSearchResult.repr",
"Repr.mk",
"Repr",
"LeanSearchClient.SearchResult"
] | true |
Nat.mul_left_comm | Init.Data.Nat.Basic | [
"Eq.mpr",
"HMul.hMul",
"congrArg",
"id",
"instMulNat",
"Nat.mul_comm",
"Nat.mul_assoc",
"Nat",
"Eq.refl",
"Eq.symm",
"Eq",
"instHMul"
] | true |
UInt16.toFin_mod | Init.Data.UInt.Lemmas | [
"instModUInt16",
"UInt16.toFin",
"UInt16.size",
"instHMod",
"HMod.hMod",
"UInt16",
"Fin",
"Eq",
"Fin.instMod",
"rfl"
] | true |
PadicSeq.valuation | Mathlib.NumberTheory.Padics.PadicNumbers | [
"padicNorm.instIsAbsoluteValueRat",
"NormedCommRing.toNormedRing",
"Nat.Prime",
"NormedRing.toRing",
"Rat",
"Rat.linearOrder",
"Classical.propDecidable",
"PadicSeq.stationaryPoint",
"Fact",
"Int",
"padicValRat",
"dite",
"Rat.instNormedField",
"Rat.instField",
"instOfNat",
"HasEquiv.Equ... | true |
SimpleGraph.sum_incMatrix_apply_of_notMem_edgeSet | Mathlib.Combinatorics.SimpleGraph.IncMatrix | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"SimpleGraph.incidenceSet",
"Finset.univ",
"Finset",
"SimpleGraph.Adj",
"DecidableRel",
"Finset.sum_eq_zero",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Membership.mem",
"SimpleGraph.incMatrix",
"NonAssocSemiring.toMulZeroOneClass",
"AddCommMonoidWi... | true |
ValueDistribution.logCounting_const | Mathlib.Analysis.Complex.ValueDistribution.LogCounting.Basic | [
"Int.instAddCommGroup",
"AddGroup.toSubtractionMonoid",
"Int.instAddCommMonoid",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"WithTop.untop₀",
"AddMonoidHom.instAddMonoidHomClass",
"MeromorphicOn.divisor_const",
"NormedSpa... | true |
PairReduction.finset_logSizeBallSeq_subset_logSizeBallSeq_init | Mathlib.Topology.EMetricSpace.PairReduction | [
"subset_refl._simp_1",
"zero_le",
"Nat.instCanonicallyOrderedAdd",
"Finset.instIsTransSubset",
"Finset",
"subset_trans",
"AddMonoid.toAddZeroClass",
"Finset.instReflSubset",
"Nat.instAddMonoid",
"AddZeroClass.toAddZero",
"HasSubset.Subset",
"instLENat",
"PseudoEMetricSpace",
"AddZero.toZer... | true |
RootPairing.coroot_eq_neg_iff | Mathlib.LinearAlgebra.RootSystem.Defs | [
"NegZeroClass.toNeg",
"CommRing",
"Equiv.instEquivLike",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"RootPairing.flip",
"AddCommGroup",
"Equiv",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"RootPairing.... | true |
UInt8.ext | Batteries.Data.UInt | [
"instPowNat",
"BitVec.ofFin",
"_private.Batteries.Data.UInt.0.UInt8.ext.match_1_1",
"Fin.mk",
"instOfNatNat",
"instNatPowNat",
"HPow.hPow",
"Nat",
"LT.lt",
"instHPow",
"instLTNat",
"UInt8.toNat",
"OfNat.ofNat",
"UInt8.ofBitVec",
"UInt8",
"Eq",
"rfl"
] | true |
Std.Roo.size_eq_match_roc | Init.Data.Range.Polymorphic.Lemmas | [
"Std.Rco.size",
"Eq.mpr",
"Std.PRange.UpwardEnumerable",
"Std.Rxo.LawfulHasSize",
"Std.Roo.upper",
"congrArg",
"Std.Rxc.Iterator.toList_eq_match.match_1",
"Std.PRange.LawfulUpwardEnumerableLT",
"Std.Roo.lower",
"id",
"instOfNatNat",
"Std.PRange.UpwardEnumerable.succ?",
"Std.Rco.upper",
"fu... | true |
_private.Mathlib.Data.Nat.Dist.0.Nat.dist_zero_right._proof_1_1 | Mathlib.Data.Nat.Dist | [
"Lean.RArray.leaf",
"False",
"Nat.zero_sub",
"congrArg",
"Classical.byContradiction",
