name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
CommRingCat.commRingObj._aux_1 | Mathlib.Algebra.Category.Ring.Limits | [
"CategoryTheory.Functor",
"CommRing",
"CommRingCat.carrier",
"CommSemiring.toSemiring",
"CommRingCat",
"CommRingCat.instConcreteCategoryRingHomCarrier",
"CategoryTheory.Functor.comp",
"RingHom",
"CommRingCat.instCategory",
"CommRing.toCommSemiring",
"RingHom.instFunLike",
"CategoryTheory.types... | false |
AddMonoidAlgebra.uniqueAlgEquiv | Mathlib.Algebra.MonoidAlgebra.Basic | [
"AddMonoidAlgebra.semiring",
"RingEquiv.toEquiv",
"Unique",
"AddMonoidAlgebra.algebra",
"AddMonoidAlgebra.uniqueAlgEquiv._proof_1",
"Algebra",
"Distrib.toAdd",
"AlgEquiv.mk",
"AddMonoidAlgebra.uniqueAlgEquiv._proof_3",
"CommSemiring",
"Distrib.toMul",
"AlgEquiv",
"NonAssocSemiring.toNonUnita... | true |
TestFunction.instAddCommGroup._proof_8 | Mathlib.Analysis.Distribution.TestFunction | [
"TestFunction.instZero",
"Real",
"instHSMul",
"NormedSpace",
"AddMonoid.toAddSemigroup",
"TestFunction.toTestFunctionClass",
"TestFunction.instAddCommGroup._proof_2",
"DistribMulAction.toDistribSMul",
"AddMonoid.nat_smulCommClass'",
"Function.Injective.subNegMonoid._proof_7",
"NormedSpace.toModu... | false |
Homeomorph.preimageImageRestrict._proof_2 | Mathlib.Topology.IsClosedRestrict | [
"congrArg",
"Compl.compl",
"Membership.mem",
"Set.Elem",
"Topology.reorderRestrictProd_mem_preimage_image_restrict",
"Topology.reorderRestrictProd",
"Prod.mk",
"Topology.reorderRestrictProd_of_mem",
"Set.instCompl",
"Prod.fst",
"Subtype.mk",
"funext",
"Set.preimage",
"Prod.ext",
"True",
... | false |
AugmentedSimplexCategory.equivAugmentedCosimplicialObject_counitIso_hom_app_left | Mathlib.AlgebraicTopology.SimplexCategory.Augmented.Basic | [
"CategoryTheory.WithInitial.equivComma._proof_2",
"CategoryTheory.Functor",
"CategoryTheory.WithInitial.mkCommaMorphism",
"CategoryTheory.CosimplicialObject.instCategoryAugmented",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.mk",
"CategoryTheory.Functor.category",
... | true |
UV.shadow_compression_subset_compression_shadow | Mathlib.Combinatorics.SetFamily.Compression.UV | [
"Iff.mpr",
"Eq.mpr",
"Finset.disjoint_of_erase_right",
"False",
"Finset.instGeneralizedBooleanAlgebra",
"Finset.shadow",
"Lattice.toSemilatticeSup",
"Finset.decidableDisjoint",
"Finset.mem_insert_self",
"outParam",
"Finset.instUnion",
"Finset.notMem_sdiff_of_notMem_left",
"Finset.instIsTrans... | true |
Lean.initFn._@.Lean.Util.SafeExponentiation.3025597618._hygCtx._hyg.4 | Lean.Util.SafeExponentiation | [
"Lean.Option",
"IO",
"Lean.Name.mkStr3",
"instOfNatNat",
"Lean.Option.Decl.mk",
"Lean.Option.register",
"Nat",
"Lean.KVMap.instValueNat",
"Lean.Name.mkStr2",
"OfNat.ofNat"
] | false |
_private.Mathlib.Algebra.Order.Ring.WithTop.0.WithBot.instPosMulStrictMono._simp_1 | Mathlib.Algebra.Order.Ring.WithTop | [
"WithBot.some",
"WithBot",
"WithBot.instLT",
"Bot.bot",
"LT.lt",
"True",
"WithBot.bot_lt_coe",
"eq_true",
"Eq",
"WithBot.bot",
"LT"
] | false |
CategoryTheory.leftDistributor_ext_left | Mathlib.CategoryTheory.Monoidal.Preadditive | [
"CategoryTheory.MonoidalCategoryStruct.whiskerLeft",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"Finite",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Limits.HasFiniteBiproducts",
"CategoryTheory.MonoidalPreadditive",
"CategoryTheory.epi_of_strongEpi",
"Nonempty.intr... | true |
Submodule.submoduleOf_sup_of_le | Mathlib.Algebra.Module.Submodule.Range | [
"Eq.mpr",
"Submodule",
"RingHomSurjective.ids",
"Lattice.toSemilatticeSup",
"congrArg",
"and_self",
"Submodule.map_comap_eq",
"Submodule.addCommMonoid",
"Submodule.completeLattice",
"PartialOrder.toPreorder",
"Submodule.map_sup",
"Preorder.toLE",
"Membership.mem",
"CompleteLattice.toCondit... | true |
Lean.Elab.Tactic.evalSimpArithBang._regBuiltin.Lean.Elab.Tactic.evalSimpArithBang_1 | Lean.Elab.Tactic.SimpArith | [
"Lean.Elab.Tactic.tacticElabAttribute",
"IO",
"Unit",
"Lean.Elab.Tactic.evalSimpArithBang",
"Lean.Elab.Tactic.Tactic",
"Lean.Name.mkStr4",
"Lean.KeyedDeclsAttribute.addBuiltin"
] | false |
