name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Grind.CommRing.instBEqPoly.beq | Init.Grind.Ring.CommSolver | [
"Lean.Grind.CommRing.instBEqPoly.beq._f",
"Lean.Grind.CommRing.Poly",
"Bool",
"Lean.Grind.CommRing.Poly.brecOn"
] | true |
CategoryTheory.MonoidalCategory.inv_tensor._simp_1 | Mathlib.CategoryTheory.Monoidal.Category | [
"CategoryTheory.IsIso",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.inv_tensor",
"CategoryTheory.MonoidalCategoryStruct.tensorObj",
"CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct",
"CategoryTheory.inv",
"Categ... | false |
NonemptyInterval.ext_iff | Mathlib.Order.Interval.Basic | [
"HEq.refl",
"NonemptyInterval.ext",
"Eq.casesOn",
"LE",
"Iff",
"Iff.intro",
"Eq.ndrec",
"Eq.refl",
"HEq",
"NonemptyInterval.toProd",
"Prod",
"Eq.symm",
"Eq",
"NonemptyInterval"
] | true |
Lean.Kernel.Exception.alreadyDeclared | Lean.Environment | [
"Lean.Kernel.Exception",
"Lean.Kernel.Environment",
"Lean.Name",
"Lean.Kernel.Exception.alreadyDeclared"
] | true |
Std.Packages.PreorderOfLEArgs.le._autoParam | Init.Data.Order.PackageFactories | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Filter.nonpos_iff | Mathlib.Order.Filter.Pointwise | [
"Filter.instMembership",
"Filter.le_pure_iff",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"LE.le",
"Set.zero",
"Iff",
"Filter.instZero",
"Zero.toOfNat0",
"OfNat.ofNat",
"Filter",
"Filter.instPartialOrder",
"Zero",
"Set"
] | true |
Std.Http.Status.ctorIdx | Std.Internal.Http.Data.Status | [
"Std.Http.Status",
"Std.Http.Status.casesOn",
"Std.Http.CustomStatus",
"Nat"
] | false |
CategoryTheory.ObjectProperty.isClosedUnderColimitsOfShape_op_iff_unop | Mathlib.CategoryTheory.ObjectProperty.ColimitsOfShape | [
"CategoryTheory.ObjectProperty.IsClosedUnderColimitsOfShape",
"Opposite",
"CategoryTheory.CategoryStruct.opposite",
"CategoryTheory.ObjectProperty.unop",
"CategoryTheory.ObjectProperty.IsClosedUnderLimitsOfShape",
"Iff",
"CategoryTheory.Category.opposite",
"CategoryTheory.Category.toCategoryStruct",
... | true |
Convex.isPreconnected | Mathlib.Analysis.Convex.PathConnected | [
"Real.partialOrder",
"Real",
"ContinuousSMul",
"Convex.isConnected",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"PseudoMetricSpace.toUniformSpace",
"AddCommGroup.toAddGroup",
"Eq.rec",
"AddZeroClass.toAddZero",
"AddCommGroup",
"Real.semiring... | true |
AddMonoidAlgebra.le_inf_support_add | Mathlib.Algebra.MonoidAlgebra.Degree | [
"OrderDual.toDual",
"Equiv.instEquivLike",
"AddMonoidAlgebra.addAddCommMonoid",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Finsupp.support",
"SemilatticeInf.toPartialOrder",
"Equiv",
"SemilatticeInf.toMin",
"LE.le",
"OrderTop",
"instHAdd",
"SemilatticeInf",
"HAdd.hAdd",
"AddMonoidAlgeb... | true |
Vector.map_uncurry_zip_eq_zipWith | Init.Data.Vector.Zip | [
"Vector.mk_zipWith_mk._proof_1",
"Vector.zip",
"Vector",
"congrArg",
"Vector.casesOn",
"Eq.rec",
"Array.map",
"Vector.map_mk._proof_1",
"Vector.map",
"Array",
"Vector.mk_zip_mk._proof_1",
"Vector.mk",
"Nat",
"True",
"eq_self",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"congrFun'",
"... | true |
Ring.instLieAdmissibleRing._proof_1 | Mathlib.Algebra.NonAssoc.LieAdmissible.Defs | [
"AddMonoid.toAddSemigroup",
"Ring.toNonAssocRing",
"congrArg",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocRing.toAddCommGroup",
"AddGroupWithOne.toAddMonoidWithOne",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"AddCommGroup.toAddGroup",
"NonUnitalRing.toNonUnitalNonAssocRing",
"NonUnitalNonAsso... | false |
_private.Mathlib.Topology.Sequences.0.FrechetUrysohnSpace.of_seq_tendsto_imp_tendsto._simp_1_7 | Mathlib.Topology.Sequences | [
"Classical.not_not",
"propext",
"Eq",
"Not"
] | false |
IsArtinianRing.quotNilradicalPowEquivPi._proof_7 | Mathlib.RingTheory.Artinian.Module | [
"IsArtinianRing.quotNilradicalEquivPi._proof_3",
"MaximalSpectrum.asIdeal",
"RingEquiv.toEquiv",
"CommRing",
"iInf",
"Semiring.toModule",
"IsArtinianRing",