"HSub.hSub",
"Nat.Linear.ExprCnstr.eq_true_of_isValid",
"id",
"False.casesOn",
"instSubNat",
"instOfNatNat",
"Nat.Linear.Expr.num",
"Bool.true",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"congr"... | false |
NNRat.divNat_zero | Mathlib.Data.NNRat.Defs | [
"NNRat.divNat",
"Rat.instOfNat",
"Subtype.mk.congr_simp",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"Rat",
"AddGroupWithOne.toAddMonoidWithOne",
"Rat.divInt",
"NonUnitalNonAssocSemiring.to... | true |
_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.activateNextGuard.go.match_1 | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Simp.Result.mk",
"Lean.Expr",
"Lean.Meta.Simp.Result",
"Bool",
"Lean.Meta.Simp.Result.casesOn",
"Option"
] | false |
Lean.Grind.CommRing.Poly.noConfusion | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly",
"Int",
"Lean.Grind.CommRing.Poly.noConfusionType",
"Eq.ndrec",
"Eq.refl",
"Lean.Grind.CommRing.Poly.casesOn",
"Eq",
"Lean.Grind.CommRing.Mon"
] | false |
RingHom.CodescendsAlong.algebraMap_tensorProduct | Mathlib.RingTheory.RingHomProperties | [
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Algebra.TensorProduct.instCommRing",
"Algebra",
"RingHom",
"Algebra.toSMul",
"algebraMap",
"Algebra.toModule",
"Algebra.... | true |
star_pow | Mathlib.Algebra.Star.Basic | [
"Monoid",
"MonoidHom.instFunLike",
"MulOpposite.op_injective",
"starMulEquiv",
"MonoidHom",
"Monoid.toMulOneClass",
"StarMul",
"MulOpposite",
"MulOpposite.op_pow",
"MulOne.toMul",
"Monoid.toPow",
"MulEquiv.toMonoidHom",
"MulOneClass.toMulOne",
"HPow.hPow",
"Nat",
"MulOpposite.instMonoi... | true |
Std.Sat.CNF.eval_empty | Std.Sat.CNF.Basic | [
"List.all",
"Array.all_congr",
"Array.all",
"congrArg",
"Std.Sat.CNF.eval",
"instOfNatNat",
"Std.Sat.CNF.empty",
"List.toArray",
"Array",
"Bool.true",
"List.all_toArray'",
"List.size_toArray",
"Nat",
"True",
"eq_self",
"Std.Sat.CNF.Clause",
"Bool",
"of_eq_true",
"Eq.refl",
"con... | true |
DiscreteMeasurableSpace.mk | Mathlib.MeasureTheory.MeasurableSpace.Defs | [
"MeasurableSet",
"DiscreteMeasurableSpace",
"DiscreteMeasurableSpace.mk",
"MeasurableSpace",
"Set"
] | true |
LocallyConstant.instCommGroup._proof_6 | Mathlib.Topology.LocallyConstant.Algebra | [
"DivInvMonoid.toZPow",
"LocallyConstant",
"Int",
"CommGroup",
"Group.toDivInvMonoid",
"TopologicalSpace",
"HPow.hPow",
"LocallyConstant.instPow",
"LocallyConstant.instFunLike",
"instHPow",
"CommGroup.toGroup",
"Eq",
"DFunLike.coe",
"rfl"
] | false |
Set.OrdConnected.isSuccArchimedean | Mathlib.Order.SuccPred.Archimedean | [
"Set.OrdConnected.succOrder",
"_private.Mathlib.Order.SuccPred.Archimedean.0.Set.OrdConnected.isSuccArchimedean._proof_2",
"PartialOrder.toPreorder",
"Membership.mem",
"PartialOrder",
"Set.Elem",
"Set.OrdConnected",
"IsSuccArchimedean",
"SuccOrder",
"Set.instMembership",
"Subtype.preorder",
"S... | true |
Lean.Parser.Term.falseVal.formatter | Lean.Parser.Term | [
"Lean.PrettyPrinter.Formatter",
"Lean.Parser.withCache.formatter",
"Lean.Parser.leadingNode.formatter",
"instOfNatNat",
"Lean.PrettyPrinter.Formatter.withAntiquot.formatter",
"Bool.true",
"Nat",
"OfNat.ofNat",
"Bool.false",
