name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
Lean.Server.GoToKind.toCtorIdx | Lean.Server.GoTo | [
"Lean.Server.GoToKind.ctorIdx",
"Nat",
"Lean.Server.GoToKind"
] | false |
CategoryTheory.GrothendieckTopology.Point.Hom.presheafFiber_comp | Mathlib.CategoryTheory.Sites.Point.Category | [
"CategoryTheory.GrothendieckTopology.Point.toPresheafFiber_presheafFiberDesc",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.GrothendieckTopology.Point.toPresheafFiber",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Concre... | true |
Lean.Meta.Grind.Arith.Cutsat.LeCnstr.casesOn | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Grind.CommRing.Poly",
"Lean.Meta.Grind.Arith.Cutsat.CooperSplit",
"Lean.Meta.Grind.Arith.Cutsat.DiseqCnstr",
"Lean.Expr",
"Lean.FVarId",
"Int",
"Int.Linear.Var",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstr",
"Array",
"List",
"Int.Linear.Expr",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof",
"... | false |
OrderDual.instGroup | Mathlib.Algebra.Order.Group.Synonym | [
"Group",
"Group.inv_mul_cancel",
"Group.toDivInvMonoid",
"OrderDual",
"OrderDual.instDivInvMonoid",
"Group.mk"
] | true |
AList.mem_lookup_union_middle | Mathlib.Data.List.AList | [
"Option.instMembership",
"Membership.mem",
"List.mem_dlookup_kunion_middle",
"AList.lookup",
"AList",
"AList.instUnion",
"Union.union",
"AList.instMembership",
"Not",
"Option",
"DecidableEq",
"AList.entries"
] | true |
CategoryTheory.Limits.ChosenPullback.hp₁._autoParam | Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
PFun.fixInduction'._proof_1 | Mathlib.Data.PFun | [
"Part",
"PFun",
"Membership.mem",
"Exists",
"Sum",
"Part.instMembership",
"Part.get",
"Sum.inl",
"PFun.fix",
"Exists.intro",
"Part.Dom",
"Eq",
"PFun.dom_of_mem_fix"
] | false |
Int.gcd_mul_right | Init.Data.Int.Gcd | [
"Nat.gcd",
"Int.gcd",
"Nat.gcd_mul_right",
"HMul.hMul",
"Int.natAbs_mul",
"congrArg",
"instMulNat",
"Int",
"Int.instMul",
"Nat",
"congr",
"True",
"Int.natAbs",
"eq_self",
"of_eq_true",
"congrFun'",
"Eq",
"Eq.trans",
"instHMul"
] | true |
_private.Lean.Environment.0.Lean.importModules.match_4 | Lean.Environment | [
"Prod.mk",
"Unit",
"Prod",
"Prod.casesOn",
"Lean.ImportState"
] | false |
CoxeterSystem.isReflection_simple | Mathlib.GroupTheory.Coxeter.Inversion | [
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"inv_one",
"Monoid.toMulOneClass",
"congrArg",
"Group",
"Group.toDivisionMonoid",
"DivisionMonoid.toDivInvOneMonoid",
"Exists",
"MulOne.toMul",
"CoxeterSystem.simple",
"DivInvMonoid.toMonoid",
"CoxeterSystem.IsReflection",
... | true |
IsRealClosed.exists_eq_pow_of_nonneg | Mathlib.FieldTheory.IsRealClosed.Basic | [
"LinearOrder",
"PartialOrder.toPreorder",
"IsRealClosed",
"IsStrictOrderedRing",
"Preorder.toLE",
"Exists",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"Ne",
"instOfNatNat",
"LE.le",
"Field.toSemifield",
"IsRealClosed.exists_eq_pow_of_isSquare",
"Monoid.toPow",
"Semifiel... | true |
CategoryTheory.BasedNatIso.id_hom | Mathlib.CategoryTheory.FiberedCategory.BasedCategory | [
"CategoryTheory.BasedFunctor",
"CategoryTheory.BasedNatIso.id",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CategoryStruct.id",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.BasedCategory",
"CategoryTheory.BasedNatTrans.homCategory",
"CategoryTh... | true |
Primrec.of_eq | Mathlib.Computability.Primrec.Basic | [
"Eq.rec",
"Primrec",
"funext",
"Primcodable",
"Eq"
] | true |
FirstOrder.Language.Symbols | Mathlib.ModelTheory.Basic | [
"Sum",
"Nat",
"FirstOrder.Language.Relations",
"FirstOrder.Language.Functions",
"FirstOrder.Language",
"Sigma"
] | true |
ProbabilityTheory.Kernel.comap_map_comm | Mathlib.Probability.Kernel.Composition.MapComap | [
"Eq.mpr",
"ProbabilityTheory.Kernel.map_apply",
"ProbabilityTheory.Kernel.comap",
"MeasureTheory.Measure",
"MeasurableSet",
"congrArg",
"ProbabilityTheory.Kernel.map",
"Measurable",
"ProbabilityTheory.Kernel.instFunLike",
"id",