"IsScalarTower.right",
"Algebra.algebraMap",
"Function.onFun",
"CommSemiring.toSemiring",
"RingHom",
"Function.comp",
"Algebra.id",
... | false |
Complex.tan_inv_eq_cot | Mathlib.Analysis.Complex.Trigonometric | [
"DivisionCommMonoid.toDivisionMonoid",
"Complex.cos",
"Complex.sin",
"Field.toSemifield",
"Complex.cot",
"Inv.inv",
"Complex.tan",
"Semifield.toCommGroupWithZero",
"CommGroupWithZero.toDivisionCommMonoid",
"inv_div",
"Complex",
"Eq",
"Complex.instInv",
"Complex.instField"
] | true |
ChainComplex.augment._proof_1 | Mathlib.Algebra.Homology.Augment | [
"CategoryTheory.Limits.HasZeroMorphisms",
"ChainComplex",
"Nat.instOne",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAddRightCancelMonoid",
"ChainComplex.truncate._proof_2",
"Nat.instAddCancelCommMonoid",
"instOfNatNat",
"C... | false |
CliffordAlgebra.contractLeft._proof_8 | Mathlib.LinearAlgebra.CliffordAlgebra.Contraction | [
"CommRing",
"Algebra.to_smulCommClass",
"instHSMul",
"Semiring.toModule",
"Ring.toNonAssocRing",
"LinearMap.ext",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"CliffordAlgebra.contractLeftAux",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"instAlgebraCliffordAlgebra",
"... | false |
AlgHom.fromOpposite | Mathlib.Algebra.Algebra.Opposite | [
"MulOne.toOne",
"RingHom.mk",
"AlgHom",
"OneHom.mk",
"AlgHom.funLike",
"MulOpposite.instAlgebra",
"MulOpposite",
"Algebra",
"Commute",
"RingHom",
"AlgHom.fromOpposite._proof_3",
"Function.comp",
"MonoidHom.mk",
"NonAssocSemiring.toMulZeroOneClass",
"MulZeroOneClass.toMulOneClass",
"ins... | true |
CategoryTheory.ComposableArrows.threeδ₂Toδ₁_app_two | Mathlib.CategoryTheory.ComposableArrows.Three | [
"instNeZeroNatHAdd_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreorder",
"CategoryTheory.CategoryStruct.id",
"Fin.instOfNat",
"Preorder.smallCategory",
"instOfNatNat",
"CategoryTheory.ComposableArrows.threeδ₂Toδ₁",
"instHAdd",
"CategoryTheory.ComposableArrows.mk₂... | true |
ST.pure | Init.System.ST | [
"ST.Out.mk",
"Void",
"ST"
] | true |
Prefunctor.pathStar_injective | Mathlib.Combinatorics.Quiver.Covering | [
"Eq.mpr",
"False",
"Quiver.Path.heq_of_cons_eq_cons",
"HEq.symm",
"Quiver.Hom",
"Quiver.Path.nil",
"congrArg",
"HEq.refl",
"False.elim",
"Quiver.Path.hom_heq_of_cons_eq_cons",
"HEq.trans",
"Quiver.Path.rec",
"Quiver.Path.eq_cast_iff_heq",
"Eq.mp",
"Sigma.mk.noConfusion",
"Eq.casesOn",
... | true |
QuadraticForm.tensorLId_symm_apply | Mathlib.LinearAlgebra.QuadraticForm.TensorProduct.Isometries | [
"LinearEquiv.symm",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"QuadraticMap.IsometryEquiv.symm",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"QuadraticMap.Iso... | true |
CategoryTheory.Limits.equalizer.condition_assoc | Mathlib.CategoryTheory.Limits.Shapes.Equalizers | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Limits.equalizer",
"CategoryTheory.Limits.equalizer.condition",
"Eq.mp",
"id",
"CategoryTheory.Limits.HasEqualizer",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"CategoryTheory.Limits.e... | true |
BoxIntegral.IntegrationParams.McShane | Mathlib.Analysis.BoxIntegral.Partition.Filter | [
"BoxIntegral.IntegrationParams.mk",
"BoxIntegral.IntegrationParams",
"Bool.false"
] | true |
Aesop.instEmptyCollectionGlobalRuleSet | Aesop.RuleSet | [
"Aesop.GlobalRuleSet.empty",
"EmptyCollection.mk",
"Aesop.GlobalRuleSet",
"EmptyCollection"
] | true |
Std.DTreeMap.Internal.Impl.self_le_maxKey!_insert | Std.Data.DTreeMap.Internal.Lemmas | [
"Eq.mpr",
"Std.Internal.List.DistinctKeys",
"Std.Internal.List.maxKey!_of_perm",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"Std.instLawfulBEqOrd",
"congrArg",
"beqOfOrd",
"Std.DTreeMap.Internal.Impl.Ordered.distinctKeys",
"Std.TransOrd",
"Std.DTreeMap.Internal.Impl.Ordered",
... | true |
_private.Mathlib.Probability.Process.LocalProperty.0.ProbabilityTheory.mkStrictMonoAux._sunfold | Mathlib.Probability.Process.LocalProperty | [
"instOfNatNat",
"_private.Mathlib.Probability.Process.LocalProperty.0.ProbabilityTheory.mkStrictMonoAux",