_private.Lean.Environment.0.Lean.ImportedModule.rec | Lean.Environment | [
"Lean.EffectiveImport",
"Lean.CompactedRegion",
"_private.Lean.Environment.0.Lean.ImportedModule.mk",
"Array",
"Bool",
"_private.Lean.Environment.0.Lean.ImportedModule",
"Lean.ModuleData",
"Prod",
"Option"
] | false |
LinearEquiv.toEquiv | Mathlib.Algebra.Module.Equiv.Defs | [
"RingHom",
"Equiv",
"LinearEquiv.toAddEquiv",
"AddCommMonoid",
"RingHomInvPair",
"LinearEquiv",
"Semiring",
"AddCommSemigroup.toAddCommMagma",
"AddEquiv.toEquiv",
"Module",
"AddCommMonoid.toAddCommSemigroup",
"Semiring.toNonAssocSemiring",
"AddCommMagma.toAdd"
] | true |
CategoryTheory.Grothendieck.fiber_eqToHom | Mathlib.CategoryTheory.Grothendieck | [
"CategoryTheory.Cat.category",
"CategoryTheory.Grothendieck.fiber_eqToHom._proof_1",
"CategoryTheory.Functor",
"CategoryTheory.Grothendieck.fiber",
"CategoryTheory.Grothendieck.base",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.eqToHom",
"CategoryTheory.Grothendieck",
"... | true |
_private.Mathlib.Topology.MetricSpace.Bounded.0.Metric.comap_dist_right_atTop._simp_1_1 | Mathlib.Topology.MetricSpace.Bounded | [
"Real",
"Real.instLT",
"Membership.mem",
"Metric.ball",
"Metric.mem_ball",
"PseudoMetricSpace",
"LT.lt",
"propext",
"Dist.dist",
"PseudoMetricSpace.toDist",
"Eq",
"Set.instMembership",
"Set"
] | false |
Stream'.get_even | Mathlib.Data.Stream.Init | [
"Eq.mpr",
"Stream'.get_succ",
"HMul.hMul",
"congrArg",
"_private.Mathlib.Data.Stream.Init.0.Stream'.get_even.match_1_1",
"Stream'.even",
"Nat.brecOn",
"id",
"instMulNat",
"instOfNatNat",
"Nat.below",
"Stream'",
"instHAdd",
"Stream'.get",
"HAdd.hAdd",
"Stream'.tail_even",
"Nat",
"in... | true |
List.bagInter.match_1.congr_eq_3 | Mathlib.Data.List.Lattice | [
"Eq.mpr",
"False",
"Nat.ne_of_beq_eq_false",
"congrArg",
"Nat.shiftRight",
"id",
"Nat.hasNotBit",
"instOfNatNat",
"List.rec",
"List.cons",
"Nat.land",
"List",
"heq_of_eq",
"absurd",
"List.bagInter.match_1",
"Nat",
"List.casesOn",
"Bool",
"Eq.ndrec",
"Eq.refl",
"HEq",
"List.... | true |
rothNumberNat_le_ruzsaSzemerediNumberNat' | Mathlib.Combinatorics.Extremal.RuzsaSzemeredi | [
"CharP.cast_eq_zero",
"Nat.cast_mul._simp_1",
"add_sub_assoc",
"add_mul",
"Real.instIsOrderedRing",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Nat.instCanonicallyOrderedAdd",
"NonAssocSemiring.toAddCommMonoidWithOne",
"div_le_iff₀",
"le_refl",
"Mathlib.Meta.NormNum.isNat_add",
"Real.partia... | true |
_private.Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral.0.integral_gaussian_complex._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral | [
"Complex.instAlgebraOfReal",
"Real",
"CommSemiring.toSemiring",
"RingHom",
"algebraMap",
"Algebra.id",
"Complex.ofReal",
"RingHom.instFunLike",
"Complex.coe_algebraMap",
"Complex",
"Eq.symm",
"Semiring.toNonAssocSemiring",
"Eq",
"DFunLike.coe",
"Real.instCommSemiring",
"Complex.instSem... | false |
mem_subalgebraOfSubring._simp_1 | Mathlib.Algebra.Algebra.Subalgebra.Basic | [
"Subalgebra.instSetLike",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"Membership.mem",
"mem_subalgebraOfSubring",
"Int",
"Subring",
"Ring.toIntAlgebra",
"propext",
"Subalgebra",
"Int.instCommSemiring",
"subalgebraOfSubring",
"Ring.toSemiring",
"Eq",
"Ring",
"SetLike.instMembership"
... | false |
_private.Lean.Elab.DocString.0.Lean.Doc.elabBlock.withSpace | Lean.Elab.DocString | [
"String.endsWith",
"String",
"instDecidableEqBool",
"Bool.true",
"instAppendString",
"instHAppendOfAppend",
"String.Slice.Pattern.BackwardSliceSearcher.instBackwardPattern_1",
"Bool",
"Eq",
"HAppend.hAppend",
"ite"
] | true |
Setoid.instPartialOrder | Mathlib.Data.Setoid.Basic | [
"LT.mk",
"Setoid.instPartialOrder._proof_2",
"Preorder.mk",
"PartialOrder",
"Setoid.instPartialOrder._proof_3",
"Setoid",
"LE.le",
"And",
"Setoid.instLE_mathlib",
"Setoid.instPartialOrder._proof_1",
"Setoid.instPartialOrder._proof_4",
"Not",
"PartialOrder.mk"
] | true |
AlgHom.toLieHom_apply | Mathlib.Algebra.Lie.OfAssociative | [
"LieHom",
"CommRing",
"AlgHom",
"AlgHom.funLike",
"Algebra",
"CommRing.toCommSemiring",