"MeasurableSpace",
"MeasureTheory.Measure.map",
"ENNReal",
"Eq... | true |
CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.iso_hom_naturality_assoc | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Categorical.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Limits.CategoricalPullback.CatCommSqOver.fst",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.e... | true |
Convex.combo_interior_closure_subset_interior | Mathlib.Analysis.Convex.Topology | [
"interior_smul₀",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"instHSMul",
"Trans.trans",
"Preorder.toLT",
"instSeparatelyContinuousAddOfContinuousAdd",
"Convex.set_combo_subset",
"IsOpen.add_closure",
"interior_mono",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMono... | true |
Group.ofRightAxioms._proof_4 | Mathlib.Algebra.Group.MinimalAxioms | [
"Eq.mpr",
"One",
"Inv",
"HMul.hMul",
"congrArg",
"Mul",
"id",
"Inv.inv",
"One.toOfNat1",
"Eq.refl",
"OfNat.ofNat",
"Eq.symm",
"Eq",
"instHMul"
] | false |
_private.Mathlib.Algebra.Group.Semiconj.Basic.0.SemiconjBy.inv_inv_symm_iff._simp_1_2 | Mathlib.Algebra.Group.Semiconj.Basic | [
"InvolutiveInv.toInv",
"InvolutiveInv",
"inv_inj",
"Inv.inv",
"propext",
"Eq"
] | false |
Lean.AssocList.brecOn.go | Lean.Data.AssocList | [
"Lean.AssocList.rec",
"Lean.AssocList.nil",
"Lean.AssocList.cons",
"PProd.mk",
"Lean.AssocList.below",
"PProd",
"PUnit",
"Lean.AssocList",
"PUnit.unit"
] | true |
CategoryTheory.FintypeCat.isoQuotientStabilizerOfIsConnected._proof_3 | Mathlib.CategoryTheory.Galois.Examples | [
"Action.instMulActionObjFiniteVFintypeCat",
"Finite",
"FintypeCat",
"Group",
"QuotientGroup.instHasQuotientSubgroup",
"DivInvMonoid.toMonoid",
"Subgroup",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"Finite.of_fintype",
"Group.toDivInvMonoid",
"HasQuotient.Quotient",
"Fintype",
"Act... | false |
RingPreordering.instHasIdealSupport | Mathlib.Algebra.Order.Ring.Ordering.Basic | [
"AddGroup.toSubtractionMonoid",
"AddSubgroup.instBot",
"IsDomain.to_noZeroDivisors",
"HMul.hMul",
"AddGroupWithOne.toAddGroup",
"congrArg",
"CommSemiring.toSemiring",
"RingPreordering.HasIdealSupport",
"Membership.mem",
"SubtractionMonoid.toSubNegZeroMonoid",
"Bot.bot",
"RingPreordering",
"S... | true |
Lean.CollectLevelMVars.State.visitedLevel | Lean.Util.CollectLevelMVars | [
"Lean.LevelSet",
"Lean.CollectLevelMVars.State"
] | true |
StarSubalgebra.range_le | Mathlib.Algebra.Star.Subalgebra | [
"Algebra.algebraMap",
"CommSemiring.toSemiring",
"Algebra",
"RingHom",
"Algebra.toSMul",
"StarSubalgebra",
"StarSubalgebra.setLike",
"LE.le",
"StarAddMonoid.toInvolutiveStar",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"StarRing.toStarAddMonoid",
"RingHom.instFunLike",
"S... | true |
CategoryTheory.ShortComplex.SnakeInput.h₃τ₁._proof_1 | Mathlib.Algebra.Homology.ShortComplex.SnakeLemma | [
"CategoryTheory.Abelian.toPreadditive",
"CategoryTheory.Limits.PreservesColimitsOfShape.preservesColimit",
"CategoryTheory.ShortComplex.instAbelian",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.ShortComplex.instPreservesColimitπ₁",
"CategoryTheory.ShortComplex.SnakeInput.L₂",
... | false |
BitVec.add_right_eq_self | Init.Data.BitVec.Lemmas | [
"Eq.mpr",
"congrArg",
"BitVec.instAdd",
"BitVec",
"id",
"instOfNatNat",
"BitVec.ofNat",
"instHAdd",
"Iff",
"HAdd.hAdd",
"BitVec.add_comm",
"Nat",
"BitVec.add_left_eq_self",
"OfNat.ofNat",
"Eq"
] | true |
Lean.Compiler.LCNF.ImpureType.object | Lean.Compiler.LCNF.Types | [
"Lean.Expr.const",
"Lean.Expr",
"Lean.Level",
"Lean.Name.mkStr1",
"List.nil"
] | true |
_private.Mathlib.Order.TypeTags.0.WithTop.instRepr.match_1.splitter | Mathlib.Order.TypeTags | [
"WithTop.instRepr.match_1",
"Option.some",
"Option.none",
"Unit",
"WithTop"
] | true |
_private.Std.Data.DHashMap.Internal.Defs.0.Std.DHashMap.Internal.Raw₀.Const.insertMany.match_1 | Std.Data.DHashMap.Internal.Defs | [
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
