name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
CategoryTheory.Functor.leftKanExtensionUnit_leftKanExtension_map_leftKanExtensionObjIsoColimit_hom | Mathlib.CategoryTheory.Functor.KanExtension.Adjunction | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.Functor.LeftExtension.mk",
"CategoryTheory.Functor.leftKanExtension",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.LeftExtension.IsPo... | true |
Std.DTreeMap.Internal.Impl.alter._sunfold | Std.Data.DTreeMap.Internal.Operations | [
"Std.DTreeMap.Internal.Impl.minView._proof_9",
"Ordering.gt",
"Std.DTreeMap.Internal.Impl.alter._proof_20",
"Ord",
"Std.DTreeMap.Internal.Impl.alter._proof_2",
"Std.DTreeMap.Internal.Impl.minView._proof_11",
"HSub.hSub",
"Std.DTreeMap.Internal.Impl.balance",
"Std.DTreeMap.Internal.Impl.Balanced",
... | false |
Lean.Meta.Simp.initFn._@.Lean.Meta.Tactic.Simp.Main.3634004939._hygCtx._hyg.4 | Lean.Meta.Tactic.Simp.Main | [
"Lean.Option",
"IO",
"Lean.Name.mkStr7",
"Lean.Option.Decl.mk",
"Lean.KVMap.instValueBool",
"Lean.Option.register",
"Bool",
"Bool.false",
"Lean.Name.mkStr4"
] | false |
CategoryTheory.rightDistrib | Mathlib.CategoryTheory.Distributive.Monoidal | [
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Limits.PreservesColimitPair.iso",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.rightDistrib._proof_2",
"CategoryTheory.Iso",
"CategoryTheory.Limits.WalkingPair",
"CategoryTheory.MonoidalCategory.tensorRight",
"CategoryTheory... | true |
Set.list_sum_subset_list_sum | Mathlib.Algebra.Group.Pointwise.Set.BigOperators | [
"List.map",
"AddMonoid.toAddZeroClass",
"List.sum",
"List.mem_cons_of_mem",
"Membership.mem",
"AddZeroClass.toAddZero",
"id",
"Set.instReflSubset",
"HasSubset.Subset",
"subset_refl",
"List.rec",
"AddCommMonoid",
"List.cons",
"AddZero.toZero",
"Set.zero",
"List",
"Set.add",
"List.in... | true |
UInt64.add_comm | Init.Data.UInt.Lemmas | [
"instAddUInt64",
"UInt64",
"UInt64.toBitVec_inj",
"BitVec",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"BitVec.add_comm",
"Nat",
"Iff.mp",
"OfNat.ofNat",
"Eq",
"UInt64.toBitVec"
] | true |
Rep.hom_ext | Mathlib.RepresentationTheory.Rep.Basic | [
"Monoid",
"Rep.V",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"Rep.instCategory",
"Rep.hV1",
"Rep",
"Rep.ρ",
"Rep.Hom.hom",
"Semiring",
"Representation.IntertwiningMap",
"CategoryTheory.Category.toCategoryStruct",
"Eq",
"Rep.Hom.e... | true |
Ordinal.veblen_gamma_zero | Mathlib.SetTheory.Ordinal.Veblen | [
"Ordinal.veblen",
"Ordinal.deriv_fp",
"Ordinal.isNormal_veblen_zero",
"Ordinal.zero",
"Zero.toOfNat0",
"Ordinal.gamma",
"OfNat.ofNat",
"Eq",
"Ordinal"
] | true |
_private.Mathlib.Order.Concept.0.mem_lowerPolar_singleton._simp_1_2 | Mathlib.Order.Concept | [
"Membership.mem",
"Set.instSingletonSet",
"Set.mem_singleton_iff",
"propext",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Set"
] | false |
CategoryTheory.Subgroupoid.hom | Mathlib.CategoryTheory.Groupoid.Subgroupoid | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"Membership.mem",
"CategoryTheory.Groupoid",
"Set.Elem",
"CategoryTheory.Subgroupoid.hom._proof_2",
"CategoryTheory.Subgroupoid.arrows",
"CategoryTheory.Subgroupoid",
"CategoryTheory.Su... | true |
_private.Init.Data.String.FindPos.0.String.Slice.posGE._unary._proof_3 | Init.Data.String.FindPos | [
"Eq.mpr",
"String.instLTRaw",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"congrArg",
"InvImage",
"Int.add_one_le_of_lt",
"String.Slice.byteIdx_rawEndPos... | false |
_private.Mathlib.Analysis.InnerProductSpace.PiL2.0.OrthonormalBasis.singleton._simp_1 | Mathlib.Analysis.InnerProductSpace.PiL2 | [
"NormedCommRing.toNormedRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"SeminormedAddCommGroup",
"NormedRing.toRing",
"Orthonormal",
"Inner.inner",
"AddGroupWithOne.toAddMonoidWithOne",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Norme... | false |
Lean.Meta.mkSub | Lean.Meta.AppBuilder | [
"_private.Lean.Meta.AppBuilder.0.Lean.Meta.mkBinaryOp",
"Lean.Expr",
"Lean.Meta.MetaM",
"Lean.Name.mkStr2",
"Lean.Name.mkStr1"
] | true |