"Lean.Parser.mkAntiquot.formatter",
"Lean.Name.mkStr4",
"Lean.Parser.n... | true |
_private.Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult.0.Std.Tactic.BVDecide.LRAT.Internal.DefaultFormula.nodup_derivedLits._proof_1_8 | Std.Tactic.BVDecide.LRAT.Internal.Formula.RupAddResult | [
"Lean.Grind.Nat.lt_eq",
"instOfNatNat",
"LE.le",
"instLENat",
"Fin.val",
"Array",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Eq.substr",
"Bool",
"instAddNat",
"instLTNat",
"Prod",
"OfNat.ofNat",
"Fin",
"Std.Tactic.BVDecide.LRAT.Internal.PosFin",
"Std.Sat.Literal",
"Array.size"
] | false |
_private.Mathlib.Order.Sublattice.0.Sublattice.map_symm_eq_iff_eq_map._simp_1_3 | Mathlib.Order.Sublattice | [
"Sublattice",
"Lattice",
"Sublattice.coe_inj",
"SetLike.coe",
"propext",
"Sublattice.instSetLike",
"Eq.symm",
"Eq",
"Set"
] | false |
Set.image_affine_Ico | Mathlib.Algebra.Order.Group.Pointwise.Interval | [
"Set.image_image",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Preorder.toLT",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"PartialOrder.toPreorder",
"DivisionSemiring.toGroupWithZero",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Preorder.toLE",
"PartialOrder",
"Eq.mp",
"id",
"Distr... | true |
AlgebraicGeometry.Scheme.Modules.pullback._proof_1 | Mathlib.AlgebraicGeometry.Modules.Sheaf | [
"CategoryTheory.Limits.hasFiniteLimits_of_hasLimits",
"CategoryTheory.GrothendieckTopology.instPreservesSheafificationForgetOfPreservesLimitsOfHasColimitsOfShapeOfPreservesColimitsOfShapeOppositeCoverOfHasLimitsOfShapeWalkingMulticospanOfReflectsIsomorphisms",
"AddCommGrpCat.FilteredColimits.forget_preservesFil... | false |
Std.HashMap.contains_modify | Std.Data.HashMap.Lemmas | [
"Std.HashMap.contains",
"Std.HashMap",
"LawfulHashable",
"EquivBEq",
"Bool",
"Std.DHashMap.Const.contains_modify",
"Hashable",
"Std.HashMap.inner",
"BEq",
"Eq",
"Std.HashMap.modify"
] | true |
CategoryTheory.MonoidalCategory.instMonoidalFunctorTensoringRight._proof_6 | Mathlib.CategoryTheory.Monoidal.End | [
"CategoryTheory.MonoidalCategory.tensoringRight",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.category",
... | false |
Lean.PrettyPrinter.Formatter.State.noConfusionType | Lean.PrettyPrinter.Formatter | [
"String",
"Lean.PrettyPrinter.Formatter.State",
"Array",
"Lean.Syntax.Traverser",
"Std.Format",
"Bool",
"Lean.PrettyPrinter.Formatter.State.casesOn",
"Eq"
] | false |
Lean.Meta.MatcherApp.remaining | Lean.Meta.Match.MatcherApp.Basic | [
"Lean.Meta.MatcherApp",
"Lean.Expr",
"Array"
] | true |
instSubNegAddMonoidLex | Mathlib.Algebra.Order.Group.Synonym | [
"Lex",
"SubNegMonoid"
] | true |
inv_eq_one_divp | Mathlib.Algebra.Group.Units.Defs | [
"Monoid",
"Units.val",
"Eq.mpr",
"MulOne.toOne",
"Monoid.toMulOneClass",
"congrArg",
"Units",
"id",
"divp",
"one_divp",
"MulOneClass.toMulOne",
"Inv.inv",
"One.toOfNat1",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"Units.instInv"
] | true |
_private.Mathlib.NumberTheory.SmoothNumbers.0.Nat.mem_factoredNumbers_iff_forall_le.match_1_3 | Mathlib.NumberTheory.SmoothNumbers | [
"Nat.Prime",
"Dvd.dvd",
"Finset",
"Membership.mem",
"Ne",
"instOfNatNat",
"And.casesOn",