"instHAdd",
"Unit",
"HAdd.hAdd",
"Max.max",
"Nat",
"instAddNat",
"Nat.instMax",
"_private.Mathlib.Probability.Process.LocalProperty.0.ProbabilityTheory.mkStrictMonoAux.match_1",
"OfNat.ofNat... | false |
_private.Mathlib.FieldTheory.Finite.Basic.0.FiniteField.card_image_polynomial_eval._simp_1_1 | Mathlib.FieldTheory.Finite.Basic | [
"Finset",
"Membership.mem",
"Finset.ext_iff",
"Iff",
"Finset.instSetLike",
"propext",
"Eq",
"SetLike.instMembership"
] | false |
Algebra.weaklyQuasiFiniteAt_iff | Mathlib.RingTheory.QuasiFinite.Weakly | [
"Algebra.WeaklyQuasiFiniteAt._proof_1",
"Iff.mpr",
"Algebra.WeaklyQuasiFiniteAt._proof_2",
"_private.Mathlib.RingTheory.QuasiFinite.Weakly.0.Algebra.weaklyQuasiFiniteAt_iff._simp_1_2",
"Ideal.Quotient.commSemiring",
"AlgEquiv.instEquivLike",
"RingHom.instRingHomClass",
"CommRing",
"Lattice.toSemilat... | true |
_private.Mathlib.Util.AtomM.Recurse.0.Mathlib.Tactic.AtomM.RecurseM.run.evalAtom._unsafe_rec | Mathlib.Util.AtomM.Recurse | [
"_private.Mathlib.Util.AtomM.Recurse.0.Mathlib.Tactic.AtomM.RecurseM.run.rctx._unsafe_rec",
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Meta.Simp.Result",
"Mathlib.Tactic.AtomM.onSubexpressions",
"Bool",
"IO.Ref",
"Mathlib.Tactic.AtomM.Recurse.Context",
"Mathlib.Tactic.AtomM",
"Bool.false",
"Mathlib.T... | false |
Int.exists_prime_and_dvd | Mathlib.RingTheory.Int.Basic | [
"Iff.mpr",
"Nat.Prime",
"Dvd.dvd",
"Nat.prime_iff_prime_int",
"Prime",
"CommSemiring.toCommMonoidWithZero",
"Exists",
"Ne",
"instOfNatNat",
"Int",
"Nat.cast",
"Int.instDvd",
"And.casesOn",
"And",
"Nat.exists_prime_and_dvd",
"Exists.casesOn",
"Nat.instDvd",
"Nat",
"And.intro",
"... | true |
Lean.Parser.Term.optIdent.formatter | Lean.Parser.Term.Basic | [
"Lean.PrettyPrinter.Formatter",
"Lean.Parser.symbol.formatter",
"Lean.Parser.ident.formatter",
"Lean.Parser.optional.formatter",
"Lean.Parser.atomic.formatter",
"Lean.PrettyPrinter.Formatter.andthen.formatter"
] | true |
orderIsoSpecializationWithUpperSetTopology._proof_1 | Mathlib.Topology.Specialization | [
"Topology.WithUpperSet.toUpperSet",
"Equiv.instEquivLike",
"Specializes",
"congrArg",
"Topology.WithUpperSet.instTopologicalSpace",
"Equiv.trans",
"Topology.WithUpperSet.toUpperSet_specializes_toUpperSet._simp_1",
"Preorder.toLE",
"Specialization.toEquiv",
"Equiv",
"Specialization.instPreorder",... | false |
Sym.exists_cons_of_mem | Mathlib.Data.Sym.Basic | [
"congrArg",
"Sym.cons",
"HEq.refl",
"AddCancelMonoid.toAddRightCancelMonoid",
"Multiset.exists_cons_of_mem",
"Membership.mem",
"Exists",
"Multiset",
"Eq.mp",
"Eq.casesOn",
"Nat.instAddCancelCommMonoid",
"Multiset.cons",
"instOfNatNat",
"add_left_inj",
"Multiset.card_cons",
"Subtype.mk"... | true |
_private.Mathlib.GroupTheory.Perm.Cycle.Basic.0.Equiv.Perm.sameCycle_subtypePerm._simp_1_1 | Mathlib.GroupTheory.Perm.Cycle.Basic | [
"Subtype",
"Subtype.ext_iff",
"propext",
"Subtype.val",
"Eq"
] | false |
CategoryTheory.GrothendieckTopology.Point.Hom.noConfusionType | Mathlib.CategoryTheory.Sites.Point.Category | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.GrothendieckTopology.Point",
"CategoryTheory.Functor.category",
"CategoryTheory.GrothendieckTopology.Point.Hom",
"CategoryTheory.GrothendieckTopology",
"CategoryTheory.types",
"HEq",
"CategoryTheory.C... | false |
AddMemClass.toAddSemigroup.eq_1 | Mathlib.Algebra.Group.Subsemigroup.Defs | [
"SetLike",
"AddMemClass.toAddSemigroup._proof_1",
"Membership.mem",
"Subtype",
"AddSemigroup.mk",
"AddSemigroup",
"AddSemigroup.toAdd",
"AddMemClass.add",
"AddMemClass",
"Eq.refl",
"AddMemClass.toAddSemigroup",
"Eq",
"SetLike.instMembership"
] | true |
_private.Mathlib.Algebra.Category.Grp.EpiMono.0.GrpCat.SurjectiveOfEpiAuxs.termH | Mathlib.Algebra.Category.Grp.EpiMono | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
_private.Mathlib.Data.Finset.Sups.0.Finset.powerset_inter._simp_1_1 | Mathlib.Data.Finset.Sups | [
"Finset",
"Membership.mem",
"HasSubset.Subset",