_private.Lean.Meta.AbstractMVars.0.Lean.Meta.AbstractMVars.abstractLevelMVars.match_1 | Lean.Meta.AbstractMVars | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Lean.Level",
"Option.none",
"Unit",
"Option"
] | false |
Submonoid.map_comap_eq | Mathlib.Algebra.Group.Submonoid.Operations | [
"Submonoid.toSubsemigroup",
"SetLike.coe_injective",
"Set.image_preimage_eq_inter_range",
"Submonoid.map",
"MulOneClass.toMulOne",
"Submonoid.comap",
"Submonoid.instMin",
"MonoidHom.mrange",
"MonoidHomClass",
"Submonoid.instSetLike",
"MulOneClass",
"Eq",
"DFunLike.coe",
"Min.min",
"Submo... | true |
AlgEquiv.piMulOpposite | Mathlib.Algebra.Algebra.Pi | [
"RingEquiv.piMulOpposite",
"RingEquiv.toEquiv",
"MulOpposite.instAlgebra",
"MulOpposite",
"Algebra",
"Distrib.toAdd",
"AlgEquiv.piMulOpposite._proof_3",
"AlgEquiv.mk",
"CommSemiring",
"Pi.semiring",
"Pi.algebra",
"Pi.instAdd",
"MulOpposite.instAdd",
"Distrib.toMul",
"AlgEquiv",
"AlgEqu... | true |
Lean.PrettyPrinter.Delaborator.TopDownAnalyze.State.annotations | Lean.PrettyPrinter.Delaborator.TopDownAnalyze | [
"Lean.PrettyPrinter.Delaborator.TopDownAnalyze.State",
"Lean.PrettyPrinter.Delaborator.OptionsPerPos"
] | true |
groupCohomology.mapShortComplexH2_id_comp_assoc | Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality | [
"CategoryTheory.Category.assoc",
"CommRing",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"groupCohomology.shortComplexH2",
"CategoryTheory.ShortComplex",
"Group",
"Rep.instCategory",
"CategoryTheory.Short... | true |
_private.Mathlib.Analysis.ODE.DiscreteGronwall.0.discrete_gronwall._proof_1_6 | Mathlib.Analysis.ODE.DiscreteGronwall | [
"False",
"Lean.Grind.and_eq_of_eq_true_right",
"Real.instLE",
"Real",
"Preorder.toLT",
"eq_false",
"Lean.Grind.iff_eq",
"Real.instZero",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"Classical.byContradiction",
"Lean.Grind.eq_false_of_imp_eq_true",
"Lean.Grind.Nat.lt_eq",
"Preorder.... | false |
Finsupp.lcomapDomain._proof_1 | Mathlib.LinearAlgebra.Finsupp.Defs | [
"Finsupp.instFunLike",
"Finsupp.ext",
"Function.Injective.injOn",
"Finset",
"AddMonoid.toAddZeroClass",
"Finsupp.support",
"AddZeroClass.toAddZero",
"AddCommMonoid",
"Finsupp.instAddCommMonoid",
"AddZero.toZero",
"instHAdd",
"SetLike.coe",
"Set.preimage",
"Finset.instSetLike",
"HAdd.hAdd... | false |
_private.Mathlib.Algebra.Exact.0.LinearEquiv.conj_exact_iff_exact._simp_1_1 | Mathlib.Algebra.Exact | [
"Function.Exact",
"Submodule",
"RingHomSurjective.ids",
"AddMonoid.toAddZeroClass",
"LinearMap.ker",
"LinearMap.instFunLike",
"AddZeroClass.toAddZero",
"LinearMap.range",
"LinearMap",
"AddCommMonoid",
"AddZero.toZero",
"propext",
"Semiring",
"AddCommMonoid.toAddMonoid",
"Module",
"Line... | false |
Polynomial.lt_rootMultiplicity_of_isRoot_iterate_derivative_of_mem_nonZeroDivisors' | Mathlib.Algebra.Polynomial.FieldDivision | [
"Polynomial.derivative",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"Nat.recAux",
"Semiring.toModule",
"le_rfl",
"HMul.hMul",
"MulZeroClass.toMul",
"congrArg",
"CommSemiring.toSemiring",
"Nat.factorial_succ",
"Polynomial.IsRoot",
"AddGroupWithOne.toAddMonoidWithOne",
... | true |
Std.LawfulOrderLeftLeaningMin.of_eq | Init.Data.Order.Lemmas | [
"Std.LawfulOrderLeftLeaningMin.mk",
"eq_false",
"congrArg",
"Std.LawfulOrderLeftLeaningMin",
"LE.le",
"ite_cond_eq_true",
"LE",
"Min",
"DecidableLE",
"True",
"eq_self",
"eq_true",
"of_eq_true",
"Eq.refl",
"congrFun'",
"implies_true",
"ite_cond_eq_false",
"Eq",
"implies_congr_ctx"... | true |
ByteSlice.contains | Std.Data.ByteSlice | [
"ByteSlice",
"instOfNatNat",
"_private.Std.Data.ByteSlice.0.ByteSlice.contains.loop",
"Nat",
"Bool",
"OfNat.ofNat",
"UInt8"
] | true |
Stream'.Seq1.ret.eq_1 | Mathlib.Data.Seq.Basic | [
"Stream'.Seq",
"Stream'.Seq1.ret",
"Prod.mk",
"Stream'.Seq.nil",
"Stream'.Seq1",
"Eq.refl",
"Eq"
] | true |
SSet.Edge.edge | Mathlib.AlgebraicTopology.SimplicialSet.CompStruct | [
"Opposite",
"SSet.Truncated.Edge.edge",