"And",
"Nat.instDvd",
"Finset.instSetLike",
"Nat",
"And.intro",
"OfNat.ofNat",
"SetLike.instMembership"
] | false |
PNat.XgcdType.y | Mathlib.Data.PNat.Xgcd | [
"PNat.XgcdType",
"Nat"
] | true |
ContinuousLinearMap.coe_projKerOfRightInverse_apply | Mathlib.Topology.Algebra.Module.LinearMap | [
"Submodule",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"Submodule.addCommMonoid",
"LinearMap.ker",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"RingHom",
"Membership.mem",
"AddCommGroup",
"Subtype",
"ContinuousLinearMap.toLinearMap",
"Submodule.module",
"RingHomInvPair",
... | true |
PseudoMetricSpace.toUniformSpace | Mathlib.Topology.MetricSpace.Pseudo.Defs | [
"UniformSpace",
"PseudoMetricSpace"
] | true |
CategoryTheory.MorphismProperty.llp_rlp_of_hasSmallObjectArgument' | Mathlib.CategoryTheory.SmallObject.Basic | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.MorphismProperty.HasSmallObjectArgument",
"CategoryTheory.MorphismProperty.pushouts",
"CategoryTheory.MorphismProperty.llp",
"CategoryTheory.MorphismProperty.transfiniteCompositionsOfShape",
"Ordinal.instSuccOrderToType",
"CategoryTheory.MorphismPropert... | true |
Submonoid.LocalizationMap.mulEquivOfLocalizations_right_inv | Mathlib.GroupTheory.MonoidLocalization.Maps | [
"Monoid.toMulOneClass",
"Submonoid.LocalizationMap.toMonoidHom",
"Submonoid.LocalizationMap.mulEquivOfLocalizations",
"Submonoid.LocalizationMap.lift_comp",
"CommMonoid.toMonoid",
"Submonoid.LocalizationMap",
"Submonoid.LocalizationMap.map_units",
"Eq",
"CommMonoid",
"Submonoid",
"Submonoid.Loca... | true |
Besicovitch.TauPackage.color.eq_1 | Mathlib.MeasureTheory.Covering.Besicovitch | [
"Preorder.toLT",
"Besicovitch.TauPackage",
"Ordinal.partialOrder",
"Besicovitch.TauPackage.index",
"Set.univ",
"PartialOrder.toPreorder",
"Besicovitch.BallPackage.r",
"Set.instSingletonSet",
"Subtype",
"Set.instInter",
"Nat.instInfSet",
"Inter.inter",
"SDiff.sdiff",
"Set.Nonempty",
"Besi... | true |
PiTensorProduct.dualDistribEquivOfBasis_symm_apply | Mathlib.LinearAlgebra.PiTensorProduct.Dual | [
"PiTensorProduct.instModule",
"LinearEquiv.symm",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Finite",
"PiTensorProduct.dualDistribEquivOf... | true |
FractionalIdeal.ne_zero_of_mul_eq_one | Mathlib.RingTheory.FractionalIdeal.Operations | [
"Eq.mpr",
"CommRing",
"FractionalIdeal.instNontrivialNonZeroDivisors",
"NeZero.one",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"HEq.refl",
"MulZeroClass.zero_mul",
"Algebra",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"nonZeroDivisors",
"Eq.casesOn",
"Ne",
"NonAssocSemiring.to... | true |
_private.Mathlib.NumberTheory.FLT.Three.0.FermatLastTheoremForThreeGen.Solution.x_mul_y_mul_z_eq_u_mul_w_cube._simp_1_8 | Mathlib.NumberTheory.FLT.Three | [
"_private.Mathlib.NumberTheory.FLT.Three.0.FermatLastTheoremForThreeGen.Solution'.b",
"_private.Mathlib.NumberTheory.FLT.Three.0.FermatLastTheoremForThreeGen.Solution.toSolution'",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"NumberField.instCommRingRingOf... | false |
Matrix.isUnit_charpolyRev_of_isNilpotent | Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff | [
"Eq.mpr",
"Polynomial.C",
"Matrix.smul",
"RingHom.instRingHomClass",
"MonoidHom.instMonoidHomClass",
"MulOne.toOne",
"Matrix.instMulOneOfFintypeOfDecidableEqOfAddCommMonoid",
"Polynomial.instOne",
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"Matrix.detMonoidHom",
"Dvd.dvd",
"Monoi... | true |
Polynomial.natDegree_mul_C_eq_of_mul_ne_zero | Mathlib.Algebra.Polynomial.Degree.Lemmas | [
"Iff.mpr",
"Eq.mpr",
"Polynomial.C",
"HMul.hMul",
"congrArg",
"Finset",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"RingHom",
"Membership.mem",
"Polynomial.mem_support_iff",
"id",
"Polynomial.leadingCoeff",
"Ne",
"Polynomial.coeff_mul_C",
"Polynomial",
"Polynomial.coeff",
"RingHom.i... | true |
PartialEquiv.transEquiv._proof_2 | Mathlib.Logic.Equiv.PartialEquiv | [
"PartialEquiv",
"PartialEquiv.trans",
"PartialEquiv.symm",
"Equiv",
"Equiv.toPartialEquiv",
"PartialEquiv.toFun",
"Eq",
"rfl"
] | false |
Lean.Meta.Simp.Stats.diag | Lean.Meta.Tactic.Simp.Types | [
"Lean.Meta.Simp.Diagnostics",
"Lean.Meta.Simp.Stats"
] | true |
Homeomorph.toEquiv_piCongrLeft | Mathlib.Topology.Homeomorph.Lemmas | [
"Equiv.instEquivLike",
"Pi.topologicalSpace",
"Homeomorph.toEquiv",
"Homeomorph.piCongrLeft",
"Equiv",
"Equiv.piCongrLeft",
"TopologicalSpace",
"Eq.refl",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
Stream'.cons_injective2 | Mathlib.Data.Stream.Init | [
"Eq.mpr",
"Stream'.get_succ_cons",
"congrArg",
"Function.Injective2",
"id",
"instOfNatNat",
"Stream'",
"Stream'.get_zero_cons",
"Stream'.get",
"Nat",
"And.intro",
"Eq.refl",
"Stream'.cons",
"OfNat.ofNat",
"Eq.symm",
"Nat.succ",
"Eq",
"Stream'.ext"
] | true |
Lean.Grind.CommRing.Poly.combine.go.match_1.congr_eq_4 | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.add",
"id",
"Int",
"heq_of_eq",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Lean.Grind.CommRing.Poly.casesOn",
"Lean.Grind.CommRing.Poly.combine.go.match_1",
"Eq.symm",
"Eq",
"Lean.Grind.CommRing.Mon",
"Lean.Grind.CommRing.Poly.num"
] | true |
DirectSum.decomposeLinearEquiv_apply | Mathlib.Algebra.DirectSum.Decomposition | [
"Submodule",
"DirectSum.Decomposition",
"Submodule.addSubmonoidClass",
"Equiv.instEquivLike",
"DirectSum.decomposeLinearEquiv",
"instAddCommMonoidDirectSum",
"DirectSum.instModule",
"Submodule.addCommMonoid",
"Membership.mem",
"Equiv",
"Subtype",
"AddSubmonoidClass.toAddCommMonoid",
"Submodu... | true |
ContinuousLinearMap.compContinuousMultilinearMapL._proof_1 | Mathlib.Topology.Algebra.Module.Multilinear.Topology | [
"congrArg",
"ContinuousLinearMap.compContinuousMultilinearMap",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"ContinuousMultilinearMap.addCommMonoid",
"AddCommGroup.toAddGroup",
"ContinuousMultilinearMap",
"Function.comp",
"NormedField.toField",
"AddCommGroup",
"map_add",
"Co... | false |
Rep.instLinearResFunctor | Mathlib.RepresentationTheory.Rep.Res | [
"Monoid",
"Eq.mpr",
"Rep.V",
"CommRing",
"instHSMul",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"CategoryTheory.Functor.Linear",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Re... | true |
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