"LieRing.ofAssociativeRing",
"LieHom.instFunLike",
"AlgHom.toLieHom",
"Ring.toSemiring",
"Eq",
"DFunLike.coe",
"LieAlgebra.ofAssociativeAlgebra",
"Ring",
"rfl"
] | true |
_private.Lean.Elab.Do.Legacy.0.Lean.Elab.Term.extractBind.match_4 | Lean.Elab.Do.Legacy | [
"Option.ctorIdx",
"Option.some",
"Lean.Expr",
"Nat.hasNotBit",
"_private.Lean.Elab.Do.Legacy.0.Lean.Elab.Term.extractBind._sparseCasesOn_4",
"Option"
] | false |
Derivation.map_smul_of_tower | Mathlib.RingTheory.Derivation.Basic | [
"Derivation",
"Derivation.toLinearMap",
"instHSMul",
"CommSemiring.toSemiring",
"SMul",
"Algebra",
"Algebra.toModule",
"Derivation.instFunLike",
"AddCommMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"HSMul.hSMul",
"Lin... | true |
MeasureTheory.IsStoppingTime | Mathlib.Probability.Process.Stopping | [
"MeasurableSet",
"MeasureTheory.Filtration.seq",
"WithTop.instPreorder",
"setOf",
"Preorder.toLE",
"MeasureTheory.Filtration",
"LE.le",
"WithTop.some",
"MeasurableSpace",
"Preorder",
"WithTop"
] | true |
List.Perm.trans | Init.Data.List.Basic | [
"List.Perm",
"List.Perm.trans",
"List"
] | true |
_private.Mathlib.Analysis.SpecialFunctions.Complex.Circle.0.Circle.exp_inj._simp_1_1 | Mathlib.Analysis.SpecialFunctions.Complex.Circle | [
"AddCommGroup.ModEq",
"instHSMul",
"AddCommGroup.toAddCommMonoid",
"HSub.hSub",
"AddCommGroup.toAddGroup",
"Exists",
"AddCommGroup",
"Int",
"SubNegMonoid.toSub",
"instHSub",
"AddGroup.toSubNegMonoid",
"AddCommGroup.modEq_iff_zsmul'",
"propext",
"HSMul.hSMul",
"Eq",
"SubNegMonoid.toZSMu... | false |
LaurentPolynomial.isLocalization | Mathlib.Algebra.Polynomial.Laurent | [
"LaurentPolynomial.T",
"Eq.mpr",
"LaurentPolynomial.mul_T_assoc",
"Int.instAddCommMonoid",
"AddMonoidAlgebra.semiring",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"HMul.hMul",
"CommRing.toNonUnitalCommRing",
"Monoid.toMulOneClass",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZ... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Basic.0.SimpleGraph.adj_incidenceSet_inter._simp_1_3 | Mathlib.Combinatorics.SimpleGraph.Basic | [
"Set.mem_inter_iff",
"Membership.mem",
"Set.instInter",
"Inter.inter",
"And",
"propext",
"Eq",
"Set.instMembership",
"Set"
] | false |
Quaternion.instGroupWithZero._proof_7 | Mathlib.Algebra.Quaternion | [
"Nontrivial",
"NegZeroClass.toNeg",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"LinearOrder",
"Quaternion.instNontrivial",
"AddGroupWithOne.toAddMonoidWithOne",
"IsStrictOrderedRing",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"SemilatticeInf.toPartialOrder",... | false |
SimpleGraph.diam_anti_of_ediam_ne_top | Mathlib.Combinatorics.SimpleGraph.Diam | [
"SimpleGraph.ediam_anti",
"instTopENat",
"SimpleGraph.ediam",
"Ne",
"LE.le",
"instLENat",
"ENat.toNat_le_toNat",
"SimpleGraph",
"Nat",
"ENat",
"Top.top",
"SimpleGraph.diam",
"SimpleGraph.instLE"
] | true |
_private.Lean.Parser.Term.Basic.0.Lean.Parser.Term.initFn._@.Lean.Parser.Term.Basic.2382944618._hygCtx._hyg.2 | Lean.Parser.Term.Basic | [
"Lean.Parser.registerBuiltinParserAttribute",
"Lean.Name.mkNum",
"IO",
"Lean.Parser.LeadingIdentBehavior.default",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Unit",
"Nat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4"
] | false |
Isometry.mapsTo_emetric_closedBall | Mathlib.Topology.MetricSpace.Isometry | [
"Isometry.mapsTo_closedEBall",
"PseudoEMetricSpace",
"Set.MapsTo",
"ENNReal",
"Metric.closedEBall",
"Isometry"
] | true |
Std.HashMap.Raw.emptyWithCapacity | Std.Data.HashMap.Raw | [
"instOfNatNat",
"Std.HashMap.Raw",
"Nat",
"Std.HashMap.Raw.mk",
"optParam",
"OfNat.ofNat",
"Std.DHashMap.Raw.emptyWithCapacity"
] | true |
SheafOfModules.Presentation.IsFinite.casesOn | Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent | [
"SheafOfModules.Presentation.IsFinite.mk",
"CategoryTheory.Functor",
"Opposite",
"AddCommGrpCat.hasLimitsOfShape",
"CategoryTheory.CategoryStruct.toQuiver",
"AddCommGrpCat.instCategory",
"Quiver.Hom",
"ModuleCat",
"CategoryTheory.Limits.WalkingParallelPair",
"AddCommGroup.toAddCommMonoid",
"Shea... | false |