Algebra.RingHom.adjoinAlgebraMap | Mathlib.RingTheory.Adjoin.Singleton | [
"Subalgebra.instSetLike",
"CommSemiring.toSemiring",
"AlgHom",
"IsScalarTower",
"AlgHom.funLike",
"Algebra.RingHom.adjoinAlgebraMap._proof_3",
"Subalgebra.val",
"Algebra",
"Algebra.adjoin",
"RingHom",
"Algebra.toSMul",
"Membership.mem",
"algebraMap",
"Algebra.id",
"Set.instSingletonSet",... | true |
Real.fromBinary._proof_2 | Mathlib.Topology.MetricSpace.HausdorffAlexandroff | [
"Real",
"Pi.topologicalSpace",
"Real.instZero",
"instTopologicalSpaceBool",
"Homeomorph.piCongrRight",
"instDiscreteTopologyBool",
"Preorder.toLE",
"Function.comp",
"instOfNatNat",
"LE.le",
"finTwoEquiv",
"Real.ofDigits_nonneg",
"Real.instOne",
"Homeomorph.instEquivLike",
"And",
"Real.... | false |
Lean.LocalContext.foldr | Lean.LocalContext | [
"Pure.pure",
"Lean.LocalContext.foldrM",
"Monad.toApplicative",
"Id.run",
"Id",
"Applicative.toPure",
"Id.instMonad",
"Lean.LocalDecl",
"Lean.LocalContext"
] | true |
CategoryTheory.MonoidalCategory.MonoidalLeftAction.actionHom_comp | Mathlib.CategoryTheory.Monoidal.Action.Basic | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.MonoidalCategory.MonoidalLeftActionStruct.actionObj",
"CategoryTheory.MonoidalCategory.MonoidalLeftAction.toMonoidalLeftActionStruct",
"CategoryTheory.MonoidalCategory.MonoidalLeftAction",
"Categor... | true |
Affine.Simplex.orthogonalProjection_eq_circumcenter_of_exists_dist_eq | Mathlib.Geometry.Euclidean.Circumcenter | [
"Set.mem_range_self",
"Iff.mpr",
"NormedCommRing.toNormedRing",
"InnerProductSpace.toNormedSpace",
"Submodule",
"complete_of_proper",
"instNeZeroNatHAdd_1",
"Set.instNonemptyRange",
"Affine.Simplex.points",
"Real",
"NormedRing.toRing",
"Set.forall_mem_range",
"Submodule.HasOrthogonalProjecti... | true |
Commute.sub_dvd_pow_sub_pow | Mathlib.Algebra.Ring.GeomSum | [
"Dvd.dvd",
"HMul.hMul",
"Ring.toNonAssocRing",
"AddGroupWithOne.toAddGroup",
"Dvd.intro",
"semigroupDvd",
"HSub.hSub",
"Commute",
"SemigroupWithZero.toSemigroup",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"instSubNat",
"instOfNatNat",
"NonUnitalSemiring.toSemigroupWithZero",
"No... | true |
Erased.join | Mathlib.Data.Erased | [
"Erased",
"id",
"Erased.bind"
] | true |
CategoryTheory.ObjectProperty.SerreClassLocalization.map_eq_zero_iff | Mathlib.CategoryTheory.Abelian.SerreClass.Localization | [
"CategoryTheory.Abelian.toPreadditive",
"Eq.mpr",
"CategoryTheory.ObjectProperty.SerreClassLocalization.instHasRightCalculusOfFractionsIsoModSerre",
"CategoryTheory.Functor",
"CategoryTheory.Abelian.image",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Iff.of_eq",
"congrArg",
"CategoryT... | true |
_private.Mathlib.RingTheory.DividedPowerAlgebra.Init.0.DividedPowerAlgebra.dp_sum_smul._simp_1_1 | Mathlib.RingTheory.DividedPowerAlgebra.Init | [
"Finset.prod_mul_distrib",
"HMul.hMul",
"Monoid.toMulOneClass",
"Finset",
"MulOne.toMul",
"Finset.prod",
"MulOneClass.toMulOne",
"CommMonoid.toMonoid",
"Eq.symm",
"Eq",
"CommMonoid",
"instHMul"
] | false |
CategoryTheory.SmallCategoryCardinalLT.exists_equivalence | Mathlib.CategoryTheory.SmallRepresentatives | [
"Eq.mpr",
"Equiv.instEquivLike",
"HasCardinalLT",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Cardinal",
"Iff.of_eq",
"congrArg",
"exists_const._simp_1",
"CategoryTheory.eqToHom",
"PartialOrder.toPreorder",
"hasCardinalLT_iff_of_equiv",
"instInhabitedTrue",
"CategoryTheory.Equ... | true |
ClosureOperator.le_closure | Mathlib.Order.Closure | [
"PartialOrder.toPreorder",
"Preorder.toLE",
"PartialOrder",
"ClosureOperator.instFunLike",
"LE.le",
"ClosureOperator",
"ClosureOperator.le_closure'",
"DFunLike.coe"
] | true |
IsCoveringMap.liftHomotopyRel._proof_1 | Mathlib.Topology.Homotopy.Lifting | [
"ContinuousMap.continuous",
"Real.instIsOrderedRing",
"Eq.mpr",
"Real.partialOrder",
"Real",
"Set.Icc.instZero",
"IsCoveringMap.liftHomotopy",
"ConnectedSpace.toPreconnectedSpace",
"congrArg",
"ContinuousMap.HomotopyRel",
"ContinuousMap",
"IsCoveringMap.liftPath_zero",
"PseudoMetricSpace.toU... | false |