"Finset.mem_powerset",
"Finset.instSetLike",
"propext",
"Finset.instHasSubset",
"Finset.powerset",
"Eq",
"SetLike.instMembership"
] | false |
TopCat.instCategorySheaf._proof_8 | Mathlib.Topology.Sheaves.Sheaf | [
"Quiver.mk",
"CategoryTheory.Functor",
"CategoryTheory.ObjectProperty.FullSubcategory.category._proof_8",
"Opposite",
"CategoryTheory.CategoryStruct.mk",
"CategoryTheory.Category.comp_id._autoParam",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"TopologicalSpace.Opens.instPartialOrder",
... | false |
Lean.Elab.Term.precheckMatch | Lean.Elab.Match | [
"Pure.pure",
"Lean.Elab.Term.getPatternVarNames",
"Lean.TSyntax",
"Lean.MonadError.mk",
"Unit.unit",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.Elab.Term.Quotation.PrecheckM",
"instMonadExceptOfMonadExceptOf",
"Lean.Elab.Term.Quotation.Precheck.C... | true |
Lean.Meta.Grind.Arith.Linear.EqCnstr.toExprProof._unsafe_rec | Lean.Meta.Tactic.Grind.Arith.Linear.Proof | [
"Pure.pure",
"Lean.Meta.Grind.GrindM",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.Grind.Arith.Linear.LinExpr",
"Lean.Meta.Grind.Arith.Linear.mkPolyDecl",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Expr",
"Lean.mkApp9",
"Lean.mkApp7",
"Lean.Meta.Grind.Goal",
... | false |
MulZeroClass.casesOn | Mathlib.Algebra.GroupWithZero.Defs | [
"HMul.hMul",
"MulZeroClass.rec",
"Mul",
"MulZeroClass",
"Zero.toOfNat0",
"MulZeroClass.mk",
"OfNat.ofNat",
"Eq",
"instHMul",
"Zero"
] | false |
CasesInfo.indName | Lean.Meta.CasesInfo | [
"CasesInfo",
"Lean.Name"
] | true |
String.Legacy.Iterator.prevn._sunfold | Init.Data.String.Iterator | [
"_private.Init.Data.String.Iterator.0.String.Legacy.Iterator.forward.match_1",
"Nat",
"String.Legacy.Iterator.prev",
"String.Legacy.Iterator",
"String.Legacy.Iterator.prevn"
] | false |
Equiv.addCommGroup._proof_3 | Mathlib.Algebra.Group.TransferInstance | [
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"Equiv",
"AddGroup.toSubNegMonoid",
"SubNegMonoid.toNeg",
"Equiv.symm",
"Eq",
"DFunLike.coe",
"Neg.neg",
"EquivLike.toFunLike"
] | false |
ENNReal.toReal_natCast | Mathlib.Data.ENNReal.Basic | [
"Real.instIsOrderedRing",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Real.partialOrder",
"Real",
"ENNReal.ofReal",
"congrArg",
"Nat.cast_nonneg",
"Real.semiring",
"id",
"AddMonoidWithOne.toNatCast",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"Nat.cast",
"ENNReal.toReal_ofReal",
... | true |
intervalIntegrable_congr_ae | Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic | [
"MeasureTheory.ae",
"TopologicalSpace.PseudoMetrizableSpace",
"Eq.mpr",
"intervalIntegrable_iff",
"Real",
"MeasureTheory.Measure",
"congrArg",
"IntervalIntegrable",
"ENormedAddMonoid",
"Iff.rfl",
"Set.uIoc",
"MeasureTheory.integrableOn_congr_fun_ae",
"MeasureTheory.Measure.restrict",
"Filt... | true |
Int.Linear.eq_dvd_subst_cert.eq_1 | Init.Data.Int.Linear | [
"Bool.and'",
"HMul.hMul",
"Int.Linear.Poly.insert",
"Int.Linear.Poly.beq'",
"Int.instNegInt",
"Int",
"Int.Linear.Var",
"Int.instMul",
"Int.beq'",
"Bool",
"Int.Linear.Poly.combine_mul_k",
"Eq.refl",
"Int.Linear.abs",
"Eq",
"Neg.neg",
"Int.Linear.Poly",
"Int.Linear.eq_dvd_subst_cert",
... | true |
Array.mapFinIdx_eq_empty_iff | Init.Data.Array.MapIdx | [
"congrArg",
"Array.casesOn",
"List.mapFinIdx",
"List.mapFinIdx_eq_nil_iff._simp_1",
"List.toArray",
"Array",
"iff_self",
"Array.mapFinIdx",
"List",
"Array.mk.injEq",
"Iff",
"Nat",
"congr",
"LT.lt",
"True",
"List.mapFinIdx_toArray",
"of_eq_true",
"Eq.ndrec",
"Eq.refl",
"congrFun... | true |
CategoryTheory.SimplicialObject.comp_left_app | Mathlib.AlgebraicTopology.SimplicialObject.Basic | [
"Quiver.mk",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.SimplicialObject.const",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"CategoryTheory.CommaMorphism.left",
"CategoryTheory.CategoryStruct.comp",
"Simpl... | true |
Lean.initFn._@.Lean.PrettyPrinter.Delaborator.Options.2248579234._hygCtx._hyg.4 | Lean.PrettyPrinter.Delaborator.Options | [
