name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
InfHom.instFunLike.eq_1 | Mathlib.Order.Hom.Lattice | [
"DFunLike.mk",
"InfHom.toFun",
"InfHom",
"InfHom.instFunLike._proof_1",
"Min",
"Eq.refl",
"InfHom.instFunLike",
"Eq",
"FunLike"
] | true |
«term_/_» | Init.Notation | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
_private.Mathlib.FieldTheory.PrimitiveElement.0.Field.isAlgebraic_of_finite_intermediateField.match_1_1 | Mathlib.FieldTheory.PrimitiveElement | [
"IntermediateField",
"Algebra",
"Exists",
"Set.instSingletonSet",
"Ne",
"Field.toSemifield",
"Monoid.toPow",
"And.casesOn",
"And",
"Semifield.toDivisionSemiring",
"Exists.casesOn",
"HPow.hPow",
"Nat",
"And.intro",
"IntermediateField.adjoin",
"Semiring.toMonoid",
"Exists.intro",
"Di... | false |
CategoryTheory.ObjectProperty.strictLimitsOfShape.limit | Mathlib.CategoryTheory.ObjectProperty.LimitsOfShape | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.HasLimit",
"CategoryTheory.ObjectProperty.strictLimitsOfShape.limit",
"CategoryTheory.Limits.limit",
"CategoryTheory.ObjectProperty.strictLimitsOfShape",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.ObjectProperty",
"CategoryTheory.Functo... | true |
CategoryTheory.Functor.Fiber.fiberCategory._proof_3 | Mathlib.CategoryTheory.FiberedCategory.Fiber | [
"CategoryTheory.Functor",
"Subtype.mk.congr_simp",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.Functor.Fiber.fiberCategory._proof_1",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.IsHomLift",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.IsHomLift.id",
"Subtype",
"Categor... | false |
Finset.image_subset_infs_right | Mathlib.Data.Finset.Sups | [
"Finset",
"Membership.mem",
"HasSubset.Subset",
"HasInfs.infs",
"SemilatticeInf.toMin",
"SemilatticeInf",
"Finset.instSetLike",
"Finset.instHasSubset",
"Finset.image_subset_image₂_right",
"Finset.image",
"SetLike.instMembership",
"Finset.hasInfs",
"Min.min",
"DecidableEq"
] | true |
_private.Mathlib.Analysis.Normed.Unbundled.SmoothingSeminorm.0.isNonarchimedean_smoothingFun._simp_1_2 | Mathlib.Analysis.Normed.Unbundled.SmoothingSeminorm | [
"ge_iff_le",
"GE.ge",
"LE.le",
"LE",
"propext",
"Eq"
] | false |
Metric.Snowflaking.image_ofSnowflaking_emetricBall | Mathlib.Topology.MetricSpace.Snowflaking | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Real.instLE",
"Real",
"Equiv.instEquivLike",
"Real.instZero",
"Real.instInv",
"ENNReal.instPowReal",
"Metric.Snowflaking.image_ofSnowflaking_eball",
"Real.instLT",
"Equiv",
"Metric.Snowflaking.instEDist",
"LE.le",
"Metric.eball",
"PseudoEMetr... | true |
Besicovitch.SatelliteConfig.ctorIdx | Mathlib.MeasureTheory.Covering.Besicovitch | [
"Besicovitch.SatelliteConfig",
"Real",
"MetricSpace",
"Nat"
] | false |
_private.Lean.Compiler.LCNF.ToImpure.0.Lean.Compiler.LCNF.Arg.toImpure.match_1 | Lean.Compiler.LCNF.ToImpure | [
"Lean.Compiler.LCNF.Arg.casesOn",
"Unit.unit",
"Lean.Compiler.LCNF.Arg",
"Lean.Compiler.LCNF.Arg.fvar",
"Lean.Expr",
"Lean.FVarId",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Purity.pure",
"autoParam",
"Unit",
"Lean.Compiler.LCNF.Arg.erased",
"Eq",
"Lean.Compiler.LCNF.Arg._auto_1",
"... | false |
Algebra.Generators.Hom.id_val | Mathlib.RingTheory.Extension.Generators | [
"CommRing",
"CommSemiring.toSemiring",
"Algebra.Generators.Hom.val",
"MvPolynomial.X",
"Algebra",
"Algebra.id",
"Algebra.Generators",
"Algebra.Generators.Hom.id",
"CommRing.toCommSemiring",
"MvPolynomial",
"Eq.refl",
"Eq"
] | true |
CategoryTheory.Functor.mapHomologicalComplexUpToQuasiIso._proof_1 | Mathlib.Algebra.Homology.Localization | [
"CategoryTheory.MorphismProperty.instCategoryLocalization'",
"HomologicalComplex.instCategory",
"HomologicalComplex.quasiIso",
"HomologicalComplex",
"ComplexShape",
"CategoryTheory.MorphismProperty.HasLocalization",
"CategoryTheory.Preadditive",
"CategoryTheory.MorphismProperty.instIsLocalizationLocal... | false |