Lean.Elab.Term.Do.ToTerm.Kind.nestedSBC | Lean.Elab.Do.Legacy | [
"Lean.Elab.Term.Do.ToTerm.Kind.nestedSBC",
"Lean.Elab.Term.Do.ToTerm.Kind"
] | true |
_private.Mathlib.Tactic.GRewrite.Core.0.Lean.MVarId.grewrite._sparseCasesOn_1 | Mathlib.Tactic.GRewrite.Core | [
"Nat.ne_of_beq_eq_false",
"Nat.shiftRight",
"Nat.rec",
"Nat.hasNotBit",
"instOfNatNat",
"Nat.land",
"Nat",
"Bool",
"Nat.ctorIdx",
"Nat.zero",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Nat.succ"
] | false |
_private.Mathlib.Combinatorics.SimpleGraph.Paths.0.SimpleGraph.Walk.IsCycle.reverse._simp_1_2 | Mathlib.Combinatorics.SimpleGraph.Paths | [
"SimpleGraph.Walk.support",
"SimpleGraph.Walk",
"List.tail",
"SimpleGraph",
"List.Nodup",
"propext",
"SimpleGraph.Walk.nodup_tail_support_reverse",
"SimpleGraph.Walk.reverse",
"Eq"
] | false |
Lean.Server.Watchdog.ServerRequestData.freshServerRequestID | Lean.Server.Watchdog | [
"Nat",
"Lean.Server.Watchdog.ServerRequestData"
] | true |
Ring.inverse_non_unit | Mathlib.Algebra.GroupWithZero.Units.Basic | [
"Units.val",
"IsUnit",
"Classical.propDecidable",
"Exists",
"Units",
"Ring.inverse",
"dif_neg",
"IsUnit.instDecidableOfExistsUnitsEqVal",
"MonoidWithZero",
"Inv.inv",
"MonoidWithZero.toMulZeroOneClass",
"IsUnit.unit",
"Zero.toOfNat0",
"MulZeroOneClass.toMulZeroClass",
"OfNat.ofNat",
"E... | true |
HasDerivAt.nonpos_of_antitone | Mathlib.Analysis.Calculus.Deriv.Slope | [
"NormedCommRing.toSeminormedCommRing",
"OrderTopology",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NormedSpace.toIsBoundedSMul",
"IsTopologicalRing.toIsTopologicalSemiring",
"Antitone.antitoneOn",
"congrArg",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsTopologicalSe... | true |
Module.Basis.addSubgroupOfClosure._proof_1 | Mathlib.LinearAlgebra.Basis.Submodule | [
"Eq.mpr",
"Submodule",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"AddSubgroup.instPartialOrder",
"Preorder.toLE",
"AddCommGroup.toAddGroup",
"AddCommGroup",
"id",
"OrderIso",
"Submodule.instPartialOrder",
"Int",
"Module.Basis.instFu... | false |
CategoryTheory.Limits.PushoutCocone.ext | Mathlib.CategoryTheory.Limits.Shapes.Pullback.PullbackCone | [
"CategoryTheory.Limits.WalkingSpan",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.PushoutCocone.ext._auto_1",
"CategoryTheory.Limits.PushoutCocone.inr",
"CategoryTheory.Iso",
"CategoryTheory.Limits.PushoutCocone.inl",
"CategoryTheory.Limits.WalkingPair",
"autoParam"... | true |
ProbabilityTheory.Kernel.condKernelReal.eq_1 | Mathlib.Probability.Kernel.Disintegration.StandardBorel | [
"Real",
"ProbabilityTheory.IsFiniteKernel",
"ProbabilityTheory.Kernel.condKernelCDF",
"ProbabilityTheory.Kernel.isCondKernelCDF_condKernelCDF",
"ProbabilityTheory.Kernel.condKernelReal",
"MeasurableSpace",
"Real.measurableSpace",
"Eq.refl",
"MeasurableSpace.CountablyGenerated",
"Prod",
"Eq",
"... | true |
Nonempty.some | Mathlib.Logic.Nonempty | [
"Classical.choice",
"Nonempty"
] | true |
_private.Mathlib.Order.Filter.AtTopBot.Archimedean.0.Filter.map_add_atTop_eq._simp_1_1 | Mathlib.Order.Filter.AtTopBot.Archimedean | [
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"AddRightMono",
"AddZeroClass.toAddZero",
"LE.le",
"LE",
"SubNegMonoid.toSub",
"instHAdd",
"AddGroup",
"instHSub",
"AddGroup.toSubNegMonoid",
"HAdd.hAdd",
"propext",
"AddZero.toAdd",
"le_sub_iff_add_le",
"SubNegMonoid.toAddMonoid",
"Eq"
] | false |
Lagrange.eval_basis_of_ne | Mathlib.LinearAlgebra.Lagrange | [
"Iff.mpr",
"Eq.mpr",
"Polynomial.eval",
"Polynomial.eval_prod",
"IsDomain.to_noZeroDivisors",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"congrArg",
"CommSemiring.toSemiring",
"Finset",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Membership.mem",
"Exist... | true |
Lean.registerOption | Lean.Data.Options | [
"Pure.pure",
"instMonadExceptOfMonadExceptOf",
"IO.instMonadLiftSTRealWorldBaseIO",
"Monad.toApplicative",
"String",
"MonadExcept.throw",
"ST.Ref.set",
"instMonadLiftT",
"IO",
"instMonadExceptOfEIO",
"Lean.OptionDecl",
"ST.Ref.get",
"Lean.initializing",
"IO.RealWorld",
"instDecidableEqBo... | true |