"Lean.Option",
"IO",
"Lean.Name.mkStr3",
"Lean.Option.Decl.mk",
"Bool.true",
"Lean.KVMap.instValueBool",
"Lean.Option.register",
"Bool",
"Lean.Name.mkStr2"
] | false |
ContinuousOn.continuous_restrict_iff_continuous_uniformOnFun | Mathlib.Topology.UniformSpace.CompactConvergence | [
"UniformSpace",
"Eq.mpr",
"Continuous",
"Equiv.instEquivLike",
"congrArg",
"ContinuousMap.mk",
"ContinuousMap",
"Function.comp",
"Membership.mem",
"Set.Elem",
"Set.instSingletonSet",
"id",
"Equiv",
"UniformOnFun.continuous_rng_iff",
"UniformOnFun.topologicalSpace",
"ContinuousMap.conti... | true |
_private.Mathlib.Topology.DiscreteSubset.0.codiscreteWithin_iff_locallyEmptyComplementWithin._simp_1_1 | Mathlib.Topology.DiscreteSubset | [
"Filter.instMembership",
"Compl.compl",
"Filter.instCompleteLatticeFilter",
"nhdsWithin",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"Membership.mem",
"CompleteLattice.toBoundedOrder",
"Set.instSingletonSet",
"Set.instCompl",
"TopologicalSpace",
"SDiff.sdiff",
"mem_codiscreteW... | false |
CategoryTheory.Functor.PushoutObjObj.ι_iso_of_iso_left_inv | Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackObjObj | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.PushoutObjObj",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.PushoutObjObj.ι",
"CategoryTheory.Arrow.left",
"CategoryTheory.Iso",
"CategoryTheory.Arrow.hom",
"CategoryTheory.instCategoryArrow",
"CategoryTheory.Functor.Pu... | true |
Lean.Parser.Attr.grind? | Init.Grind.Attr | [
"Lean.ParserDescr.nonReservedSymbol",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.Parser.Attr.grindMod",
"Lean.ParserDescr",
"Lean.ParserDescr.unary",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.const",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | true |
_private.Mathlib.Topology.CWComplex.Classical.Basic.0.Topology.RelCWComplex.Subcomplex.mk'._simp_1 | Mathlib.Topology.CWComplex.Classical.Basic | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"Set.instUnion",
"DistribLattice.toLattice",
"Set.instDistribLattice",
"And",
"Set.instBoundedOrder",
"BoundedOrder.toOrderBot",
"propext",
"Union.union",
"Eq",
"Set.disjoint_union_left",
"Lattice.to... | false |
AntilipschitzWith | Mathlib.Topology.MetricSpace.Antilipschitz | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"ENNReal.ofNNReal",
"HMul.hMul",
"CommSemiring.toSemiring",
"NNReal",
"ENNReal.instCommSemiring",
"LE.le",
"PseudoEMetricSpace",
"instDistribOfSemiring",
"Distrib.toMul",
"WeakPseudoEMetricSpace.toEDist",
"PseudoEMetricSpace.toUniformSpace",
"EN... | true |
OreLocalization.liftExpand._proof_7 | Mathlib.GroupTheory.OreLocalization.Basic | [
"Monoid",
"Eq.mpr",
"instHSMul",
"Submonoid.mul",
"HMul.hMul",
"SetLike.coe_mem",
"Monoid.toMulOneClass",
"congrArg",
"Membership.mem",
"Submonoid.instSubmonoidClass",
"id",
"MulOne.toMul",
"Subtype",
"Prod.mk",
"MulMemClass.mul",
"Submonoid.smul",
"Prod.fst",
"Subtype.mk",
"MulO... | false |
Option.filter_none | Init.Data.Option.Lemmas | [
"Option.none",
"Option.filter",
"Bool",
"Eq",
"rfl",
"Option"
] | true |
CategoryTheory.Comma.mapRightEq | Mathlib.CategoryTheory.Comma.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Comma.mapRightEq._proof_4",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma.left",
"CategoryTheory.Comma.isoMk",
"CategoryTheory.Iso.refl",
"CategoryTheory.Iso",... | true |
CategoryTheory.MorphismProperty.fst'_self_eq_snd | Mathlib.CategoryTheory.MorphismProperty.Representable | [
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.instCompleteBooleanAlgebra",
"congrArg",
"PartialOrder.toPreorder",
"CategoryTheory.Functor.category"... | true |
ZMod.cast_eq_val | Mathlib.Data.ZMod.Basic | [
"False",
"Nat.instMulZeroClass",
"ZMod.cast",
"AddGroupWithOne.toAddMonoidWithOne",
"False.casesOn",
"AddMonoidWithOne.toNatCast",
"instOfNatNat",
"Nat.cast",
"ZMod",
"Nat.casesAuxOn",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Eq.ndrec",
"instAddNat",
"Zero.toOfNat0",