CommRingCat.prodFan.eq_1 | Mathlib.Algebra.Category.Ring.Constructions | [
"CommRingCat.carrier",
"CommSemiring.toSemiring",
"CommRingCat",
"CategoryTheory.Limits.BinaryFan",
"CommRingCat.ofHom",
"CategoryTheory.Limits.BinaryFan.mk",
"CommRingCat.instCategory",
"RingHom.snd",
"CommRingCat.instCommRingObjForgetRingHomCarrier",
"CommRing.toCommSemiring",
"Prod.instCommRi... | true |
DirectLimit.map₀ | Mathlib.Order.DirectedInverseSystem | [
"DirectLimit.setoid",
"Preorder.toLE",
"LE.le",
"DirectLimit",
"Quotient.mk",
"IsDirectedOrder",
"Classical.arbitrary",
"Nonempty",
"DirectedSystem",
"Sigma.mk",
"DFunLike.coe",
"Sigma",
"Preorder",
"FunLike"
] | true |
MeasureTheory.Measure.absolutelyContinuous_rfl | Mathlib.MeasureTheory.Measure.AbsolutelyContinuous | [
"MeasureTheory.Measure",
"MeasureTheory.Measure.AbsolutelyContinuous",
"MeasurableSpace",
"MeasureTheory.Measure.AbsolutelyContinuous.rfl"
] | true |
Filter.exists_forall_mem_of_hasBasis_mem_blimsup' | Mathlib.Order.LiminfLimsup | [
"trivial",
"Filter.exists_forall_mem_of_hasBasis_mem_blimsup",
"setOf",
"Membership.mem",
"Exists",
"CompleteLattice.toConditionallyCompleteLattice",
"Filter.blimsup",
"Set.Elem",
"Subtype.mk",
"And",
"Filter.HasBasis",
"Exists.casesOn",
"True",
"Exists.intro",
"CompleteBooleanAlgebra.to... | true |
FirstOrder.Field.genericMonicPoly | Mathlib.ModelTheory.Algebra.Field.IsAlgClosed | [
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"FreeCommRing",
"Finset.univ",
"CommSemiring.toSemiring",
"instCommRingFreeCommRing",
"FreeCommRing.of",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"instOfNatNat",
"Fin.val"... | true |
instErgodicSMulMulOppositeOfIsMulRightInvariant | Mathlib.Dynamics.Ergodic.Action.Regular | [
"MeasureTheory.Measure.QuasiMeasurePreserving.ae",
"Filter.instMembership",
"MeasurableSet.mem",
"MeasureTheory.ae",
"MeasureTheory.Measure.IsMulRightInvariant.toSMulInvariantMeasure_op",
"MeasurableSet.preimage",
"Eq.mpr",
"_private.Mathlib.Dynamics.Ergodic.Action.Regular.0.instErgodicSMulOfIsMulLeft... | true |
CategoryTheory.InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_hom_naturality | Mathlib.CategoryTheory.Abelian.RightDerived | [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"HomologicalComplex.instCategory",
"CategoryTheory.InjectiveResolution.iso_hom_naturality",
"Nat.instIsOrderedAddMonoid",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"Nat.instOne",
"Homolog... | true |
Submodule.galgebra._proof_6 | Mathlib.Algebra.DirectSum.Internal | [
"LinearMap.toAddMonoidHom",
"GradedMonoid.instSMul",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Submodule",
"Submodule.addSubmonoidClass",
"instHSMul",
"Semiring.toModule",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"Sigma.subtype_ext",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul... | false |
Equiv.Perm.SameCycle.pow_right | Mathlib.GroupTheory.Perm.Cycle.Basic | [
"Iff.mpr",
"Equiv.instEquivLike",
"Equiv.Perm.instPowNat",
"Equiv.Perm.SameCycle",
"Equiv.Perm.sameCycle_pow_right",
"HPow.hPow",
"Equiv.Perm",
"Nat",
"instHPow",
"DFunLike.coe",
"EquivLike.toFunLike"
] | true |
Lean.Meta.SynthInstance.State._sizeOf_inst | Lean.Meta.SynthInstance | [
"Lean.Meta.SynthInstance.State._sizeOf_1",
"SizeOf.mk",
"SizeOf",
"Lean.Meta.SynthInstance.State"
] | false |
Mathlib.Tactic.Choose.mkFreshNameFrom | Mathlib.Tactic.Choose | [
"Pure.pure",
"IO.RealWorld",
"EIO",
"instMonadEIO",
"Applicative.toPure",
"Lean.Core.State",
"Lean.Core.CoreM",
"StateRefT'",
"Lean.Core.mkFreshUserName",
"StateRefT'.instMonad",
"Lean.Name",
"Lean.Name.instDecidableEq",
"Lean.Name.mkStr1",
"ReaderT.instApplicativeOfMonad",
"Eq",
"Lean... | true |
_private.Mathlib.Combinatorics.Enumerative.Catalan.Tree.0.Tree.treesOfNumNodesEq_card_eq_catalan._simp_1_1 | Mathlib.Combinatorics.Enumerative.Catalan.Tree | [