"CategoryTheory.Functor.category",
"SSet.Truncated",
"SSet.truncation",
"instOfNatNat",
"SSet",
"LE.le",
"instLENat",
"SimplexCategory.mk",
"Opposite.op",
"Nat",
"CategoryTheory.types",
"SimplexCategory",
"CategoryTheory.Category.opposite",
"SSet... | true |
CategoryTheory.Adjunction.fullyFaithfulROfCompIsoId | Mathlib.CategoryTheory.Monad.Adjunction | [
"CategoryTheory.Functor",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Adjunction.isIso_counit_of_iso",
"CategoryTheory.Functor.id",
"CategoryTheory.Adjunction.fullyFaithfulROfIsIsoCounit",
"CategoryTheory.Iso",
"CategoryTheory.Adjunction",
"CategoryTheory.Functo... | true |
Lean.Meta.RefinedDiscrTree.Trie.pending | Mathlib.Lean.Meta.RefinedDiscrTree.Basic | [
"Array",
"Lean.Meta.RefinedDiscrTree.LazyEntry",
"Prod",
"Lean.Meta.RefinedDiscrTree.Trie"
] | true |
AlgebraicGeometry.QuasiCompact.of_comp | Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated | [
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AlgebraicGeometry.instHasOfPostcompPropertySchemeQuasiCompactQuasiSeparated",
"AlgebraicGeometry.QuasiCompact",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"AlgebraicGeometry.Sche... | true |
CategoryTheory.Monad.beckAlgebraCoequalizer._proof_2 | Mathlib.CategoryTheory.Monad.Coequalizer | [
"CategoryTheory.Monad",
"CategoryTheory.Monad.Algebra.Hom.h",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Monad.Algebra.a",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.Monad.FreeCoequalizer.topMap",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
... | false |
CategoryTheory.Iso.isoCongr | Mathlib.CategoryTheory.HomCongr | [
"Equiv.mk",
"Equiv",
"CategoryTheory.Iso",
"CategoryTheory.Iso.isoCongr._proof_4",
"CategoryTheory.Iso.isoCongr._proof_2",
"CategoryTheory.Iso.trans",
"CategoryTheory.Iso.symm",
"CategoryTheory.Category"
] | true |
_private.Mathlib.Analysis.SpecificLimits.FloorPow.0.sum_div_nat_floor_pow_sq_le_div_sq._simp_1_9 | Mathlib.Analysis.SpecificLimits.FloorPow | [
"GroupWithZero.toMonoidWithZero",
"False",
"GroupWithZero.toDivInvMonoid",
"eq_false",
"GroupWithZero",
"DivInvMonoid.toZPow",
"Ne",
"Int",
"MonoidWithZero.toMulZeroOneClass",
"HPow.hPow",
"Zero.toOfNat0",
"zpow_ne_zero",
"instHPow",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"Eq... | false |
_private.Mathlib.RingTheory.Valuation.ValuativeRel.Trivial.0.ValuativeRel.eq_trivialRel_of_compatible_one._simp_1_1 | Mathlib.RingTheory.Valuation.ValuativeRel.Trivial | [
"Nontrivial",
"MulOne.toOne",
"Valuation.one",
"PartialOrder.toPreorder",
"LinearOrderedCommMonoidWithZero.toLinearOrder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"DistribLattice.toLattice",
"CommMonoidWithZero.toMonoidWithZero",
"LE.le",
"LinearOrderedCommMonoidWithZero.toCommMonoidWi... | false |
Lean.JsonNumber.mk.sizeOf_spec | Lean.Data.Json.Basic | [
"Lean.JsonNumber",
"Lean.JsonNumber._sizeOf_inst",
"Lean.JsonNumber.mk",
"instOfNatNat",
"Int",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Int._sizeOf_inst",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"instSizeOfNat",
"OfNat.ofNat",
"Eq"
] | true |
_private.Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory.0.CategoryTheory.Monoidal.ComonFunctorCategoryEquivalence.inverse._proof_7 | Mathlib.CategoryTheory.Monoidal.Internal.FunctorCategory | [
"CategoryTheory.ComonObj.comul",
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"Quiver.Hom",
"congrArg",
"CategoryTheory.IsComonHom",
"CategoryTheory.IsComonHom.hom_comul",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Functor.... | false |
_private.Mathlib.Algebra.Module.ZLattice.Basic.0.ZSpan.fundamentalDomain_measurableSet._simp_1_5 | Mathlib.Algebra.Module.ZLattice.Basic | [
"Set.univ",
"Membership.mem",
"True",
"Set.mem_univ",
"eq_true",
"Eq",
"Set.instMembership",
"Set"
] | false |
CategoryTheory.ObjectProperty.Nonempty.recOn | Mathlib.CategoryTheory.ObjectProperty.Basic | [
"Exists",
"CategoryTheory.ObjectProperty.Nonempty",