_private.Mathlib.Topology.Separation.Basic.0.t1Space_TFAE._simp_1_7 | Mathlib.Topology.Separation.Basic | [
"Set.subset_compl_singleton_iff",
"Compl.compl",
"Membership.mem",
"Set.instSingletonSet",
"HasSubset.Subset",
"Set.instCompl",
"propext",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"Not",
"Set.instHasSubset",
"Set"
] | false |
commutator_def | Mathlib.GroupTheory.Commutator.Basic | [
"Bracket.bracket",
"Group",
"Subgroup",
"commutator",
"Subgroup.instTop",
"Top.top",
"Subgroup.commutator",
"Eq",
"rfl"
] | true |
Pi.mulZeroClass._proof_2 | Mathlib.Algebra.GroupWithZero.Pi | [
"HMul.hMul",
"MulZeroClass.toMul",
"MulZeroClass",
"Pi.instZero",
"MulZeroClass.mul_zero",
"funext",
"Pi.instMul",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq",
"MulZeroClass.toZero",
"instHMul"
] | false |
contDiff_one_iff_fderiv | Mathlib.Analysis.Calculus.ContDiff.Defs | [
"Differentiable",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"ContinuousLinearMap.toNormedAddCommGroup",
"False",
"Continuous",
"instAddMonoidWithOneENat",
"NormedSpace",
"ContinuousLinearMap.topologicalSpace",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"contDiff_zero._simp_1",
"contD... | true |
FiberBundleCore.mk_mem_localTrivAt_source | Mathlib.Topology.FiberBundle.Basic | [
"FiberBundleCore.Fiber",
"instTopologicalSpaceProd",
"Membership.mem",
"Bundle.TotalSpace.mk",
"FiberBundleCore.mem_localTrivAt_baseSet._simp_1",
"FiberBundleCore.toTopologicalSpace",
"FiberBundleCore.TotalSpace",
"TopologicalSpace",
"Bundle.TotalSpace.proj",
"FiberBundleCore.mem_localTrivAt_sourc... | true |
CategoryTheory.SingleObj | Mathlib.CategoryTheory.SingleObj | [
"Quiver.SingleObj"
] | true |
Std.Tactic.BVDecide.LRAT.instBEqAction.beq._sparseCasesOn_2 | Std.Tactic.BVDecide.LRAT.Actions | [
"Std.Tactic.BVDecide.LRAT.Action.addEmpty",
"Nat.ne_of_beq_eq_false",
"Std.Tactic.BVDecide.LRAT.Action.rec",
"Std.Tactic.BVDecide.LRAT.Action",
"Nat.shiftRight",
"Std.Tactic.BVDecide.LRAT.Action.del",
"Std.Tactic.BVDecide.LRAT.Action.addRat",
"Nat.hasNotBit",
"instOfNatNat",
"Array",
"Nat.land",... | false |
AlgebraicGeometry.Scheme.IdealSheafData.ofIdeals_mono | Mathlib.AlgebraicGeometry.IdealSheaf.Basic | [
"GaloisConnection.monotone_u",
"Pi.preorder",
"AlgebraicGeometry.Scheme",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"Opposite",
"CommRingCat.carrier",
"CommRing.toNonUnitalCommRing",
"AlgebraicGeometry.PresheafedSpace.carrier",
"TopologicalSpace.Opens.instPartialOrder",... | true |
_private.Lean.Level.0.Lean.Level.normLtAux._unary.eq_def | Lean.Level | [
"Eq.mpr",
"bne",
"Lean.LevelMVarId.name",
"congrArg",
"invImage",
"_private.Lean.Level.0.Lean.Level.normLtAux._unary._proof_7",
"Lean.Level.mvar",
"_private.Lean.Level.0.Lean.Level.normLtAux._unary._proof_6",
"namedPattern",
"Lean.Level._sizeOf_inst",
"PSigma.casesOn",
"id",
"Lean.Level.para... | false |
Mathlib.Tactic.Linarith.SimplexAlgorithm.SparseMatrix.noConfusionType | Mathlib.Tactic.Linarith.Oracle.SimplexAlgorithm.Datatypes | [
"Rat",
"Mathlib.Tactic.Linarith.SimplexAlgorithm.SparseMatrix",
"Std.HashMap",
"instHashableNat",
"instBEqOfDecidableEq",
"Array",
"Nat",
"instDecidableEqNat",
"Eq",
"Mathlib.Tactic.Linarith.SimplexAlgorithm.SparseMatrix.casesOn"
] | false |
_private.Mathlib.Analysis.Analytic.Within.0.analyticWithinAt_of_singleton_mem._simp_1_3 | Mathlib.Analysis.Analytic.Within | [
"Set.mem_inter_iff",
"Membership.mem",
"Set.instInter",
"Inter.inter",
"And",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
_private.Init.Data.List.MinMaxIdx.0.List.minIdxOn.eq_1 | Init.Data.List.MinMaxIdx | [
"List.minIdxOn",
"_private.Init.Data.List.MinMaxIdx.0.List.minIdxOn.go",
"Ne",
"instOfNatNat",
"LE",
"List.cons",
"List",
"DecidableLE",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Eq",
"List.nil"
] | true |
PresheafOfModules.instMonoidalCompOppositeCommRingCatRingCatForget₂RingHomCarrierCarrierOpPushforward₀OfCommRingCat._proof_1 | Mathlib.Algebra.Category.ModuleCat.Presheaf.PushforwardZeroMonoidal | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"Opposite",