"Finset",
"Disjoint",
"Membership.mem",
"Finset.partialOrder",
"Finset.instSetLike",
"propext",
"Finset.disjoint_left",
"Finset.instOrderBot",
"Eq",
"Not",
"SetLike.instMembership"
] | false |
Lean.Meta.SimpAll.Entry.mk.sizeOf_spec | Lean.Meta.Tactic.Simp.SimpAll | [
"Lean.Meta.SimpAll.Entry.mk",
"Lean.FVarId._sizeOf_inst",
"Lean.Expr",
"Lean.FVarId",
"instOfNatNat",
"Lean.Meta.SimpAll.Entry",
"instHAdd",
"HAdd.hAdd",
"Lean.instSizeOfName",
"Nat",
"Lean.Meta.Origin._sizeOf_inst",
"SizeOf.sizeOf",
"instAddNat",
"Lean.Name",
"Eq.refl",
"OfNat.ofNat",... | true |
CommGrpCat.μ_forget_apply | Mathlib.Algebra.Category.Grp.CartesianMonoidal | [
"MonoidHom.instFunLike",
"CategoryTheory.typesCartesianMonoidalCategory",
"MonoidHom",
"Monoid.toMulOneClass",
"CategoryTheory.ConcreteCategory.hom",
"CommGrpCat.instBraidedCategory",
"CommGrpCat.instCategory",
"TypeCat.instFunLikeFun",
"CategoryTheory.SemiCartesianMonoidalCategory.snd",
"CommGrpC... | true |
_private.Mathlib.Geometry.Euclidean.Incenter.0.Affine.Simplex.ExcenterExists.excenterWeights_eq_excenterWeights_iff._simp_1_9 | Mathlib.Geometry.Euclidean.Incenter | [
"InnerProductSpace.toNormedSpace",
"Affine.Simplex.height",
"Nat.instMulZeroClass",
"Real",
"Real.instZero",
"Real.instRCLike",
"NormedSpace.toModule",
"Real.instLT",
"Affine.Simplex",
"Real.instRing",
"instOfNatNat",
"Affine.Simplex.height_pos",
"instHAdd",
"NormedAddTorsor.toAddTorsor",
... | false |
CategoryTheory.Limits.isColimitCoconeLeftOpOfCone._proof_1 | Mathlib.CategoryTheory.Limits.Opposites | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.Cocone",
"CategoryTheory.Limits.Cone",
"Opposite",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Quiver.Hom.op",
"CategoryTheory.Functor.category",
"Quiver.Hom.unop",
"CategoryTheory.Limits.Cone.pt",
"... | false |
Asymptotics.IsBigO.abs_right | Mathlib.Analysis.Asymptotics.Defs | [
"Iff.mpr",
"Real",
"Real.lattice",
"abs",
"Asymptotics.IsBigO",
"Norm",
"Real.instAddGroup",
"Filter",
"Real.norm",
"Asymptotics.isBigO_abs_right"
] | true |
PLift.map | Mathlib.Control.ULift | [
"PLift",
"PLift.down",
"PLift.up"
] | true |
Nat.brecOn.go._@.Mathlib.Util.CompileInductive.1571041013._hygCtx._hyg.3 | Mathlib.Util.CompileInductive | [
"PProd.mk",
"Nat.rec",
"Nat.below",
"PProd",
"PUnit",
"Nat",
"Nat.zero",
"PUnit.unit",
"Nat.succ"
] | false |
WithZero.instAddCommMonoid._proof_1 | Mathlib.Algebra.Group.WithOne.Defs | [
"AddMonoid.toAddSemigroup",
"Option.some",
"AddCommSemigroup.toAddSemigroup",
"add_comm",
"WithZero.instZero",
"congr_arg",
"instHAdd",
"AddSemigroup.toAdd",
"Unit",
"HAdd.hAdd",
"WithZero",
"WithZero.instAddMonoid",
"WithZero.coe",
"Zero.toOfNat0",
"AddCommSemigroup.toAddCommMagma",
"... | false |
Int.getElem?_toList_rcc_eq_none_iff._simp_1 | Init.Data.Range.Polymorphic.IntLemmas | [
"Int.getElem?_toList_rcc_eq_none_iff",
"Std.PRange.instUpwardEnumerableInt",
"HSub.hSub",
"List.instGetElem?NatLtLength",
"Int.decLe",
"Int",
"LE.le",
"instLENat",
"Option.none",
"List",
"instHAdd",
"instHSub",
"instOfNat",
"HAdd.hAdd",
"Nat",
"Std.Rcc.toList",
"LT.lt",
"propext",
... | false |
Option.le.eq_1 | Init.Data.Option.Lemmas | [
"Option.some",
"Option.none",
"True",
"Eq.refl",
"Option.le",
"Eq"
] | true |
_private.Mathlib.Topology.Category.Stonean.Basic.0.Stonean.epi_iff_surjective._simp_1_5 | Mathlib.Topology.Category.Stonean.Basic | [
"Exists",
"propext",
"Classical.not_forall",
"Eq",
"Not"
] | false |
_private.Batteries.Data.List.Lemmas.0.List.isChain_iff_pairwise._simp_1_8 | Batteries.Data.List.Lemmas | [
"iff_self_and",
"And",
"Iff",
"propext",
"Eq"
] | false |
ModuleCat.ExtendRestrictScalarsAdj.HomEquiv.fromExtendScalars._proof_3 | Mathlib.Algebra.Category.ModuleCat.ChangeOfRings | [
"CommRing",
"instHSMul",
"Semiring.toModule",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"LinearMap.ext",
"CommSemiring.toSemiring",