"Eq.refl",
"AddGroupWi... | true |
_private.Mathlib.RingTheory.WittVector.MulCoeff.0.WittVector.term𝕄 | Mathlib.RingTheory.WittVector.MulCoeff | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
_private.Mathlib.Algebra.BigOperators.Group.Finset.Piecewise.0.Finset.sum_dite_of_true._proof_1_4 | Mathlib.Algebra.BigOperators.Group.Finset.Piecewise | [
"False",
"Lean.Grind.nestedProof",
"Finset.univ",
"congrArg",
"Finset",
"Classical.byContradiction",
"_private.Mathlib.Algebra.BigOperators.Group.Finset.Piecewise.0.Finset.sum_dite_of_true._proof_1_2",
"Subtype.casesOn",
"Membership.mem",
"Subtype",
"False.casesOn",
"Subtype.mk",
"Finset.ins... | false |
instBooleanAlgebraSubtypeIsIdempotentElem | Mathlib.Algebra.Order.Ring.Idempotent | [
"CommMonoidWithZero.toCommMonoid",
"BooleanAlgebra",
"CommRing",
"Lattice.toSemilatticeSup",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"CommMonoid.toCommSemigroup",
"MulZeroClass.toMul",
"instOrderTopSubtypeIsIdempotentElem",
"Monoid.toMulOneClass",
"AddGroupWithOne.toAddGroup",
"instBoolea... | true |
InitialSeg.«_aux_Mathlib_Order_InitialSeg___macroRules_InitialSeg_term_≺i__1» | Mathlib.Order.InitialSeg | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.instMonad"... | false |
_private.Mathlib.Algebra.Category.ModuleCat.Biproducts.0.lequivProdOfRightSplitExact'._proof_2 | Mathlib.Algebra.Category.ModuleCat.Biproducts | [
"RingHomCompTriple",
"RingHom.id",
"RingHomCompTriple.ids",
"Semiring.toNonAssocSemiring",
"Ring.toSemiring",
"Ring"
] | false |
Polynomial.natDegree_X_add_C | Mathlib.Algebra.Polynomial.Degree.Operations | [
"Nontrivial",
"Polynomial.C",
"RingHom",
"instOfNatNat",
"Polynomial.instAdd",
"Polynomial.natDegree_eq_of_degree_eq_some",
"Polynomial",
"instHAdd",
"RingHom.instFunLike",
"HAdd.hAdd",
"Polynomial.semiring",
"Nat",
"Semiring",
"Polynomial.natDegree",
"OfNat.ofNat",
"Polynomial.X",
"... | true |
_private.Batteries.Data.RBMap.WF.0.Batteries.RBNode.balRight.match_1.eq_3 | Batteries.Data.RBMap.WF | [
"Batteries.RBNode",
"Eq.mpr",
"Batteries.RBColor.casesOn",
"False",
"Batteries.RBNode.balLeft._sparseCasesOn_1.else_eq",
"Batteries.RBNode.balLeft._sparseCasesOn_1",
"Nat.ne_of_beq_eq_false",
"congrArg",
"False.elim",
"_private.Batteries.Data.RBMap.WF.0.Batteries.RBNode.balRight.match_1.splitter._... | true |
DilationEquiv.smulTorsor.congr_simp | Mathlib.Analysis.Normed.Affine.AddTorsor | [
"SeminormedAddCommGroup",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"NormedDivisionRing.toNorm",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"NormedDivisionRing.toDivisionRing",
"Eq.rec",
"DivisionRing.toDivisionSemiring",
"AddZeroClass.toAddZero",
"DistribSMul... | true |
Std.LinearPreorderPackage.ofLE | Init.Data.Order.PackageFactories | [
"Std.Packages.LinearPreorderOfLEArgs",
"Std.PreorderPackage.ofLE",
"Ord",
"Std.Packages.LinearPreorderOfLEArgs.toPreorderOfLEArgs",
"autoParam",
"Std.Packages.LinearPreorderOfLEArgs.le_total",
"Std.LinearPreorderPackage.mk",
"Std.LinearPreorderPackage.ofLE._proof_1",
"Std.PreorderPackage",
"Std.Li... | true |
tsum_eisSummand_eq_riemannZeta_mul_eisensteinSeries | Mathlib.NumberTheory.ModularForms.EisensteinSeries.QExpansion | [
"zpow_natCast",
"CharP.cast_eq_zero",
"Iff.mpr",
"one_pow",
"Norm.norm",
"Eq.mpr",
"inv_eq_zero._simp_1",
"GroupWithZero.toMonoidWithZero",
"NormedCommRing.toSeminormedCommRing",
"MulOne.toOne",
"SeminormedRing.toNorm",
"False",
"Nat.instMulZeroClass",
"Real",
"NeZero.mk",
"DivInvMonoi... | true |
_private.Mathlib.Combinatorics.Additive.Corner.Roth.0.corners_theorem_nat._simp_1_6 | Mathlib.Combinatorics.Additive.Corner.Roth | [
"Set.mem_Iio",
"Preorder.toLT",
"Membership.mem",
"LT.lt",
"propext",
"Set.Iio",
"Eq",
"Set.instMembership",
"Preorder",
"Set"
] | false |
Module.End.toContinuousLinearMap._proof_7 | Mathlib.Topology.Algebra.Module.FiniteDimension | [
"instSMulOfMul",
"NormedSpace",
"Monoid.toMulOneClass",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"NormedSpace.toModule",