"CommRingCat.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommSemiring.toSemiring",
"CommRingCat",
"PresheafOfModules.monoidalCategory",
"CommRingCat.instConcreteCategoryRingHomCarrier",
"RingCat.ring",
"C... | false |
CategoryTheory.StructuredArrow.pre_obj_hom | Mathlib.CategoryTheory.Comma.StructuredArrow.Basic | [
"CategoryTheory.Functor",
"CategoryTheory.Comma.right",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.comp",
"CategoryTheory.Comma.hom",
"CategoryTheory.Comma",
"CategoryTheory.discreteCategory",
"PUnit",
"Eq.refl",
"CategoryTheory... | true |
_private.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AC.0.Lean.Elab.Tactic.BVDecide.Frontend.Normalize.VarStateM.computeCoefficients.go._sunfold | Lean.Elab.Tactic.BVDecide.Frontend.Normalize.AC | [
"Pure.pure",
"Lean.Core.instMonadTraceCoreM",
"StateT.instMonadFunctor",
"Lean.MessageData",
"Lean.Elab.Tactic.BVDecide.Frontend.Normalize.Op",
"StateT.instMonadLift",
"String",
"Lean.instMonadTraceOfMonadLift",
"Lean.Meta.State",
"Lean.MessageData.instAppend",
"Lean.Core.instMonadOptionsCoreM",... | false |
_private.Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting.0.CategoryTheory.Limits._aux_Mathlib_CategoryTheory_Limits_Shapes_Pullback_Pasting___macroRules__private_Mathlib_CategoryTheory_Limits_Shapes_Pullback_Pasting_0_CategoryTheory_Limits_termI₂_1 | Mathlib.CategoryTheory.Limits.Shapes.Pullback.Pasting | [
"Pure.pure",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Name.mkNum",
"Lean.Syntax.ident",
"instMonadExceptOfMonadExceptOf",
"String",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.TSyntax.mk",
"Lean.Syntax",
"Lean.Name.mkStr... | false |
Prod.Lex.uniqueProd | Mathlib.Order.Hom.Lex | [
"Prod.Lex.uniqueProd._proof_4",
"Inhabited.default",
"Preorder.toLT",
"Equiv.instEquivLike",
"RelIso.mk",
"Lex",
"Unique",
"Equiv.mk",
"Prod.Lex.uniqueProd._proof_5",
"Equiv",
"OrderIso",
"Prod.mk",
"LE.le",
"LE",
"Prod.Lex.uniqueProd._proof_1",
"Unique.instInhabited",
"Prod",
"ofL... | true |
AnalyticOn.contDiff | Mathlib.Analysis.Calculus.ContDiff.Defs | [
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"AnalyticOn",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedSpace.toIsBoundedSMul",
"NormedSpace",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Set.univ",
"NormedSpace.toModule",
"AddMonoid.toAddZeroCl... | true |
AlgebraicIndependent.matroid.congr_simp | Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis | [
"CommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"CommSemiring.toSemiring",
"Algebra",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Algebra.toSMul",
"AlgebraicIndependent.matroid",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"FaithfulSMul",
"C... | true |
CategoryTheory.Functor.additive_of_comp_faithful | Mathlib.CategoryTheory.Preadditive.AdditiveFunctor | [
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.comp",
"CategoryTheory.Functor.map_add",
"id",
"CategoryTheory.Functor.map",
"CategoryTheory.Preadd... | true |
WithLp.prodContinuousLinearEquiv_symm_apply_ofLp | Mathlib.Analysis.Normed.Lp.ProdLp | [
"WithLp",
"ContinuousLinearEquiv.symm",
"WithLp.prodContinuousLinearEquiv",
"WithLp.instProdTopologicalSpace",
"AddCommGroup.toAddCommMonoid",
"instTopologicalSpaceProd",
"WithLp.instAddCommGroup",
"AddCommGroup",
"ContinuousLinearEquiv.equivLike",
"TopologicalSpace",
"ContinuousLinearEquiv",
... | true |
Algebra.intNorm_eq_of_isLocalization | Mathlib.RingTheory.IntegralClosure.IntegralRestrict | [
"Algebra.algebraMapSubmonoid._proof_1",
"Iff.mpr",
"Eq.mpr",
"IsIntegralClosure",
"IsDomain",
"FractionRing.field",
"FractionRing.instIsScalarTower",
"CommRing",
"IsDomain.to_noZeroDivisors",
"MonoidHom.instFunLike",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"IsIntegralClosure.of_isInte... | true |
Lean.Elab.Term.LetRecToLift.termination | Lean.Elab.Term.TermElabM | [
"Lean.Elab.TerminationHints",
"Lean.Elab.Term.LetRecToLift"
] | true |
_private.Mathlib.Data.WSeq.Basic.0.Stream'.WSeq.drop.match_1.eq_1 | Mathlib.Data.WSeq.Basic | [
"Unit.unit",
"Stream'.WSeq.drop.match_1",