"CategoryTheory.ConcreteCategory.hom",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
... | false |
ContinuousLinearMap.isVonNBounded_iff | Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap | [
"NormedCommRing.toSeminormedCommRing",
"Bornology.IsVonNBounded",
"ContinuousLinearMap.topologicalSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"AddMonoid.toAddZeroClass",
"setOf",
"NormedDivisionRing.toNormedRing",
"AddCommGroup.toAddGrou... | true |
String.charactersIn | Lean.Server.Completion.CompletionUtils | [
"String",
"instOfNatNat",
"_private.Lean.Server.Completion.CompletionUtils.0.String.charactersIn.goFastScalar",
"String.Pos.Raw.mk",
"Nat",
"Bool",
"OfNat.ofNat"
] | true |
Num.castNum_or._simp_1 | Mathlib.Data.Num.Lemmas | [
"Nat.instMulZeroClass",
"instHOrOfOrOp",
"Nat.instOne",
"Num.castNum_or",
"castNum",
"HOr.hOr",
"Num",
"Nat",
"instAddNat",
"Num.instOrOp",
"Eq.symm",
"Eq",
"Nat.instOrOp",
"MulZeroClass.toZero"
] | false |
Complex.rec | Mathlib.Data.Complex.Basic | [
"Real",
"Complex",
"Complex.mk"
] | false |
Std.DTreeMap.Raw.minKey?_insertIfNew_of_isEmpty | Std.Data.DTreeMap.Raw.Lemmas | [
"Ord.mk",
"Std.DTreeMap.Raw.minKey?",
"Option.some",
"Ordering",
"Std.DTreeMap.Raw.isEmpty",
"Std.TransCmp",
"Bool.true",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Bool",
"Std.DTreeMap.Internal.Impl.minKey?_insertIfNew!_of_isEmpty",
"Eq",
"Std.DTreeMap.Raw.insertIfNew",
"Std.DT... | true |
LinOrd.hasForgetToLat._proof_2 | Mathlib.Order.Category.LinOrd | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreorder",
"LinOrd.carrier",
"Lat.of",
"SemilatticeInf.toPartialOrder",
"LinOrd.str",
"DistribLattice.toLattice",
"id",
"LinOrd",
"Lat.instCategory",
"OrderHomClass.toLatticeHom",
"LinOrd.instCategory",
"OrderHom.instF... | false |
CategoryTheory.EffectiveEpi.mk | Mathlib.CategoryTheory.EffectiveEpi.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Nonempty",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.EffectiveEpiStruct",
"CategoryTheory.EffectiveEpi",
"CategoryTheory.Category",
"CategoryTheory.EffectiveEpi.mk"
] | true |
Std.DTreeMap.Raw.Const.getThenInsertIfNew?_snd | Std.Data.DTreeMap.Raw.Lemmas | [
"Std.DTreeMap.Raw.Const.getThenInsertIfNew?",
"Ord.mk",
"Ordering",
"Std.TransCmp",
"Std.DTreeMap.Internal.Impl.Const.getThenInsertIfNew?!_snd",
"_private.Std.Data.DTreeMap.Raw.Lemmas.0.Std.DTreeMap.Raw.ext",
"Std.DTreeMap.Raw.WF.out",
"Std.DTreeMap.Raw.inner",
"Eq",
"Prod.snd",
"Std.DTreeMap.Ra... | true |
Lean.Elab.Command.InductiveElabStep2.recOn | Lean.Elab.MutualInductive | [
"Lean.CollectFVars.State",
"Lean.Elab.Command.InductiveElabStep2",
"Lean.Elab.Command.InductiveElabStep3",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Lean.Level",
"Array",
"List",
"Unit",
"Lean.Elab.Command.InductiveElabStep2.mk",
"StateRefT'",
"Nat",
"Lean.Elab.Term.TermElabM",
"L... | false |
Lean.Core.Context.cancelTk?._default | Lean.CoreM | [
"id",
"Option.none",
"IO.CancelToken",
"Option"
] | false |
OrderHom.piIso._proof_2 | Mathlib.Order.Hom.Basic | [
"Pi.preorder",
"OrderHom.comp",
"OrderHom.pi",
"Function.RightInverse",
"Eq.refl",
"OrderHom",
"Preorder",
"Pi.evalOrderHom"
] | false |
Directed.ciInf_le | Mathlib.Order.ConditionallyCompletePartialOrder.Defs | [
"Set.mem_range_self",
"iInf",
"Directed",
"Directed.directedOn_range",
"PartialOrder.toPreorder",
"Preorder.toLE",
"LE.le",
"ConditionallyCompletePartialOrderInf.toPartialOrder",
"BddBelow",
"DirectedOn.csInf_le",
"Set.range",
"ConditionallyCompletePartialOrderInf.toInfSet",
"ConditionallyCo... | true |
_private.Mathlib.RingTheory.Polynomial.Chebyshev.0.Polynomial.Chebyshev.T.match_1.eq_3 | Mathlib.RingTheory.Polynomial.Chebyshev | [
"Int.ofNat",
"Int",
"Unit",
"instOfNat",
"Nat",
"Eq.refl",
"Int.negSucc",
"OfNat.ofNat",
"Nat.succ",
"Eq",
"Polynomial.Chebyshev.T.match_1"
] | true |
_private.Mathlib.Tactic.ToExpr.0.Mathlib.toExprMData | Mathlib.Tactic.ToExpr | [