TensorProduct.norm_map | Mathlib.Analysis.InnerProductSpace.TensorProduct | [
"LinearIsometry",
"Norm.norm",
"InnerProductSpace.toNormedSpace",
"Real",
"LinearIsometry.norm_map",
"CommSemiring.toSemiring",
"TensorProduct.mapIsometry",
"AddCommGroup.toAddCommMonoid",
"TensorProduct.addCommMonoid",
"NormedSpace.toModule",
"LinearMap.instFunLike",
"PseudoMetricSpace.toUnif... | true |
Finsupp.sum_ite_eq | Mathlib.Algebra.BigOperators.Finsupp.Basic | [
"Finsupp.instFunLike",
"Eq.mpr",
"congrArg",
"Finset",
"AddMonoid.toAddZeroClass",
"Finsupp.sum",
"Finsupp.support",
"Membership.mem",
"AddZeroClass.toAddZero",
"id",
"AddCommMonoid",
"AddZero.toZero",
"Finset.instSetLike",
"Zero.toOfNat0",
"Eq.refl",
"AddCommMonoid.toAddMonoid",
"Fi... | true |
Lean.PersistentHashMap.mk.injEq | Lean.Data.PersistentHashMap | [
"Eq.propIntro",
"Lean.PersistentHashMap.Node",
"Lean.PersistentHashMap.mk.inj",
"Lean.PersistentHashMap",
"Lean.PersistentHashMap.mk",
"Eq.ndrec",
"Eq.refl",
"Hashable",
"BEq",
"Eq"
] | true |
Lean.ExternEntry.inline.noConfusion | Lean.Compiler.ExternAttr | [
"String",
"Lean.ExternEntry.inline",
"id",
"Lean.ExternEntry.noConfusion",
"Lean.Name",
"Eq",
"Lean.ExternEntry"
] | false |
FirstOrder.Language.Term.inhabitedOfConstant | Mathlib.ModelTheory.Syntax | [
"Inhabited.default",
"FirstOrder.Language.Constants.term",
"FirstOrder.Language.Term",
"FirstOrder.Language.Constants",
"Inhabited",
"FirstOrder.Language",
"Inhabited.mk"
] | true |
Mathlib.Tactic.Order.AtomicFact.le.sizeOf_spec | Mathlib.Tactic.Order.CollectFacts | [
"Mathlib.Tactic.Order.AtomicFact.le",
"Lean.Expr",
"instOfNatNat",
"Mathlib.Tactic.Order.AtomicFact._sizeOf_inst",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"instAddNat",
"Eq.refl",
"instSizeOfNat",
"Mathlib.Tactic.Order.AtomicFact",
"OfNat.ofNat",
"Eq",
"Lean.Expr._sizeOf_inst"
] | true |
OrderDual.instSemigroup | Mathlib.Algebra.Order.Group.Synonym | [
"Semigroup",
"Semigroup.toMul",
"Semigroup.mul_assoc",
"Semigroup.mk",
"OrderDual.instMul",
"OrderDual"
] | true |
EReal.instInv | Mathlib.Data.EReal.Inv | [
"Inv",
"EReal",
"Inv.mk",
"EReal.inv"
] | true |
RegularSpace.inf | Mathlib.Topology.Separation.Regular | [
"cond",
"Iff.mpr",
"Eq.mpr",
"iInf",
"inf_eq_iInf",
"CompleteLattice.toLattice",
"RegularSpace",
"congrArg",
"CompleteLattice.toConditionallyCompleteLattice",
"TopologicalSpace.instCompleteLattice",
"id",
"Bool.forall_bool",
"SemilatticeInf.toMin",
"regularSpace_iInf",
"CompleteLattice.t... | true |
Fin.reduceBin | Lean.Meta.Tactic.Simp.BuiltinSimprocs.Fin | [
"Pure.pure",
"Lean.Expr.isAppOfArity",
"_private.Lean.Meta.Tactic.Simp.BuiltinSimprocs.Fin.0.Fin.reduceOp.match_1",
"ReaderT",
"Fin.Value.n",
"Lean.Expr.appArg!",
"Lean.Meta.Simp.MethodsRef",
"Eq.rec",
"ReaderT.instMonad",
"Lean.Expr",
"Lean.Meta.MetaM",
"IO.RealWorld",
"instDecidableEqBool"... | true |
_private.Mathlib.Combinatorics.SimpleGraph.Trails.0.SimpleGraph.Walk.IsTrail.even_countP_edges_iff._simp_1_6 | Mathlib.Combinatorics.SimpleGraph.Trails | [
"Exists",
"exists_prop",
"And",
"propext",
"Eq"
] | false |
FirstOrder.Language.IsOrdered.recOn | Mathlib.ModelTheory.Order | [
"instOfNatNat",
"Nat",
"FirstOrder.Language.Relations",
"FirstOrder.Language.IsOrdered",
"FirstOrder.Language",
"OfNat.ofNat",
"FirstOrder.Language.IsOrdered.rec",
"FirstOrder.Language.IsOrdered.mk"
] | false |
DomAddAct.mk_vadd_indicatorConstLp._proof_1 | Mathlib.MeasureTheory.Function.LpSpace.DomAct.Basic | [
"Eq.mpr",
"MeasureTheory.Measure",
"MeasurableSet",
"congrArg",
"MeasureTheory.VAddInvariantMeasure",
"VAdd",
"id",
"Ne",
"HVAdd.hVAdd",
"MeasurableSpace",
"Set.preimage",
"ENNReal",
"instHVAdd",
"instTopENNReal",
"Top.top",
"MeasureTheory.VAddInvariantMeasure.measure_preimage_vadd",
... | false |
HasEnoughRootsOfUnity.finite_rootsOfUnity | Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity | [
"Int.cast",
"Eq.mpr",
"MulOne.toOne",
"Nat.instMulZeroClass",
"Subgroup.instSubgroupClass",
"ZMod.cast",
"ZMod.commRing",
"IsCyclic.exists_generator",
"Monoid.toMulOneClass",
"congrArg",
"Finite",
"ZMod.fintype",