"NormedField.toField",
"MulOne.toMul",
"Field.toSemifield",
"IsScalarTower.left",
"MulOneClass.toMulOne",
"Semifield.toDivisionSemiring",
"Semiring.toMonoid",
"M... | false |
Nat.sub_one_lt_of_le | Init.Data.Nat.Lemmas | [
"Nat.pred_lt_of_lt",
"HSub.hSub",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENat",
"instHSub",
"Nat",
"LT.lt",
"Nat.sub",
"instLTNat",
"OfNat.ofNat",
"Nat.lt_of_lt_of_le"
] | true |
ByteArray.casesOn | Init.Prelude | [
"ByteArray.mk",
"Array",
"ByteArray.rec",
"ByteArray",
"UInt8"
] | false |
_private.Mathlib.Topology.EMetricSpace.Defs.0.EMetric.tendsto_nhdsWithin_nhds._simp_1_1 | Mathlib.Topology.EMetricSpace.Defs | [
"Set.univ",
"Membership.mem",
"True",
"Set.mem_univ",
"eq_true",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Mathlib.MeasureTheory.Group.Action.0.MeasureTheory.isLocallyFiniteMeasure_of_vaddInvariant.match_1_1 | Mathlib.MeasureTheory.Group.Action | [
"AddMonoid.toAddSemigroup",
"Membership.mem",
"Exists",
"HVAdd.hVAdd",
"AddAction",
"AddAction.toAddSemigroupAction",
"AddGroup",
"Exists.casesOn",
"AddSemigroupAction.toVAdd",
"AddGroup.toSubNegMonoid",
"Exists.intro",
"instHVAdd",
"SubNegMonoid.toAddMonoid",
"Set.instMembership",
"Set"... | false |
_private.Batteries.CodeAction.Misc.0.Batteries.CodeAction.findTermInfo?._sparseCasesOn_1 | Batteries.CodeAction.Misc | [
"Lean.Elab.PartialTermInfo",
"Lean.Elab.Info.ofOptionInfo",
"Nat.ne_of_beq_eq_false",
"Lean.Elab.Info.ofTacticInfo",
"Lean.Elab.FieldRedeclInfo",
"Lean.Elab.CompletionInfo",
"Lean.Elab.OptionInfo",
"Nat.shiftRight",
"Lean.Elab.Info.rec",
"Lean.Elab.MacroExpansionInfo",
"Nat.hasNotBit",
"instOf... | false |
Finset.disjoint_preimage._simp_1 | Mathlib.Data.Finset.Preimage | [
"Finset",
"Disjoint",
"Finset.disjoint_preimage",
"Finset.partialOrder",
"SetLike.coe",
"Set.preimage",
"Finset.instSetLike",
"Finset.preimage",
"True",
"eq_true",
"Set.InjOn",
"Finset.instOrderBot",
"Eq"
] | false |
Std.Http.Response.forbidden | Std.Internal.Http.Data.Response | [
"Std.Http.Response.Builder.status",
"Std.Http.Status.forbidden",
"Std.Http.Response.Builder.new",
"Std.Http.Response.Builder"
] | true |
Lean.instOfNatLeanOptionValue | Lean.Util.LeanOptions | [
"Lean.LeanOptionValue.ofNat",
"Nat",
"OfNat.mk",
"Lean.LeanOptionValue",
"OfNat"
] | true |
Lean.Grind.Order.eq_of_le_of_le | Init.Grind.Order | [
"Std.IsPartialOrder",
"LE.le",
"LE",
"Std.IsPartialOrder.le_antisymm",
"Eq"
] | true |
UInt16.mul_def | Init.Data.UInt.Lemmas | [
"UInt16.toBitVec",
"HMul.hMul",
"UInt16.ofBitVec",
"instMulUInt16",
"BitVec",
"instOfNatNat",
"UInt16",
"Nat",
"OfNat.ofNat",
"Eq",
"BitVec.instMul",
"rfl",
"instHMul"
] | true |
Continuous.tendsto_nhdsSet_nhds | Mathlib.Topology.ContinuousOn | [
"Eq.mpr",
"Continuous",
"congrArg",
"nhds",
"Set.instSingletonSet",
"Continuous.tendsto_nhdsSet",
"id",
"Set.EqOn",
"TopologicalSpace",
"Filter.Tendsto",
"Singleton.singleton",
"Eq.symm",
"nhdsSet_singleton",
"nhdsSet",
"Eq",
"Filter",
"Set"
] | true |
RingCon.lift_bijective_iff | Mathlib.RingTheory.Congruence.Hom | [
"congrArg",
"_private.Mathlib.RingTheory.Congruence.Hom.0.RingCon.lift_bijective_iff._simp_1_1",
"RingHom",
"RingCon.instLE",
"RingCon",
"RingCon.ker",
"id",
"Distrib.toAdd",
"RingCon.Quotient",
"LE.le",
"iff_self",
"And",
"Iff",
"NonAssocSemiring",
"RingHom.instFunLike",
"Distrib.toMu... | true |
QuadraticAlgebra.C_smul | Mathlib.Algebra.QuadraticAlgebra.Defs | [
"QuadraticAlgebra.re",
"QuadraticAlgebra.instSMul",
"QuadraticAlgebra.ext",
"instHSMul",
"QuadraticAlgebra",
"SMulZeroClass",
"QuadraticAlgebra.C",
"smul_zero",
"Zero.toOfNat0",
"HSMul.hSMul",
"SMulZeroClass.toSMul",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"rfl",
"Zero"
] | true |
Lean.Lsp.DocumentColorParams._sizeOf_1 | Lean.Data.Lsp.LanguageFeatures | [
"Lean.Lsp.WorkDoneProgressParams",
"Lean.Lsp.DocumentColorParams",
"Lean.Lsp.PartialResultParams",
"instOfNatNat",
"Lean.Lsp.PartialResultParams._sizeOf_inst",