"instOfNatNat",
"Unit",
"Nat",
"Eq.refl",
"OfNat.ofNat",
"Nat.succ",
"Eq"
] | true |
GromovHausdorff.instMetricSpaceOptimalGHCoupling._proof_22 | Mathlib.Topology.MetricSpace.GromovHausdorffRealized | [
"PseudoEMetricSpace.toPseudoMetricSpaceOfDist._proof_4",
"SeparationQuotient.instMetricSpace._proof_2",
"Bornology.ofDist._proof_2",
"Real.instLE",
"Bornology.ofDist._proof_3",
"Real",
"SeparationQuotient.instDist",
"PartialOrder.toPreorder",
"setOf",
"PseudoMetricSpace.toUniformSpace",
"Preorde... | false |
TypeVec.prod.diag.eq_1 | Mathlib.Data.TypeVec | [
"TypeVec.prod.diag",
"TypeVec.prod",
"Fin2.fs",
"Nat",
"Eq.refl",
"TypeVec.drop",
"Nat.succ",
"Eq",
"Fin2",
"TypeVec"
] | true |
FreeMonoid.of_injective | Mathlib.Algebra.FreeMonoid.Basic | [
"FreeMonoid",
"List.singleton_injective",
"FreeMonoid.of",
"Function.Injective"
] | true |
Lean.Grind.instCommRingBitVec._proof_1 | Init.GrindInstances.Ring.BitVec | [
"BitVec.instOfNat",
"BitVec",
"Nat.cast",
"Nat",
"Eq.refl",
"BitVec.instNatCast",
"OfNat.ofNat",
"Eq"
] | false |
_private.Mathlib.Data.Finset.Defs.0.Finset.forall_mem_not_eq._proof_1_1 | Mathlib.Data.Finset.Defs | [
"Lean.Grind.of_eq_eq_true",
"False",
"Lean.Grind.not_not",
"eq_false",
"Lean.Grind.iff_eq",
"congrArg",
"Finset",
"Classical.byContradiction",
"Lean.Grind.imp_false_eq",
"Membership.mem",
"Exists",
"Eq.mp",
"id",
"Lean.Grind.eq_false_of_imp_eq_false",
"Or.casesOn",
"And.casesOn",
"An... | false |
SimplexCategoryGenRel.δ_comp_δ_assoc | Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic | [
"CategoryTheory.Category.assoc",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Fin.succ",
"congrArg",
"SimplexCategoryGenRel.mk",
"Eq.mp",
"id",
"Mathlib.Tactic.Reassoc.eq_whisker'",
"instOfNatNat",
"LE.le",
"instLEFin",
"instHAdd",
"HAdd.hAdd",
"Nat",
"congr",
"CategoryTh... | true |
CategoryTheory.Abelian.Ext.mono_postcomp_mk₀_of_mono | Mathlib.Algebra.Homology.DerivedCategory.Ext.ExactSequences | [
"Iff.mpr",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Abelian.Ext.postcomp",
"CategoryTheory.Abelian.Ext.instAddCommGroup",
"AddMonoid.toAddZeroClass",
"Nat.instAddMonoid",
"A... | true |
PNat.XgcdType.instSizeOf | Mathlib.Data.PNat.Xgcd | [
"PNat.XgcdType",
"SizeOf.mk",
"PNat.XgcdType.bp",
"SizeOf"
] | true |
Lean.InductiveType.noConfusionType | Lean.Declaration | [
"Lean.InductiveType",
"Lean.Expr",
"List",
"Lean.Name",
"Lean.InductiveType.casesOn",
"Lean.Constructor",
"Eq"
] | false |
IsLocalization.mk'_eq_mk' | Mathlib.Algebra.Module.LocalizedModule.IsLocalization | [
"Eq.mpr",
"instHSMul",
"Semiring.toModule",
"IsLocalization",
"IsLocalization.smul_mk'_self",
"congrArg",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"LinearMap.instFunLike",
"Algebra",
"Membership.mem",
"AddZeroClass.toAddZero",
"Algebra.toModu... | true |
Submodule.ker_inl | Mathlib.LinearAlgebra.Prod | [
"Eq.mpr",
"Submodule",
"LinearMap.inl",
"congrArg",
"LinearMap.ker",
"id",
"Bot.bot",
"Submodule.prod",
"AddCommMonoid",
"Submodule.instBot",
"LinearMap.ker.eq_1",
"Submodule.comap",
"Submodule.prod_comap_inl",
"Submodule.prod_bot",
"Semiring",
"Eq.refl",
"Module",
"Prod",
"Prod.... | true |
Batteries.Tactic.DiscrTreeCache.getMatch | Batteries.Util.Cache | [
"Pure.pure",
"Array.instAppend",
"Batteries.Tactic.DiscrTreeCache",
"Array.reverse",
"Lean.Meta.State",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"Batteries.Tactic.DeclCache.get",
"Applicative.toPure",
"Array",
"instHAppendOfAppend",
"Lean.Core.CoreM",
"Lean.Meta.DiscrTree.getMatch",... | true |
Nat.factorial_pos | Mathlib.Data.Nat.Factorial.Basic | [
"Nat.mul_pos",
"Nat.brecOn",
"instOfNatNat",
"Nat.below",
"Unit",
"Nat.factorial",
"Nat",
"Nat.succ_pos",
"LT.lt",
"instLTNat",
"OfNat.ofNat",
"Nat.succ",
"_private.Mathlib.Data.Nat.Factorial.Basic.0.Nat.factorial_pos.match_1_1",
"Nat.zero_lt_one"
] | true |
IsAddCyclic.index_nsmulAddMonoidHom_range | Mathlib.GroupTheory.SpecificGroups.Cyclic | [
"Nat.gcd",
"Eq.mpr",
"congrArg",
"AddSubgroup.index",
"AddCommGroup.toAddCommMonoid",
"Finite",
"AddMonoid.toAddZeroClass",
"AddMonoidHom.range",