"CategoryTheory.ObjectProperty.Nonempty.mk",
"CategoryTheory.ObjectProperty.Nonempty.rec",
"CategoryTheory.CategoryStruct",
"CategoryTheory.ObjectProperty"
] | false |
MeasureTheory.Measure.conv_zero | Mathlib.MeasureTheory.Group.Convolution | [
"MeasureTheory.Measure",
"congrArg",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"id",
"MeasureTheory.Measure.conv",
"MeasureTheory.Measure.instZero",
"Prod.fst",
"MeasurableSpace",
"instHAdd",
"MeasureTheory.Measure.prod",
"HAdd.hAdd",
"MeasureTheory.Measure.map",
"True",
"eq_... | true |
spectrum.subset_circle_of_unitary | Mathlib.Analysis.CStarAlgebra.Spectrum | [
"NormedCommRing.toSeminormedCommRing",
"Real",
"CompleteSpace",
"NormedRing.toRing",
"spectrum",
"Ring.toNonAssocRing",
"Monoid.toMulOneClass",
"unitary",
"PseudoMetricSpace.toUniformSpace",
"Membership.mem",
"NormedField.toField",
"NormedRing.toNonUnitalNormedRing",
"NonUnitalNonAssocRing.t... | true |
IsGaloisGroup.of_mulEquiv | Mathlib.FieldTheory.Galois.IsGaloisGroup | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"MulEquiv.instEquivLike",
"FaithfulSMul.eq_of_smul_eq_smul",
"Monoid.toMulOneClass",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Algebra.IsInvariant.mk",
"Group",
"Algebra",
"Algebra.toSMul",
"... | true |
Lean.Server.RequestContext.rec | Lean.Server.Requests | [
"Lean.Server.RequestContext",
"Lean.Lsp.InitializeParams",
"UInt64",
"UInt64.instOrd",
"Lean.Server.FileWorker.RpcSession",
"Lean.Server.FileWorker.EditableDocument",
"Ord.compare",
"Lean.Server.RequestContext.mk",
"Lean.Server.RequestCancellationToken",
"IO.Ref",
"IO.FS.Stream",
"Std.TreeMap"... | false |
Classical.exists_or_forall_not | Init.Classical | [
"Eq.mpr",
"congrArg",
"Exists",
"not_exists",
"id",
"Classical.em",
"propext",
"Or",
"Eq.symm",
"Eq",
"Not"
] | true |
Polynomial.UniversalFactorizationRing.factor₁_mul_factor₂ | Mathlib.RingTheory.Polynomial.UniversalFactorizationRing | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.instMulZeroClass",
"AddMonoidAlgebra.semiring",
"CommRing",
"Semiring.toModule",
"Equiv.instEquivLike",
"HMul.hMul",
"Polynomial.MonicDegreeEq",
"AddMonoidAlgebra.addAddCommMonoid",
"Polynomial.UniversalFactorizationRing.factor₂",
"CommSemiring.toS... | true |
LinearMap.BilinForm.toMatrixAux_apply | Mathlib.LinearAlgebra.Matrix.BilinearForm | [
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Matrix.module",
"LinearMap.BilinForm.toMatrixAux",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"Matrix",
"LinearMap.instSMulCommClass",
"LinearMap.instFunLike",
"Algebra.id",
"Matrix.addCommMonoid",
"Li... | true |
affineSpan_eq_top_of_nonempty_interior | Mathlib.Analysis.Normed.Affine.AddTorsorBases | [
"Real.partialOrder",
"Real",
"Lattice.toSemilatticeSup",
"LE.le.trans_eq",
"ChainCompletePartialOrder.instOfCompleteLattice",
"interior_subset",
"NormedSpace",
"CompleteLattice.toLattice",
"NormedAddCommGroup.toMetricSpace",
"AddCommGroup.toAddCommMonoid",
"isOpen_interior",
"NormedSpace.toMod... | true |
_private.Std.Data.HashMap.Lemmas.0.Std.HashMap.mem_toArray_iff_getKey?_eq_some_and_getElem?_eq_some._simp_1_1 | Std.Data.HashMap.Lemmas | [
"Std.HashMap.toList",
"Std.HashMap",
"List.toArray",
"Array",
"Std.HashMap.toArray_toList",
"Hashable",
"Std.HashMap.toArray",
"Prod",
"Eq.symm",
"BEq",
"Eq"
] | false |
SimpleGraph.deleteEdges_of_subset_diagSet | Mathlib.Combinatorics.SimpleGraph.DeleteEdges | [
"SimpleGraph.deleteEdges",
"Eq.mpr",
"SimpleGraph.Adj.ne",
"Sym2.mk",
"congrArg",
"SimpleGraph.Adj",
"SimpleGraph.deleteEdges_adj._simp_1",
"Membership.mem",
"id",
"HasSubset.Subset",
"SimpleGraph",
"funext",
"And",
"Iff",
"propext",
"SimpleGraph.ext",
"Sym2.diagSet",
"congrFun'",
... | true |
hasDerivAt_tsum | Mathlib.Analysis.Calculus.SmoothSeries | [
"Norm.norm",
"NormedCommRing.toSeminormedCommRing",
"Real.instLE",
"Real",
"CompleteSpace",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"ConnectedSpace.toPreconnectedSpace",