"DivInvMonoid.toZPow",
"HasEnoughRootsOfUnity.rootsOfUnity_isCyclic",
"Memb... | true |
_private.Mathlib.Order.Filter.Map.0.Filter.mem_comap_prodMk._simp_1_5 | Mathlib.Order.Filter.Map | [
"eq_comm",
"propext",
"Eq"
] | false |
Submodule.spanRank_finite_iff_fg._simp_1 | Mathlib.Algebra.Module.SpanRank | [
"Submodule",
"Preorder.toLT",
"Cardinal",
"PartialOrder.toPreorder",
"Submodule.spanRank_finite_iff_fg",
"Cardinal.aleph0",
"Submodule.FG",
"AddCommMonoid",
"Cardinal.partialOrder",
"LT.lt",
"propext",
"Semiring",
"Module",
"Eq",
"Submodule.spanRank"
] | false |
MvPolynomial.decomposition | Mathlib.RingTheory.MvPolynomial.Homogeneous | [
"Submodule",
"DirectSum.Decomposition",
"Nat.instMulZeroClass",
"Submodule.addSubmonoidClass",
"Semiring.toModule",
"Nat.instOne",
"AddMonoidAlgebra.addAddCommMonoid",
"CommSemiring.toSemiring",
"MvPolynomial.homogeneousSubmodule",
"CommSemiring",
"Pi.instOne",
"Nat",
"Submodule.setLike",
... | true |
Lean.pp.safeShadowing | Lean.PrettyPrinter.Delaborator.Options | [
"Inhabited.default",
"instInhabitedBool",
"Lean.Option",
"Lean.instInhabitedOption",
"Bool"
] | true |
CategoryTheory.Over.coprod._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts | [
"CategoryTheory.Over",
"CategoryTheory.Over.OverMorphism.ext",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Over.coprodObj._proof_1",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.instCategoryOve... | false |
CategoryTheory.Distributive.«_aux_Mathlib_CategoryTheory_Distributive_Monoidal___macroRules_CategoryTheory_Distributive_term∂R_1» | Mathlib.CategoryTheory.Distributive.Monoidal | [
"Pure.pure",
"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",
"Lean.Name.mkStr3",
"ReaderT.instMo... | false |
_private.Mathlib.MeasureTheory.Measure.LevyConvergence.0.MeasureTheory.isTightMeasureSet_of_tendsto_charFun._proof_1_6 | Mathlib.MeasureTheory.Measure.LevyConvergence | [
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"instAddNat",
"OfNat.ofNat",
"Nat.AtLeastTwo"
] | false |
_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.NormalizePattern.Context.mk.sizeOf_spec | Lean.Meta.Tactic.Grind.EMatchTheorem | [
"_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.NormalizePattern.Context._sizeOf_inst",
"_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.Grind.NormalizePattern.Context",
"Lean.Meta.Grind.SymbolPriorities",
"instOfNatNat",
"_private.Lean.Meta.Tactic.Grind.EMatchTheorem.0.Lean.Meta.... | true |
Lean.Kernel.Exception.unknownConstant.elim | Lean.Environment | [
"Lean.Kernel.Exception",
"PULift.up",
"Lean.Kernel.Environment",
"Lean.Kernel.Exception.unknownConstant",
"Lean.Kernel.Exception.ctorIdx",
"Nat",
"Lean.Name",
"Eq.symm",
"Eq",
"Lean.Kernel.Exception.ctorElim"
] | false |
CategoryTheory.imageOpUnop | Mathlib.CategoryTheory.Abelian.Opposite | [
"CategoryTheory.Limits.HasImages.has_image",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"Quiver.Hom.unop",
"CategoryTheory.Abelian",
"CategoryTheory.imageOpUnop._proof_1",
"CategoryTheory.Iso",
"CategoryTheory.instAbelianOpposite",
"CategoryTheory.Limits... | true |
UInt64.le_antisymm_iff | Init.Data.UInt.Lemmas | [
"UInt64",
"LE.le",
"UInt64.toNat",
"And",
"Iff",
"Nat",
"Nat.le_antisymm_iff",
"Iff.trans",
"instLEUInt64",
"Eq",
"UInt64.toNat_inj",
"Iff.symm"
] | true |
GaloisCoinsertion.liftCompleteLattice | Mathlib.Order.GaloisConnection.Basic | [
"OrderDual.toDual",
"GaloisCoinsertion.choice",
"GaloisCoinsertion.liftCompleteLattice._proof_3",
"Equiv.instEquivLike",
"OrderDual.ofDual",
"CompleteLattice.toLattice",
"PartialOrder.toPreorder",
"GaloisCoinsertion.liftCompleteLattice._proof_2",
"GaloisCoinsertion.liftCompleteLattice._proof_1",
"... | true |
_private.Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Basic.0.exists_continuous_add_one_of_isCompact_nnreal._simp_1_2 | Mathlib.MeasureTheory.Integral.RieszMarkovKakutani.Basic | [
"False",
"One",
"eq_false",
"One.toOfNat1",
"Zero.toOfNat0",
"NeZero",
"one_ne_zero",
"OfNat.ofNat",
"Eq",
"Zero"
] | false |
SimpleGraph.UnitDistEmbedding.mk | Mathlib.Combinatorics.SimpleGraph.UnitDistance.Basic | [