"Pure.pure",
"Lean.mkNatLit",
"Lean.instToExprBool",
"Lean.KVMap.instForInProdNameDataValueOfMonad",
"Monad.toApplicative",
"String",
"Mathlib.instToExprSyntax_mathlib",
"Lean.Syntax",
"Lean.Name.mkStr3",
"Lean.mkStrLit",
"Lean.Expr",
"_private.Mathlib.Tactic.ToExpr.0.Mathlib.toExprMData.match... | true |
instLawfulBEqLex | Mathlib.Order.Lex | [
"instBEqLex",
"Lex",
"LawfulBEq",
"BEq"
] | true |
AffineBasis.basisOf_reindex | Mathlib.LinearAlgebra.AffineSpace.Basis | [
"AffineBasis.instFunLike",
"Equiv.instEquivLike",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddCommGroup.toAddGroup",
"Function.comp",
"Equiv.subtypeEquiv._proof_3",
"Equiv.subtypeEquiv",
"AddCommGroup",
"Equiv",
"Subtype",
"Iff.not",
"Ne",
"Module.Basis.coe_reindex",
"Module.Basis.in... | true |
Interval.pure_one | Mathlib.Algebra.Order.Interval.Basic | [
"One",
"Interval.pure",
"Preorder.toLE",
"Interval",
"One.toOfNat1",
"OfNat.ofNat",
"Eq",
"instOneInterval",
"rfl",
"Preorder"
] | true |
CategoryTheory.Localization.Construction.ψ₂.eq_1 | Mathlib.CategoryTheory.Localization.Construction | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Localization.Construction.LocQuiver",
"CategoryTheory.Paths.categoryPaths",
"CategoryTheory.Paths",
"CategoryTheory.Localization.Construction.LocQuiver.obj",
"Subtype",
"CategoryTheory.Localiza... | true |
Qq.Impl.PatVarDecl.noConfusion | Qq.MatchImpl | [
"Qq.Impl.PatVarDecl.noConfusionType",
"Qq.Impl.PatVarDecl",
"Lean.Expr.const",
"Lean.FVarId",
"Lean.Level",
"Qq.Impl.PatVarDecl.casesOn",
"Qq.Quoted",
"Eq.ndrec",
"Lean.Name.mkStr2",
"Lean.Name",
"Eq.refl",
"Eq",
"List.nil",
"Option"
] | false |
Set.powersetCard.mulActionHom_compl_bijective | Mathlib.GroupTheory.GroupAction.SubMulAction.Combination | [
"Iff.mpr",
"Function.LeftInverse",
"MulActionHom.comp",
"Finset",
"CompTriple.instId_comp",
"MulActionHom.id",
"CompTriple.instIsIdId",
"Group",
"Membership.mem",
"Exists",
"Set.powersetCard.instMulActionElemFinset",
"Set.Elem",
"Fintype.card",
"id",
"Subtype",
"DivInvMonoid.toMonoid",... | true |
Lean.Widget.WidgetSource.mk.sizeOf_spec | Lean.Widget.UserWidget | [
"Lean.Widget.WidgetSource",
"String",
"instOfNatNat",
"Lean.Widget.WidgetSource.mk",
"Lean.Widget.WidgetSource._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"String._sizeOf_inst",
"Eq.refl",
"OfNat.ofNat",
"Eq"
] | true |
CategoryTheory.PreGaloisCategory.hasQuotientsByFiniteGroups._autoParam | Mathlib.CategoryTheory.Galois.Basic | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
LinearMap.BilinForm.IsSymm.recOn | Mathlib.LinearAlgebra.BilinearForm.Properties | [
"Semiring.toModule",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"LinearMap.BilinForm.IsSymm.rec",
"LinearMap.BilinForm.IsSymm.mk",
"LinearMap.module",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.to... | false |
_private.Init.Data.List.MinMaxIdx.0.List.maxIdxOn_eq_iff._simp_1_1 | Init.Data.List.MinMaxIdx | [
"LE.le_opposite_iff",
"LE.le",
"LE",
"propext",
"Eq",
"LE.opposite"
] | false |
Std.Sat.AIG.ExtendingEntrypoint | Std.Sat.AIG.LawfulOperator | [
"Std.Sat.AIG.Entrypoint.aig",
"Std.Sat.AIG.Decl",
"Subtype",
"Std.Sat.AIG.Entrypoint",
"LE.le",
"instLENat",
"Std.Sat.AIG",
"Nat",
"Hashable",
"Array.size",
"Std.Sat.AIG.decls",
"DecidableEq"
] | true |
_private.Init.Data.SInt.Lemmas.0.Int32.toInt64_ne_minValue._proof_1_2 | Init.Data.SInt.Lemmas | [
"instPowNat",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"HSub.hSub",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
"Int.instNegInt",
"Int.s... | false |
ContMDiffMul.mk | Mathlib.Geometry.Manifold.Algebra.Monoid | [
"ContMDiffMul",
"Prod.normedSpace",
"HMul.hMul",
"Prod.normedAddCommGroup",
"NormedSpace",
"ContMDiff",
"instTopologicalSpaceProd",
"Mul",
"IsManifold",
"instTopologicalSpaceModelProd",
"ContMDiffMul.mk",
"Prod.fst",
"TopologicalSpace",