"AddCommGroup.toAddGroup",
"Membership.mem",
"AddCommGroup",
"id",
"Subtype",
"Nat.card",
"IsAddCyclic.card_nsmulAddMonoidHom_ker",
"nsmulAd... | true |
_private.Lean.Server.AsyncList.0.IO.AsyncList.getFinishedPrefixWithTimeout.go.match_1 | Lean.Server.AsyncList | [
"Except.ok",
"Except.error",
"Sum.casesOn",
"Sum",
"Sum.inl",
"Unit",
"Sum.inr",
"Except.casesOn",
"Except",
"IO.AsyncList"
] | false |
ValuativeRel.inv_vle_one | Mathlib.RingTheory.Valuation.ValuativeRel.Basic | [
"DivInvMonoid.toInv",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"DivisionCommMonoid.toDivisionMonoid",
"DivInvOneMonoid.toInvOneClass",
"congrArg",
"ValuativeRel.div_vle_one_iff",
"AddGroupWithOne.toAddMonoidWithOne",
"NonUnitalNonAssocSemiring.to... | true |
Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.noConfusionType | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"Lean.Grind.CommRing.Poly",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.reorder.elim",
"Lean.Meta.Grind.Arith.Cutsat.CooperSplit",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.casesOn",
"Lean.Expr",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.core.elim",
"Int.Linear.Var",
"Lean.Meta.Grind.Arith.Cutsat.... | false |
_private.Init.Data.List.Basic.0.List.getLast?.match_1.eq_2 | Init.Data.List.Basic | [
"List.cons",
"List",
"Unit",
"Eq.refl",
"Eq",
"List.getLast?.match_1",
"List.nil"
] | true |
TannakaDuality.FiniteGroup.equiv._proof_2 | Mathlib.RepresentationTheory.Tannaka | [
"IsDomain",
"CommRing",
"MonoidHom.instFunLike",
"MonoidHom",
"ModuleCat",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"CategoryTheory.ObjectProperty.fullMonoidalSubcategory",
"Finite",
"Group",
"ModuleCat.isFG",
"DivInvMonoid.toMonoid",
"Action.instMonoidalCategory",
"FDRep",
"Mo... | false |
Std.ExtDTreeMap.maxKeyD_alter_eq_self | Std.Data.ExtDTreeMap.Lemmas | [
"Iff.mpr",
"Std.ExtDTreeMap.mk",
"Std.ExtDTreeMap.isEmpty_eq_false_iff",
"Std.DTreeMap",
"Std.ExtDTreeMap.alter",
"Membership.mem",
"Ordering",
"Ne",
"Std.ExtDTreeMap.instEmptyCollection",
"Std.TransCmp",
"Std.ExtDTreeMap.isEmpty",
"Bool.true",
"And",
"Iff",
"Std.ExtDTreeMap.maxKeyD",
... | true |
_private.Mathlib.Geometry.Manifold.PartitionOfUnity.0.exists_contMDiff_support_eq_eq_one_iff._simp_1_2 | Mathlib.Geometry.Manifold.PartitionOfUnity | [
"left_eq_add",
"AddMonoid.toAddZeroClass",
"AddZeroClass.toAddZero",
"AddZero.toZero",
"instHAdd",
"HAdd.hAdd",
"IsLeftCancelAdd",
"AddMonoid",
"propext",
"AddZero.toAdd",
"Zero.toOfNat0",
"OfNat.ofNat",
"Eq"
] | false |
Lean.Util.ParamMinimizer.Result._sizeOf_inst | Lean.Util.ParamMinimizer | [
"Lean.Util.ParamMinimizer.Result._sizeOf_1",
"Lean.Util.ParamMinimizer.Result",
"SizeOf.mk",
"SizeOf"
] | false |
_private.Init.Data.Range.Polymorphic.SInt.0.Int16.toBitVec_minValueSealed_eq_intMinSealed | Init.Data.Range.Polymorphic.SInt | [
"_private.Init.Data.Range.Polymorphic.Internal.SignedBitVec.0.BitVec.Signed.intMinSealed_def",
"_private.Init.Data.Range.Polymorphic.SInt.0.Int16.minValueSealed_def",
"Int16",
"congrArg",
"Int16.instOfNat",
"Int16.toBitVec_ofNat",
"BitVec",
"_private.Init.Data.Range.Polymorphic.SInt.0.Int16.minValueSe... | true |
Lean.Lsp.DiagnosticTag.deprecated | Lean.Data.Lsp.Diagnostics | [
"Lean.Lsp.DiagnosticTag.deprecated",
"Lean.Lsp.DiagnosticTag"
] | true |
Polynomial.ofFinsupp_pow | Mathlib.Algebra.Polynomial.Basic | [
"MulOne.toOne",
"Polynomial.instOne",
"AddMonoidAlgebra.semiring",
"Nat.recAux",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"pow_succ",
"Nat.instAddMonoid",
"Polynomial.pow",
"id",
"MulOne.toMul",
"instOfNatNat",
"npowRec",
"Polynomial",
"pow_zero",
"Monoid.toPow",
"instHAdd"... | true |
HahnSeries.instIsOrderedAddMonoidLex | Mathlib.RingTheory.HahnSeries.Lex | [
"Eq.mpr",
"LE.le.eq_or_lt",
"add_left_strictMono",
"Preorder.toLT",
"Equiv.instEquivLike",
"AddMonoid.toAddSemigroup",
"instAddCommMonoidLex",
"instReflLe",
"congrArg",
"Lex",
"LinearOrder",
"covariant_swap_add_of_covariant_add",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"le... | true |