"Real",
"SimpleGraph.Adj",
"Function.Embedding",
"SimpleGraph",
"SimpleGraph.UnitDistEmbedding",
"Real.instOne",
"SimpleGraph.UnitDistEmbedding.mk",
"MetricSpace",
"One.toOfNat1",
"MetricSpace.toPseudoMetricSpace",
"Dist.dist",
"PseudoMetricSpace.toDist",
"Function.instFunLikeEmbedding",
"... | true |
isProperMap_iff_isCompact_preimage | Mathlib.Topology.Maps.Proper.CompactlyGenerated | [
"CompactlyCoherentSpace",
"Iff.mpr",
"Set.ext",
"Eq.mpr",
"Continuous",
"continuous_subtype_val",
"congrArg",
"and_self",
"HEq.refl",
"CompactlyCoherentSpace.isClosed_iff",
"IsCompact.inter_left",
"Set.mem_image._simp_1",
"Subtype.casesOn",
"Membership.mem",
"Exists",
"Set.Elem",
"Se... | true |
LinearMap.instDistribMulActionDomMulActOfSMulCommClass._proof_2 | Mathlib.Algebra.Module.LinearMap.Basic | [
"Monoid",
"DomMulAct",
"MulOne.toOne",
"instHSMul",
"Monoid.toMulOneClass",
"LinearMap.ext",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"RingHom",
"AddZeroClass.toAddZero",
"DomMulAct.instMonoidOfMulOpposite",
"DistribSMul.toSMulZeroClass",
"LinearMap.toAddHom",
"LinearM... | false |
_private.Mathlib.Analysis.Normed.Group.Bounded.0.Bornology.IsBounded.exists_pos_norm_le'.match_1_1 | Mathlib.Analysis.Normed.Group.Bounded | [
"Norm.norm",
"Real.instLE",
"Real",
"SeminormedGroup",
"Membership.mem",
"Exists",
"LE.le",
"Exists.casesOn",
"SeminormedGroup.toNorm",
"Exists.intro",
"Set.instMembership",
"Set"
] | false |
LinearMap.BilinForm.SeparatingRight.toMatrix | Mathlib.LinearAlgebra.Matrix.BilinearForm | [
"Iff.mpr",
"CommRing",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Matrix.module",
"LinearMap.BilinForm",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"Matrix",
"LinearMap.instSMulCommClass",
"LinearMap.BilinForm.toMatrix",
"AddCommGroup"... | true |
NumberField.mixedEmbedding.convexBodySum_isBounded | Mathlib.NumberTheory.NumberField.CanonicalEmbedding.ConvexBody | [
"Iff.mpr",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"Prod.seminormedAddGroup",
"NumberField.mixedEmbedding.convexBodySumFun",
"Real.instLE",
"Real",
"NumberField.mixedEmbedding.convexBodySum",
"pseudoMetricSpacePi",
"NumberField.mixedEmbedding.... | true |
Mathlib.Meta.Nat.UnifyZeroOrSuccResult.succ.noConfusion | Mathlib.Tactic.NormNum.BigOperators | [
"Qq.QuotedDefEq",
"Lean.Expr.const",
"id",
"Lean.Expr.sort",
"Lean.Level",
"heq_of_eq",
"Qq.Quoted",
"Lean.Level.zero",
"Mathlib.Meta.Nat.UnifyZeroOrSuccResult.succ",
"Qq.Quoted.unsafeMk",
"Mathlib.Meta.Nat.UnifyZeroOrSuccResult.noConfusion",
"Mathlib.Meta.Nat.UnifyZeroOrSuccResult",
"Lean.N... | false |
Filter.EventuallyEq.isTheta | Mathlib.Analysis.Asymptotics.Theta | [
"Norm",
"Filter.EventuallyEq",
"Asymptotics.IsTheta",
"Filter.EventuallyEq.trans_isTheta",
"Asymptotics.isTheta_rfl",
"Filter"
] | true |
Std.DTreeMap.Const.minKey!_modify_eq_minKey! | Std.Data.DTreeMap.Lemmas | [
"Std.DTreeMap",
"Std.DTreeMap.Const.modify",
"Ord.mk",
"Ordering",
"Std.DTreeMap.inner",
"Std.TransCmp",
"Std.LawfulEqCmp",
"Std.DTreeMap.wf",
"Std.DTreeMap.Internal.Impl.Const.minKey!_modify_eq_minKey!",
"Inhabited",
"Std.DTreeMap.minKey!",
"Eq"
] | true |
Algebra.IsUnramifiedAt.exists_hasStandardEtaleSurjectionOn | Mathlib.RingTheory.Unramified.LocalStructure | [
"Subalgebra.instSetLike",
"Iff.mpr",
"Eq.mpr",
"PrimeSpectrum.mk",
"Submodule",
"SetLike.mem_coe._simp_1",
"False",
"dvd_mul_left._simp_1",
"Semigroup.toMul",
"CommRing",
"Algebra.instIsStandardEtaleRing",
"Dvd.dvd",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"... | true |
Std.Internal.Small.casesOn | Std.Data.Iterators.Lemmas.Equivalence.HetT | [
"Std.Internal.Small",
"Std.Internal.ComputableSmall",
"Std.Internal.Small.rec",
"Nonempty",
"Std.Internal.Small.mk"
] | false |
_private.Mathlib.MeasureTheory.Measure.Restrict.0.MeasureTheory.Measure.restrictₗ._simp_2 | Mathlib.MeasureTheory.Measure.Restrict | [
"Set.instInter",
"Inter.inter",
"SDiff.sdiff",
"Set.inter_diff_assoc",
"Eq.symm",
"Eq",
"Set.instSDiff",
"Set"
] | false |
AlgebraicGeometry.PresheafedSpace.instInhabited | Mathlib.Geometry.RingedSpace.PresheafedSpace | [