"PathConnectedSpace.connectedSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Set.univ",
"... | true |
ProbabilityTheory.stdGaussian_map | Mathlib.Probability.Distributions.Gaussian.Multivariate | [
"ContinuousLinearMap.comp",
"LinearIsometryEquiv.instEquivLike",
"Norm.norm",
"Eq.mpr",
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"complete_of_proper",
"LinearIsometryEquiv.toLinearIsometry",
"LinearEquiv.finiteDimensional",
"Real",
"MeasureTheory.Measure",
"ins... | true |
Lean.Grind.CommRing.Poly.mul_nc.go.eq_def | Init.Grind.Ring.CommSolver | [
"Eq.mpr",
"Lean.Grind.CommRing.Poly.rec",
"Lean.Grind.CommRing.Poly",
"Lean.Grind.CommRing.Poly.add",
"congrArg",
"Lean.Grind.CommRing.Poly.mul_nc.go",
"Lean.Grind.CommRing.Poly.mul_nc.go._f",
"id",
"Lean.Grind.CommRing.Poly.below",
"Lean.Grind.CommRing.Poly.denote.match_1",
"Int",
"Lean.Grind... | true |
Finset.instGeneralizedBooleanAlgebra._proof_7 | Mathlib.Data.Finset.SDiff | [
"Lattice.toSemilatticeSup",
"Finset",
"OrderBot.toBot",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Finset.instSDiff",
"DistribLattice.toLattice",
"Bot.bot",
"Finset.partialOrder",
"SemilatticeInf.toMin",
"SemilatticeInf.mk",
"SDiff.sdiff",
"Lattice.inf_le_left",
"Lattice.le_inf",
"Latt... | false |
CategoryTheory.Limits.createsLimitsOfShapeOfCreatesEqualizersAndProducts._proof_2 | Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.HasLimitsOfShape",
"CategoryTheory.CreatesLimitsOfShape",
"CategoryTheory.SmallCategory",
"Prod.fst",
"CategoryTheory.discreteCategory",
"CategoryTheory.hasLimitsOfShape_of_hasLimitsOfShape_creat... | false |
Submonoid.LocalizationMap.mulEquivOfLocalizations_left_inv_apply | Mathlib.GroupTheory.MonoidLocalization.Maps | [
"MulEquiv.instEquivLike",
"Monoid.toMulOneClass",
"congrArg",
"MulOne.toMul",
"Submonoid.LocalizationMap.mulEquivOfLocalizations",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"True",
"Submonoid.LocalizationMap",
"eq_self",
"Submonoid.LocalizationMap.mulEquivOfLocalizations_left_inv",
"of_eq... | true |
Module.FaithfullyFlat.tensorProduct_mk_injective | Mathlib.RingTheory.Flat.FaithfullyFlat.Algebra | [
"Eq.mpr",
"Module.FaithfullyFlat.lTensor_injective_iff_injective",
"LinearEquiv.symm",
"CommRing",
"Algebra.to_smulCommClass",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemiring",
"Ad... | true |
CategoryTheory.Limits.WalkingPair.right.sizeOf_spec | Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | [
"CategoryTheory.Limits.WalkingPair.right",
"instOfNatNat",
"CategoryTheory.Limits.WalkingPair",
"Nat",
"SizeOf.sizeOf",
"Eq.refl",
"CategoryTheory.Limits.WalkingPair._sizeOf_inst",
"OfNat.ofNat",
"Eq"
] | true |
CategoryTheory.Functor.map_inv_hom' | Mathlib.CategoryTheory.Iso | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso",
"CategoryTheory.Functor.map",
"CategoryTheory.Iso.map_inv_hom_id",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"of_eq_true",
"C... | true |
Lean.Grind.CommRing.Expr.denoteS._f | Init.Grind.Ring.CommSemiringAdapter | [
"Lean.Grind.CommRing.Expr.below",
"Lean.Grind.CommRing.Expr",
"HMul.hMul",
"Lean.Grind.CommRing.Expr.mul",
"Lean.Grind.CommRing.Expr.var",
"Lean.Grind.CommRing.Expr.sub",
"Lean.Grind.CommRing.Expr.natCast",
"Lean.Grind.Semiring.toAdd",
"Lean.Grind.CommRing.Expr.neg",
"Lean.Grind.AddCommMonoid.toZe... | false |
TopologicalSpace.isTopologicalBasis_empty._simp_1 | Mathlib.Topology.Bases | [
"IsEmpty",
"TopologicalSpace.isTopologicalBasis_empty",
"TopologicalSpace",
"propext",
"TopologicalSpace.IsTopologicalBasis",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Set"
] | false |
_private.Mathlib.MeasureTheory.PiSystem.0.isPiSystem_piiUnionInter._simp_1_5 | Mathlib.MeasureTheory.PiSystem | [
"Set.mem_inter_iff",
"Membership.mem",
"Set.instInter",
"Inter.inter",
"And",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
IsometryEquiv.mulLeft._proof_1 | Mathlib.Topology.MetricSpace.IsometricSMul | [