Multiset.map_subset_map | Mathlib.Data.Multiset.MapFold | [
"Iff.mpr",
"Multiset.map",
"_private.Mathlib.Data.Multiset.MapFold.0.Multiset.map_subset_map.match_1_1",
"Multiset.mem_map",
"Multiset.instHasSubset",
"Membership.mem",
"Exists",
"Multiset",
"HasSubset.Subset",
"Multiset.instMembership",
"And",
"And.intro",
"Exists.intro",
"Iff.mp",
"Eq"... | true |
CategoryTheory.Functor.IsCoverDense.Types.sheafIso_inv_hom | Mathlib.CategoryTheory.Sites.DenseSubsite.Basic | [
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"CategoryTheory.Functor.IsCoverDense",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.category",
"CategoryTheory.Functor.comp",
"CategoryTheory.Iso",
"CategoryTheory.ObjectProperty.FullSubcategory.o... | true |
_private.Mathlib.Data.Multiset.Powerset.0.Multiset.powersetCard_le_powerset._simp_1_1 | Mathlib.Data.Multiset.Powerset | [
"Multiset.coe_le",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Multiset",
"LE.le",
"List",
"Multiset.ofList",
"List.Subperm",
"propext",
"Eq",
"Multiset.instPartialOrder"
] | false |
CategoryTheory.Limits.coend.hom_ext_iff | Mathlib.CategoryTheory.Limits.Shapes.End | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.Limits.coend",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Functor.category",
"Eq.casesOn",
"CategoryTheory.Limits.HasCoend",
"CategoryTheory.Limits.coend.ι",
"Iff",
"Opposite.op",
"Iff.intro",
"C... | true |
_private.Mathlib.CategoryTheory.Localization.Monoidal.Basic.0.CategoryTheory.Localization.Monoidal.associator_naturality₃._simp_1_1 | Mathlib.CategoryTheory.Localization.Monoidal.Basic | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.Functor",
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MorphismProperty.IsMonoidal",
"CategoryTheory.Localization.Monoidal.id_tensorHom",
"CategoryTheory.MonoidalCategory"... | false |
Lean.IR.Expr.lit.elim | Lean.Compiler.IR.Basic | [
"Lean.IR.Expr.ctorElim",
"PULift.up",
"Lean.IR.Expr",
"Nat",
"Lean.IR.Expr.lit",
"Eq.symm",
"Lean.IR.Expr.ctorIdx",
"Eq",
"Lean.IR.LitVal"
] | false |
_private.Batteries.Data.Random.MersenneTwister.0.Batteries.Random.MersenneTwister.Config.init.loop._unary | Batteries.Data.Random.MersenneTwister | [
"BitVec.instHShiftRightNat",
"HMul.hMul",
"BitVec.instXorOp",
"BitVec.instOfNat",
"Vector",
"Array.push",
"InvImage",
"HSub.hSub",
"WellFounded.Nat.fix",
"BitVec.instAdd",
"_private.Batteries.Data.Random.MersenneTwister.0.Batteries.Random.MersenneTwister.Config.init.loop._unary._proof_1",
"Bit... | false |
ExistsAndEq.instInhabitedGoTo.default | Mathlib.Tactic.Simproc.ExistsAndEq | [
"ExistsAndEq.GoTo",
"ExistsAndEq.GoTo.left"
] | true |
ConvexOn.le_left_of_right_le' | Mathlib.Analysis.Convex.Function | [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"NonAssocSemiring.toAddCommMonoidWithOne",
"instHSMul",
"Trans.trans",
"Preorder.toLT",
"PosSMulStrictMono.toPosSMulMono",
"lt_irrefl",
"DistribMulAction.toDistribSMul",
"instIsLeftCancelAddOfAddLeftReflectLE",
"LinearOrder",
"SMul",
"cova... | true |
String.utf8InductionOn._sunfold | Batteries.Data.String.Lemmas | [
"Eq.rec",
"Ne",
"String.utf8InductionOn",
"String.Pos.Raw",
"dite",
"List.cons",
"List",
"Unit",
"instDecidableEqRaw",
"HAdd.hAdd",
"Char",
"Eq.symm",
"Eq",
"String.utf8Len.match_1",
"Not",
"List.nil",
"String.instHAddRawChar"
] | false |
AlgCat.instRingElemForallObjCompForgetAlgHomCarrierSections._proof_23 | Mathlib.Algebra.Category.AlgCat.Limits | [
"AlgCat.instRingElemForallObjCompForgetAlgHomCarrierSections._proof_3",
"CategoryTheory.Functor",
"Mul.mk",
"CommRing",
"AlgCat.instRingElemForallObjCompForgetAlgHomCarrierSections._aux_8",
"One.mk",
"HMul.hMul",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"AlgCat.instRingElemForallObjCompForget... | false |
Std.Internal.IO.Async.EAsync.ofETask | Std.Internal.Async.Basic | [
"Std.Internal.IO.Async.BaseAsync.mk",
"Std.Internal.IO.Async.ETask",
"Std.Internal.IO.Async.BaseAsync.ofTask",
"Std.Internal.IO.Async.EAsync",
"Except"
] | true |
Std.Rxc.Iterator.toList_eq_toList_rxoIterator | Init.Data.Range.Polymorphic.Lemmas | [
"Eq.mpr",