"Inhabited.default",
"AlgebraicGeometry.PresheafedSpace.const",
"instTopologicalSpacePEmpty",
"PEmpty",
"Inhabited",
"AlgebraicGeometry.PresheafedSpace",
"TopCat.of",
"CategoryTheory.Category",
"Inhabited.mk"
] | true |
IsAlgClosure.of_exists_root | Mathlib.FieldTheory.Isaacs | [
"Algebra.IsIntegral.isIntegral",
"minpoly.monic",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"AlgHom",
"AlgHom.funLike",
"Polynomial.algebraOfAlgebra"... | true |
CategoryTheory.Limits.MulticospanIndex.mk | Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer | [
"CategoryTheory.Limits.MulticospanShape.snd",
"CategoryTheory.Limits.MulticospanShape.L",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.MulticospanIndex.mk",
"CategoryTheory.Limits.MulticospanIndex",
"CategoryTheory.Limits.MulticospanShape.fst",
"CategoryTheory.Categor... | true |
_private.Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula.0.WeierstrassCurve.Projective.toAffine_negAddY_of_eq._simp_1_3 | Mathlib.AlgebraicGeometry.EllipticCurve.Projective.Formula | [
"False",
"eq_false",
"four_ne_zero",
"instOfNatNat",
"Nat",
"Zero.toOfNat0",
"NeZero",
"OfNat.ofNat",
"Eq",
"OfNat",
"Zero"
] | false |
bddAbove_smul_iff_of_neg._simp_1 | Mathlib.Algebra.Order.Module.Pointwise | [
"instHSMul",
"Preorder.toLT",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"CommRing.toNonUnitalCommRing",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LinearOrder",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"IsStrictOrderedRing",
"NonUnitalNonAssocSemiring... | false |
Matrix.frobeniusNormedRing._proof_10 | Mathlib.Analysis.Matrix.Normed | [
"NormedCommRing.toNormedRing",
"Semiring.toNatCast",
"NormedRing.toRing",
"Semiring.toOne",
"AddMonoid.toAddSemigroup",
"Semiring.natCast_succ",
"Matrix",
"Matrix.instRing",
"NonUnitalSemiring.toNonUnitalNonAssocSemiring",
"instOfNatNat",
"NatCast.natCast",
"RCLike.toDenselyNormedField",
"No... | false |
ByteArray.utf8Decode?.eq_1 | Init.Data.String.Basic | [
"ByteArray.utf8Decode?.go",
"instOfNatNat",
"List.toArray",
"Array",
"ByteArray.utf8Decode?._proof_1",
"Nat",
"Eq.refl",
"Char",
"ByteArray",
"OfNat.ofNat",
"ByteArray.utf8Decode?",
"Eq",
"List.nil",
"Option"
] | true |
_private.Batteries.Tactic.Init.0.Batteries.Tactic._aux_Batteries_Tactic_Init___macroRules_Batteries_Tactic_byContra_1.match_1 | Batteries.Tactic.Init | [
"Lean.TSyntax",
"Option.ctorIdx",
"Option.some",
"Nat.hasNotBit",
"List.cons",
"_private.Batteries.Tactic.Init.0.Batteries.Tactic._aux_Batteries_Tactic_Init___macroRules_Batteries_Tactic_byContra_1._sparseCasesOn_1",
"Lean.SyntaxNodeKind",
"Lean.Name.mkStr1",
"List.nil",
"Option"
] | false |
MvFunctor.exists_iff_exists_of_mono | Mathlib.Control.Functor.Multivariate | [
"LawfulMvFunctor.id_map",
"Eq.mpr",
"congrArg",
"Exists",
"id",
"TypeVec.comp",
"LawfulMvFunctor",
"Iff",
"Exists.casesOn",
"Nat",
"True",
"Iff.intro",
"MvFunctor",
"propext",
"Exists.intro",
"Iff.mp",
"eq_true",
"of_eq_true",
"congrFun'",
"TypeVec.Arrow",
"Eq",
"MvFunctor.... | true |
Lean.Lsp.SemanticTokenType.ctorElimType | Lean.Data.Lsp.LanguageFeatures | [
"cond",
"Lean.Lsp.SemanticTokenType.comment",
"Lean.Lsp.SemanticTokenType.function",
"Lean.Lsp.SemanticTokenType.typeParameter",
"Lean.Lsp.SemanticTokenType.macro",
"Lean.Lsp.SemanticTokenType.leanSorryLike",
"Lean.Lsp.SemanticTokenType.operator",
"Nat.ble",
"Lean.Lsp.SemanticTokenType.method",
"L... | false |
Subgroup.HasDetOne.recOn | Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | [
"CommRing",
"Subgroup.HasDetOne",
"MonoidHom.instFunLike",
"MonoidHom",
"CommSemiring.toSemiring",
"Matrix",
"Membership.mem",
"Units",
"Subgroup",
"Units.instGroup",
"Units.instOne",
"Subgroup.HasDetOne.mk",
"MulOneClass.toMulOne",
"CommRing.toCommSemiring",
"Fintype",
"One.toOfNat1",... | false |
String.Pos.next.congr_simp | Init.Data.String.Basic | [
"String.Pos.next",
"String",
"Eq.rec",
"Ne",
"String.endPos",
"String.Pos",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
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