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"instSMulOfMul",
"HMul.hMul",
"Monoid.toMulOneClass",
"IsIsometricSMul",
"Group",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"PseudoEMetricSpace",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"WeakPseudoEMetricSpace.toEDist",
"PseudoEMetricSpac... | false |
FirstOrder.Language.DirectLimit.unify_sigma_mk_self | Mathlib.ModelTheory.DirectLimit | [
"FirstOrder.Language.Structure.Sigma.mk",
"Eq.mpr",
"trans",
"instReflLe",
"congrArg",
"FirstOrder.Language.DirectedSystem.map_self",
"Preorder.toLE",
"Function.comp",
"Membership.mem",
"id",
"FirstOrder.Language.DirectLimit.unify.eq_1",
"Sigma.fst",
"LE.le",
"FirstOrder.Language.Embedding... | true |
OnePoint.isClosed_image_coe._simp_1 | Mathlib.Topology.Compactification.OnePoint.Basic | [
"OnePoint.isClosed_image_coe",
"OnePoint.some",
"IsClosed",
"TopologicalSpace",
"And",
"propext",
"Set.image",
"Eq",
"OnePoint.instTopologicalSpace",
"IsCompact",
"OnePoint",
"Set"
] | false |
Nat.lt_add_one_of_lt | Init.Data.Nat.Basic | [
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"LT.lt",
"instAddNat",
"Nat.le_succ_of_le",
"instLTNat",
"OfNat.ofNat",
"Nat.succ"
] | true |
Finset.inv_subset_div_right | Mathlib.Algebra.Group.Pointwise.Finset.Basic | [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"InvOneClass.toOne",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Finset.divisionMonoid",
"Monoid.toMulOneClass",
"congrArg",
"Finset",
"Finset.subset_mul_right",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"DivisionMonoid",
"id",
... | true |
ContinuousLinearMap.ofIsTopCompl_zero | Mathlib.Topology.Algebra.Module.Complement | [
"Submodule",
"ContinuousLinearMap.ofIsTopCompl",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"Submodule.addCommMonoid",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddCommGroup",
"... | true |
_private.Init.Data.List.Attach.0.List.attach_filterMap._simp_1_3 | Init.Data.List.Attach | [
"False",
"eq_false",
"Exists",
"exists_false",
"Eq"
] | false |
Nat._aux_Mathlib_Data_Nat_Factorial_Basic___macroRules_Nat_term_!_1 | Mathlib.Data.Nat.Factorial.Basic | [
"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 |
AffineIsometry | Mathlib.Analysis.Normed.Affine.Isometry | [
"SeminormedAddCommGroup",
"NormedSpace",
"AffineIsometry.mk",
"NormedField",
"PseudoMetricSpace",
"NormedAddTorsor"
] | true |
Lean.Compiler.LCNF.UnreachableBranches.Value.merge._unsafe_rec | Lean.Compiler.LCNF.ElimDeadBranches | [
"Lean.Compiler.LCNF.UnreachableBranches.Value.merge._unsafe_rec",
"Lean.Compiler.LCNF.UnreachableBranches.Value.top",
"_private.Lean.Compiler.LCNF.ElimDeadBranches.0.Lean.Compiler.LCNF.UnreachableBranches.Value.merge.match_4",
"Bool.and",
"Lean.Compiler.LCNF.UnreachableBranches.Value.addChoice._unsafe_rec",... | false |
_private.Lean.Elab.Match.0.Lean.Elab.Term.ToDepElimPattern.throwInvalidPattern | Lean.Elab.Match | [
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"String",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.MessageData.instAppend",
"Lean.throwError",
"Lean.MonadQuotation.toMonadRef",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.Re... | true |
Fin.foldl_zero | Init.Data.Fin.Fold | [
"_private.Init.Data.Fin.Fold.0.Fin.foldl_loop_eq",
"instOfNatNat",
"Fin.foldl",
"Nat",
"OfNat.ofNat",
"Fin",
"Eq"
] | true |
Lean.Meta.zetaDeltaLocalDecl | Lean.Meta.Tactic.Unfold | [
"Lean.instantiateMVars",
"Lean.MessageData",
"Lean.MonadError.mk",
"Lean.MVarId.withContext",
"Lean.instMonadExceptOfExceptionCoreM",
"instMonadControlTOfPure",
"Lean.Expr.instBEq",
"String",
"Lean.Meta.State",
"Lean.instAddErrorMessageContextOfAddMessageContextOfMonad",
"Lean.MessageData.instAp... | true |
_private.Mathlib.Tactic.CategoryTheory.Elementwise.0.Mathlib.Tactic.Elementwise.elementwiseExpr.mkHomElementwise.match_9 | Mathlib.Tactic.CategoryTheory.Elementwise | [
"Lean.Expr",
"Prod.mk",
"Prod",
"Prod.casesOn"
] | false |