"Lean.Lsp.TextDocumentIdentifier",
"instHAdd",
"Lean.Lsp.WorkDoneProgressParams._sizeOf_inst",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"L... | false |
Valuation.Uniformizer.mk.inj | Mathlib.RingTheory.Valuation.Discrete.Basic | [
"LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero",
"Valuation.IsUniformizer",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"Valuation.Uniformizer.mk",
"Membership.mem",
"Subtype",
"Valuation.IsRankOneDiscrete",
"LinearOrderedCommGroupWithZero",
"Valuation.Uniformizer",
"Subring... | true |
bijective_of_isLocalized_span | Mathlib.RingTheory.LocalProperties.Exactness | [
"Semiring.toModule",
"CommSemiring.toSemiring",
"LinearMap.instFunLike",
"Membership.mem",
"Set.Elem",
"Submodule.instTop",
"Ideal",
"LinearMap.module",
"LinearMap",
"smulCommClass_self",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"surjective_of_isLocaliz... | true |
AlgebraicGeometry.basicOpen_eq_of_affine | Mathlib.AlgebraicGeometry.Scheme | [
"Set.ext",
"Eq.mpr",
"AlgEquiv.instEquivLike",
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.SheafedSpace.instTopologicalSpaceCarrierCarrier",
"Lattice.toSemilatticeSup",
"Semiring.toModule",
"trivial",
"Opposite",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"PrimeSpectr... | true |
SchwartzMap.decay' | Mathlib.Analysis.Distribution.SchwartzSpace.Basic | [
"Norm.norm",
"Real.instLE",
"Real",
"HMul.hMul",
"NormedSpace",
"Real.denselyNormedField",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"ContinuousMultilinearMap.hasOpNorm'",
"PseudoMetricSpace.toUniformSpace",
"ContinuousMultilinearMap",
"NormedField.toField",
"Exists",
"LE.le"... | true |
CategoryTheory.FreeBicategory.Rel.whisker_right_id | Mathlib.CategoryTheory.Bicategory.Free | [
"CategoryTheory.FreeBicategory.Hom.comp",
"CategoryTheory.FreeBicategory.Hom₂.vcomp",
"CategoryTheory.FreeBicategory.Rel.whisker_right_id",
"CategoryTheory.FreeBicategory.Hom₂.right_unitor_inv",
"CategoryTheory.FreeBicategory.Hom.id",
"CategoryTheory.FreeBicategory.Rel",
"CategoryTheory.FreeBicategory.H... | true |
MonTypeEquivalenceMon.monMonoid._proof_1 | Mathlib.CategoryTheory.Monoidal.Internal.Types.Basic | [
"Eq.mpr",
"Mul.mk",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.MonObj.mul_assoc",
"HMul.hMul",
"CategoryTheory.typesCartesianMonoidalCategory",
"CategoryTheory.ConcreteCategory.hom",
"HEq.refl",
"TypeCat.instFunLikeFun",
"Eq.casesOn",
"Prod.mk",
"CategoryTheory.SemiCa... | false |
Lean.instBEqOpaqueVal.beq | Lean.Declaration | [
"Lean.instBEqConstantVal",
"Lean.ConstantVal",
"Lean.Expr.instBEq",
"Lean.Expr",
"Bool.and",
"instDecidableEqBool",
"instBEqOfDecidableEq",
"List",
"BEq.beq",
"Lean.OpaqueVal",
"_private.Lean.Declaration.0.Lean.instBEqOpaqueVal.beq.match_1",
"Bool",
"Lean.Name",
"List.instBEq",
"Bool.fal... | true |
FreeAddSemigroup.lift.eq_1 | Mathlib.Algebra.Free | [
"AddHom",
"FreeAddSemigroup.of",
"Function.comp",
"Equiv.mk",
"Equiv",
"List.foldl",
"AddHom.funLike",
"AddSemigroup",
"instHAdd",
"AddSemigroup.toAdd",
"FreeAddSemigroup.lift._proof_2",
"HAdd.hAdd",
"FreeAddSemigroup.lift",
"FreeAddSemigroup.lift._proof_3",
"Eq.refl",
"FreeAddSemigrou... | true |
Lean.Meta.Simp.Stats.rec | Lean.Meta.Tactic.Simp.Types | [
"Lean.Meta.Simp.Stats.mk",
"Lean.Meta.Simp.Diagnostics",
"Lean.Meta.Simp.UsedSimps",
"Lean.Meta.Simp.Stats"
] | false |
Std.ExtDHashMap.get?_map | Std.Data.ExtDHashMap.Lemmas | [
"instLawfulHashableOfLawfulBEq",
"LawfulBEq",
"Std.ExtDHashMap.inductionOn",
"Option.map",
"Std.ExtDHashMap",
"Std.ExtDHashMap.map",
"Hashable",
"Std.DHashMap.get?_map",
"instEquivBEqOfLawfulBEq",
"BEq",
"Eq",
"Std.DHashMap",
"Option",
"Std.ExtDHashMap.get?"
] | true |
CategoryTheory.Functor.RightExtension.IsPointwiseRightKanExtension.hom_ext | Mathlib.CategoryTheory.Functor.KanExtension.Pointwise | [
"CategoryTheory.Limits.Cone.π",
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.comp",
"CategoryTheo... | true |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.