"ModelWithCorners",
"ENat",
"NontriviallyNormedFi... | true |
_private.Mathlib.RingTheory.Polynomial.UniversalFactorizationRing.0.Polynomial.monic_freeMonic._simp_1_1 | Mathlib.RingTheory.Polynomial.UniversalFactorizationRing | [
"Polynomial.coeff_natDegree",
"Polynomial.leadingCoeff",
"Polynomial",
"Polynomial.coeff",
"Semiring",
"Polynomial.natDegree",
"Eq.symm",
"Eq"
] | false |
Lean.Meta.Grind.instNonemptyMethodsRef | Lean.Meta.Tactic.Grind.Types | [
"Lean.Meta.Grind.MethodsRef",
"Nonempty",
"_private.Lean.Meta.Tactic.Grind.Types.0.Lean.Meta.Grind.MethodsRefPointed",
"Subtype.property"
] | true |
SkewPolynomial.monomial_add | Mathlib.Algebra.SkewPolynomial.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Semiring.toModule",
"Equiv.instEquivLike",
"SkewMonoidAlgebra.instModule",
"LinearMap.instFunLike",
"SkewPolynomial",
"Equiv",
"Distrib.toAdd",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"LinearMap",
"instDistribOfSemiring",
"NonUnitalNonAssocSemirin... | true |
_private.Batteries.Data.String.Lemmas.0.Substring.Raw.takeWhile.match_1.splitter | Batteries.Data.String.Lemmas | [
"Substring.Raw.mk",
"String",
"String.Pos.Raw",
"Substring.Raw",
"Bool",
"Char",
"_private.Init.Data.String.Substring.0.Substring.Raw.takeWhile.match_1"
] | true |
Set.update_preimage_pi | Mathlib.Data.Set.Prod | [
"Set.ext",
"Eq.mpr",
"Function.update",
"outParam",
"congrArg",
"HEq.refl",
"Membership.mem",
"Eq.casesOn",
"id",
"Ne",
"Membership",
"Or.casesOn",
"Set.preimage",
"True",
"Iff.intro",
"eq_self",
"of_eq_true",
"eq_of_heq",
"Eq.ndrec",
"eq_or_ne",
"Eq.refl",
"HEq",
"Set.pi... | true |
_private.Init.Data.Range.Polymorphic.IntLemmas.0.Int.induct_rcc_right._proof_1_1 | Init.Data.Range.Polymorphic.IntLemmas | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"Int.instMax",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Int.decLe",
"Lean.Omega.LinearCombo.eval",
"Opt... | false |
Affine.Simplex.abs_inner_vsub_altitudeFoot_lt_mul | Mathlib.Geometry.Euclidean.Altitude | [
"Int.instAddCommGroup",
"Set.mem_range_self",
"Iff.mpr",
"NormedCommRing.toNormedRing",
"EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal",
"Norm.norm",
"Mathlib.Tactic.Ring.Common.neg_zero",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NegZeroClass.toNeg",
"NonAssocSemiring... | true |
Filter.eventually_inf_principal | Mathlib.Order.Filter.Basic | [
"Filter.Eventually",
"setOf",
"Membership.mem",
"Filter.instInf",
"Iff",
"Filter.principal",
"Filter.mem_inf_principal",
"Set.instMembership",
"Filter",
"Min.min",
"Set"
] | true |
Ideal.Quotient.factor | Mathlib.RingTheory.Ideal.Quotient.Defs | [
"Semiring.toModule",
"Ideal.Quotient.mk",
"PartialOrder.toPreorder",
"Preorder.toLE",
"RingHom",
"Ideal.IsTwoSided",
"Submodule.instPartialOrder",
"LE.le",
"Ideal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"HasQuotient.Quotient",
"Ideal.Quotient.ring",
"Ideal.instHasQuotient",
"NonAsso... | true |
Computation.liftRel_think_right | Mathlib.Data.Seq.Computation | [
"Eq.mpr",
"Computation.think",
"congrArg",
"Function.swap",
"id",
"Computation.LiftRel.swap",
"Computation",
"Iff",
"propext",
"Eq.symm",
"Eq",
"Computation.liftRel_think_left",
"Computation.LiftRel"
] | true |
_private.Batteries.Data.Array.Monadic.0.Array.SatisfiesM_anyM_iff_exists.match_1_3 | Batteries.Data.Array.Monadic | [
"Exists",
"LE.le",
"instLENat",
"Fin.val",
"Array",
"And.casesOn",
"And",
"Nat",
"And.intro",
"LT.lt",
"instLTNat",
"Fin",
"Array.size",
"Not"
] | false |
_private.Batteries.Data.String.Lemmas.0.String.Legacy.Iterator.Valid.prevn.match_1_1 | Batteries.Data.String.Lemmas | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
CategoryTheory.Limits.kernelIsKernel._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Kernels | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Limits.Fork.ofι",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"congrArg",