Semiquot.partialOrder | Mathlib.Data.Semiquot | [
"LT.mk",
"Preorder.mk",
"PartialOrder",
"LE.le",
"Semiquot.partialOrder._proof_1",
"And",
"Semiquot.instLE",
"Semiquot.partialOrder._proof_3",
"Semiquot.partialOrder._proof_2",
"Semiquot",
"Semiquot.partialOrder._proof_4",
"Not",
"PartialOrder.mk"
] | true |
ISize.minValue_div_neg_one | Init.Data.SInt.Lemmas | [
"instPowNat",
"Eq.mpr",
"ISize.toBitVec_ofNat",
"ISize.minValue",
"instHDiv",
"congrArg",
"ISize.toBitVec_inj",
"HSub.hSub",
"BitVec",
"Eq.mp",
"id",
"HDiv.hDiv",
"Int.instNegInt",
"BitVec.ofInt",
"instSubNat",
"instOfNatNat",
"Int",
"Int.instNatPow",
"BitVec.ofNat",
"BitVec.in... | true |
Fin.finsetImage_natAdd_Ici | Mathlib.Order.Interval.Finset.Fin | [
"Fin.natAdd",
"Set.Ici",
"congrArg",
"Fin.image_natAdd_Ici",
"Finset",
"PartialOrder.toPreorder",
"instDecidableEqFin",
"Finset.coe_image",
"Finset.Ici",
"_private.Mathlib.Order.Interval.Finset.Fin.0.Fin.finsetImage_natAdd_Ici._simp_1_1",
"instHAdd",
"Fin.instPartialOrder",
"SetLike.coe",
... | true |
Bundle.Trivialization.symm_apply_of_notMem | Mathlib.Topology.FiberBundle.Trivialization | [
"Bundle.Trivialization.symm",
"Classical.propDecidable",
"cast",
"Membership.mem",
"PartialEquiv.symm",
"Bundle.Pretrivialization.symm._proof_1",
"Prod.mk",
"dif_neg",
"TopologicalSpace",
"Bundle.TotalSpace.proj",
"Bundle.TotalSpace",
"Bundle.Trivialization",
"Bundle.Pretrivialization.toPart... | true |
Std.HashMap.Raw.mem_insertMany_of_mem | Std.Data.HashMap.RawLemmas | [
"Std.HashMap.Raw.WF.out",
"Membership.mem",
"Std.HashMap.Raw.WF",
"Id",
"LawfulHashable",
"Std.HashMap.Raw",
"EquivBEq",
"ForIn",
"Std.HashMap.Raw.inner",
"Std.HashMap.Raw.instMembershipOfBEqOfHashable",
"Hashable",
"Std.HashMap.Raw.insertMany",
"Prod",
"BEq",
"Std.DHashMap.Raw.Const.mem... | true |
BoundedContinuousFunction.instCommMonoid | Mathlib.Topology.ContinuousMap.Bounded.Basic | [
"PseudoMetricSpace.toBornology",
"BoundedContinuousFunction.instCommMonoid._proof_1",
"BoundedMul",
"Monoid.toMulOneClass",
"PseudoMetricSpace.toUniformSpace",
"MulOne.toMul",
"TopologicalSpace",
"MulOneClass.toMulOne",
"ContinuousMul",
"PseudoMetricSpace",
"CommMonoid.toMonoid",
"BoundedConti... | true |
_private.Mathlib.MeasureTheory.Function.SimpleFunc.0.MeasureTheory.SimpleFunc.eapproxDiff.match_1.splitter | Mathlib.MeasureTheory.Function.SimpleFunc | [
"MeasureTheory.SimpleFunc.eapproxDiff.match_1",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ"
] | true |
Finset.mulLECancellable_prod._simp_2 | Mathlib.Algebra.Order.BigOperators.Group.Finset | [
"Monoid.toMulOneClass",
"Finset",
"Membership.mem",
"MulLeftMono",
"MulOne.toMul",
"LE",
"Finset.prod",
"MulOneClass.toMulOne",
"Finset.instSetLike",
"CommMonoid.toMonoid",
"propext",
"Finset.mulLECancellable_prod",
"MulLECancellable",
"Eq",
"CommMonoid",
"SetLike.instMembership"
] | false |
_private.Mathlib.GroupTheory.Perm.Cycle.Type.0.Equiv.Perm.IsThreeCycle.nodup_iff_mem_support._proof_1_170 | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Equiv.instEquivLike",
"Lean.Grind.Nat.lt_eq",
"List.getElem_filter_eq_getElem_getElem_findIdxs._proof_2",
"Equiv",
"instOfNatNat",
"LE.le",
"instLENat",
"instBEqOfDecidableEq",
"List.cons",
"List.idxOfNth",
"List.findIdxs",
"instHAdd",
"HAdd.hAdd",
"Equiv.Perm",
"Nat",
"List.filter",
... | false |
_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable.computeDistance._unary | Init.Data.String.Pattern.String | [
"_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable.computeDistance._unary._proof_6",
"_private.Init.Data.String.Pattern.String.0.String.Slice.Pattern.ForwardSliceSearcher.buildTable.computeDistance._unary._proof_1",
"_private.Init.Data.String.Pattern.String.0.String... | false |
Lean.Doc.MarkdownBlock.toMarkdown | Lean.DocString.Markdown | [
"Lean.Doc.Block",
"Lean.Doc.MarkdownBlock",
"Array",
"Unit",
"Lean.Doc.MarkdownM",
"Lean.Doc.Inline"
] | true |
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