"Std.Rxc.Iterator",
"False",
"Decidable.casesOn",
"_private.Init.Data.Range.Polymorphic.Lemmas.0.Std.Rxc.Iterator.toList_eq_match.match_1.splitter",
"_private.Init.Data.Range.Polymorphic.Lemmas.0.Std.Rxc.Iterator.toList_eq_toList_rxoIterator._simp_1_3",
"Std.IterStep",
"Classical.not_not._si... | true |
Cardinal.mk_list_eq_max_mk_aleph0 | Mathlib.SetTheory.Cardinal.Arithmetic | [
"Eq.mpr",
"Lattice.toSemilatticeSup",
"Cardinal",
"congrArg",
"Cardinal.mk",
"SemilatticeSup.toMax",
"Cardinal.mk_list_eq_max",
"id",
"Cardinal.aleph0",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"LinearOrder.toMax",
"Cardinal.instConditionallyCompleteLinearOrderBot",
... | true |
_private.Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong.0._auto_83 | Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.Name.mkStr2",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
CategoryTheory.Iso.cancel_iso_hom_left._simp_2 | Mathlib.CategoryTheory.Iso | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Iso",
"CategoryTheory.Iso.cancel_iso_hom_left",
"propext",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTheory.Iso.hom",
"Eq",
"CategoryTheory.Category"
] | false |
DerivedCategory.instHasZeroObject | Mathlib.Algebra.Homology.DerivedCategory.Basic | [
"CategoryTheory.Abelian.toPreadditive",
"instCategoryDerivedCategory",
"HomologicalComplex.instCategory",
"DerivedCategory",
"DerivedCategory.Q",
"CategoryTheory.Functor.hasZeroObject_of_additive",
"AddGroupWithOne.toAddMonoidWithOne",
"AddRightCancelSemigroup.toAddSemigroup",
"AddCancelMonoid.toAdd... | true |
Part._sizeOf_inst | Mathlib.Data.Part | [
"Part",
"Part._sizeOf_1",
"SizeOf.mk",
"SizeOf"
] | false |
idealFactorsEquivOfQuotEquiv._proof_6 | Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas | [
"OrderHom.id",
"CommRing",
"Dvd.dvd",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"IsScalarTower.right",
"CommRing.toNonUnitalCommRing",
"idealFactorsFunOfQuotHom_comp",
"congrArg",
"CommSemiring.toSemiring",
"Submodule.instNonUnitalSemiring",
"RingEquiv.instEquivLike... | false |
Lean.Elab.Structural.State | Lean.Elab.PreDefinition.Structural.Basic | [
"Lean.Elab.Structural.State.mk"
] | true |
TannakaDuality.FiniteGroup.equivHom._proof_3 | Mathlib.RepresentationTheory.Tannaka | [
"Eq.mpr",
"MonoidHom.instMonoidHomClass",
"MulOne.toOne",
"CommRing",
"MonoidHom.instFunLike",
"CategoryTheory.CategoryStruct.toQuiver",
"CategoryTheory.NatTrans.ext'",
"MonoidHom",
"Quiver.Hom",
"ModuleCat",
"Monoid.toMulOneClass",
"LinearMap.ext",
"congrArg",
"CommSemiring.toSemiring",
... | false |
HahnModule.instAddCommMonoid._proof_8 | Mathlib.RingTheory.HahnSeries.Multiplication | [
"HahnModule.instZero",
"HahnModule.instAddCommMonoid._aux_6",
"SMul",
"AddMonoid.toAddZeroClass",
"AddMonoid.nsmul_zero._autoParam",
"HahnModule",
"AddZeroClass.toAddZero",
"PartialOrder",
"instOfNatNat",
"autoParam",
"AddCommMonoid",
"AddZero.toZero",
"Nat",
"HahnSeries.instAddMonoid._pro... | false |
groupHomology.chainsMap_f_hom | Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality | [
"Rep.V",
"CommRing",
"MonoidHom.instFunLike",
"Finsupp.module",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"MonoidHom",
"Quiver.Hom",
"ModuleCat",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Rep.hV2",
"AddM... | true |
_private.Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic.0.ValueDistribution.proximity_mul_top_le._simp_1_2 | Mathlib.Analysis.Complex.ValueDistribution.Proximity.Basic | [
"Norm.norm",
"Real",
"HMul.hMul",
"Mul",
"Norm",
"norm_mul",
"NormMulClass",
"Real.instMul",
"Eq.symm",
"Eq",
"instHMul"
] | false |
HopfAlgCat.instMonoidalCategoryStruct._proof_1 | Mathlib.Algebra.Category.HopfAlgCat.Monoidal | [
"CommRing",
"HopfAlgebraStruct.toBialgebra",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"IsScalarTower",
"Algebra.toModule",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"HopfAlgCat",
"NonAssocRing.toNonUnitalNonAssocRing",
"IsScalarTower.left",
"NonUnitalNonAssocSemiring.toAddCom... | false |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.