"CategoryTheory.Limits.comp_zero",
"CategoryTheory.Limits.kernel",
"CategoryTheory.Limits.walkingParallelPairHo... | false |
ExceptT.ext_iff | Init.Control.Lawful.Instances | [
"ExceptT.ext",
"HEq.refl",
"Eq.casesOn",
"ExceptT.run",
"ExceptT",
"Iff",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"Except",
"Eq.symm",
"Eq"
] | true |
_private.Batteries.Tactic.PermuteGoals.0.Batteries.Tactic.splitGoalsAndGetNth.match_1 | Batteries.Tactic.PermuteGoals | [
"Lean.MVarId",
"Nat.hasNotBit",
"Prod.mk",
"List.cons",
"_private.Batteries.Tactic.PermuteGoals.0.Batteries.Tactic.splitGoalsAndGetNth._sparseCasesOn_1",
"List",
"Prod",
"Prod.casesOn",
"List.ctorIdx"
] | false |
Lean.Meta.Grind.AC.ACM.Context.opId | Lean.Meta.Tactic.Grind.AC.Util | [
"Nat",
"Lean.Meta.Grind.AC.ACM.Context"
] | true |
Std.IsLinearOrder.toIsLinearPreorder | Init.Data.Order.Classes | [
"Std.IsLinearOrder.toIsPartialOrder",
"Std.IsLinearOrder",
"LE",
"Std.IsLinearOrder.le_total",
"Std.IsLinearPreorder.mk",
"Std.IsLinearPreorder",
"Std.IsPartialOrder.toIsPreorder"
] | true |
Lean.MessageData.stripTraceResultPrefix | Mathlib.Lean.MessageData.Trace | [
"String.toSlice",
"Option.isNone",
"Lean.MessageData.traceResultOf",
"Bool.not",
"Lean.TraceResult",
"String",
"String.Slice.dropPrefix",
"instDecidableEqBool",
"Char.isWhitespace",
"Bool.true",
"String.Slice.copy",
"String.Slice.Pattern.CharPred.instForwardPatternForallCharBool",
"Bool",
... | true |
Polynomial.SplittingField.instField._proof_9 | Mathlib.FieldTheory.SplittingField.Construction | [
"GroupWithZero.toMonoidWithZero",
"Semigroup.toMul",
"GroupWithZero.toInv",
"HMul.hMul",
"GroupWithZero.mul_inv_cancel",
"Polynomial.SplittingField",
"Ne",
"Field.toSemifield",
"Polynomial",
"Polynomial.SplittingField.instGroupWithZero",
"Inv.inv",
"Semifield.toDivisionSemiring",
"MonoidWith... | false |
TensorProduct.rightComm._proof_5 | Mathlib.LinearAlgebra.TensorProduct.Associator | [
"TensorProduct.leftHasSMul",
"CommSemiring.toSemiring",
"TensorProduct.addCommMonoid",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
"CommMonoid.toMonoid",
"TensorProduct.instSMul._proof_1",
"CommSemiring.toCommMonoid",
"Semiring.toMonoid",
"TensorProduct.rightComm._proof_4",
"TensorP... | false |
Tree.traverse_eq_map_id | Mathlib.Data.Tree.Traversable | [
"Pure.pure",
"Tree.node",
"Eq.mpr",
"congrArg",
"Tree.map.eq_1",
"Tree.traverse.eq_1",
"Tree.rec",
"Monad.toApplicative",
"Function.comp",
"Tree.nil",
"id",
"Seq.seq",
"Id",
"Applicative.toPure",
"CommApplicative.toLawfulApplicative",
"Tree.map.eq_2",
"Tree",
"Unit",
"LawfulAppli... | true |
AddGrpCat.FilteredColimits.G.mk | Mathlib.Algebra.Category.Grp.FilteredColimits | [
"CategoryTheory.Functor",
"AddGrpCat.instCategory",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.comp",
"AddZeroClass.toAddZero",
"CategoryTheory.SmallCategory",
"Sigma.fst",
"AddGrpCat",
"AddGroup.toSubNegMonoid",
"AddGrpCat.carrier",
"AddGrpCat.FilteredColimits.G",
"CategoryTheory.typ... | true |
DivisionMonoid.noConfusion | Mathlib.Algebra.Group.Defs | [
"Semigroup.toMul",
"DivInvMonoid.toInv",
"HMul.hMul",
"DivisionMonoid.noConfusionType",
"HEq.refl",
"DivisionMonoid.casesOn",
"DivisionMonoid",
"DivInvMonoid.toMonoid",
"DivInvMonoid",
"Inv.inv",
"Monoid.toSemigroup",
"eq_of_heq",
"Eq.ndrec",
"One.toOfNat1",
"HEq",
"Monoid.toOne",
"O... | false |
Lean.Lsp.RpcReleaseParams.mk.sizeOf_spec | Lean.Data.Lsp.Extra | [
"Lean.Json",
"Lean.Lsp.RpcReleaseParams._sizeOf_inst",
"UInt64",
"instOfNatNat",
"Lean.Json._sizeOf_inst",
"Array._sizeOf_inst",
"Array",
"Lean.Lsp.DocumentUri",
"instHAdd",
"HAdd.hAdd",
"UInt64._sizeOf_inst",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"String._sizeOf_inst",
"Eq.refl",
"O... | true |
Std.Sat.AIG.mkAtomCached_eval_eq_mkAtom_eval | Std.Sat.AIG.CachedLemmas | [
"Eq.mpr",
"Std.Sat.AIG.Entrypoint.aig",
"Std.Sat.AIG.Decl",
"Std.Sat.AIG.mkAtomCached._proof_7",
"Std.Sat.AIG.Ref.mk",
"Std.Sat.AIG.denote._proof_5",
"Array.push",
"congrArg",
"Option.some",
"Std.Sat.AIG.hzero",
"id",
"Std.Sat.AIG.mkAtomCached.match_1",
"Std.Sat.AIG.hconst",
"Bool.bne_fals... | true |
Std.DTreeMap.Internal.Impl.entryAtIdx?.match_3 | Std.Data.DTreeMap.Internal.Queries | [
"Std.DTreeMap.Internal.Impl.casesOn",
"Std.DTreeMap.Internal.Impl.inner",
"Std.DTreeMap.Internal.Impl.leaf",
"Nat",
"Std.DTreeMap.Internal.Impl"
] | false |
CategoryTheory.OrthogonalReflection.instSmallLMultispanShape | Mathlib.CategoryTheory.Presentable.OrthogonalReflection | [
"CategoryTheory.OrthogonalReflection.instSmallD₂",
"CategoryTheory.MorphismProperty",
"CategoryTheory.OrthogonalReflection.D₁",
"CategoryTheory.OrthogonalReflection.D₁.obj₂",
"CategoryTheory.Limits.MultispanShape.L",
"CategoryTheory.MorphismProperty.IsSmall",
"CategoryTheory.LocallySmall",
"CategoryTh... | true |
Lean.Elab.DerivingClassView.mk.sizeOf_spec | Lean.Elab.Deriving.Basic | [
"Lean.TSyntax._sizeOf_inst",
"Lean.Syntax._sizeOf_inst",
"Lean.Syntax",
"instOfNatNat",
"Lean.Syntax.Term",
"List.cons",
"Lean.Elab.DerivingClassView",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Bool",
"instAddNat",
"Eq.refl",
"Lean.Elab.DerivingClassView._sizeOf_inst",
"Lean.Sy... | true |
RestrictedProduct.mapAlongRingHom._proof_2 | Mathlib.Topology.Algebra.RestrictedProduct.Basic | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"RingHomClass.toAddMonoidHomClass",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"AddMonoidHomClass",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"RingHom.instFunLike",
"AddMonoidWithOne.toAddMonoid",
"Semi... | false |
Std.ExtDTreeMap.inter | Std.Data.ExtDTreeMap.Basic | [
"Std.ExtDTreeMap.mk",
"Std.DTreeMap",
"Std.ExtDTreeMap.inter._proof_1",
"Ordering",
"Std.TransCmp",
"Std.DTreeMap.inter",
"Std.ExtDTreeMap",
"Std.DTreeMap.Equiv",
"Std.ExtDTreeMap.lift₂"
] | true |
CategoryTheory.Limits.map_lift_equalizerComparison._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.Equalizers | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.map",
"congr",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"of_eq_true",
"CategoryTheory.Functor.map_comp",
"CategoryTheory.Category.toCategoryStruct",
"Eq.symm"... | false |
List.prefix_concat_iff | Init.Data.List.Sublist | [
"Eq.mpr",
"congrArg",
"_private.Init.Data.List.Sublist.0.List.prefix_concat_iff._simp_1_4",
"id",
"List.cons",
"iff_self",
"_private.Init.Data.List.Sublist.0.List.prefix_concat_iff._simp_1_2",
"instHAppendOfAppend",
"List",
"Iff",
"List.reverse_reverse",
"List.IsPrefix",
"congr",
"True",
... | true |
AlgebraicGeometry.Scheme.Pullback.gluing.match_1 | Mathlib.AlgebraicGeometry.Pullbacks | [
"AlgebraicGeometry.Scheme",
"AlgebraicGeometry.Scheme.OpenCover",
"Prod.mk",
"CategoryTheory.PreZeroHypercover.I₀",
"AlgebraicGeometry.IsOpenImmersion",
"AlgebraicGeometry.Scheme.instCategory",
"Prod",
"Prod.casesOn",
"AlgebraicGeometry.Scheme.precoverage",
"CategoryTheory.Precoverage.ZeroHypercov... | false |
CategoryTheory.Pi.eval | Mathlib.CategoryTheory.Pi.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"CategoryTheory.pi",
"CategoryTheory.Pi.eval._proof_2",
"CategoryTheory.Pi.eval._proof_1",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Category"
] | true |
IO.FS.SystemTime.sec | Init.System.IO | [
"IO.FS.SystemTime",
"Int"
] | true |
CategoryTheory.SemiadditiveOfBinaryBiproducts.addCommMonoidHomOfHasBinaryBiproducts._proof_1 | Mathlib.CategoryTheory.Preadditive.OfBiproducts | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Add.mk",
"instOfNatNat",
"CategoryTheory.Limits.HasZeroMorphisms.zero",
"CategoryTheory.SemiadditiveOfBinaryBiproducts.rightAdd",
"nsmulRec",
"Nat",
"Zero.toOfNat0",
"Eq.refl",
"CategoryTheory.Ca... | false |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.