name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
MeasureTheory.measureReal_biUnion_finset₀ | Mathlib.MeasureTheory.Measure.Real | [
"Real",
"MeasureTheory.Measure",
"Function.onFun",
"ENNReal.instAddCommMonoid",
"congrArg",
"Finset",
"MeasureTheory.NullMeasurableSet",
"MeasureTheory.Measure.real",
"Membership.mem",
"MeasureTheory.measureReal_biUnion_finset₀._auto_1",
"Ne",
"Set.Pairwise",
"MeasureTheory.AEDisjoint",
"a... | true |
IsCyclotomicExtension.Rat.inertiaDeg_span_zeta_sub_one | Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal | [
"instPowNat",
"Eq.mpr",
"Nat.instMulZeroOneClass",
"IsDedekindDomain.toIsDomain",
"Nat.Prime",
"LinearOrderedCommMonoidWithZero.toIsBotZeroClass",
"Ideal.absNorm",
"Nat.instOne",
"NumberField.instCommRingRingOfIntegers",
"Nat.Prime.one_lt",
"Ideal.absNorm_eq_pow_inertiaDeg'",
"AddGroupWithOne.... | true |
_private.Lean.Elab.Tactic.Grind.BuiltinTactic.0.Lean.Elab.Tactic.Grind.showStateAt.match_1 | Lean.Elab.Tactic.Grind.BuiltinTactic | [
"Lean.Meta.Grind.Goal",
"Nat.hasNotBit",
"List.cons",
"List",
"_private.Lean.Elab.Tactic.Grind.BuiltinTactic.0.Lean.Elab.Tactic.Grind.showStateAt._sparseCasesOn_1",
"List.ctorIdx"
] | false |
HasProdUniformly.hasProdUniformlyOn | Mathlib.Topology.Algebra.InfiniteSum.UniformOn | [
"Iff.mpr",
"UniformSpace",
"Finset",
"PartialOrder.toPreorder",
"TendstoUniformly.tendstoUniformlyOn",
"Finset.partialOrder",
"TendstoUniformlyOn",
"Finset.prod",
"Filter.atTop",
"hasProdUniformlyOn_iff_tendstoUniformlyOn",
"HasProdUniformly.tendstoUniformly",
"CommMonoid",
"HasProdUniformly... | true |
Batteries.PairingHeapImp.Heap.WF.node | Batteries.Data.PairingHeap | [
"Batteries.PairingHeapImp.Heap.WF",
"Batteries.PairingHeapImp.Heap.NodeWF",
"Batteries.PairingHeapImp.Heap",
"Bool",
"Batteries.PairingHeapImp.Heap.WF.node",
"Batteries.PairingHeapImp.Heap.nil",
"Batteries.PairingHeapImp.Heap.node"
] | true |
Lean.Meta.Grind.Arith.Linear.Struct.type | Lean.Meta.Tactic.Grind.Arith.Linear.Types | [
"Lean.Expr",
"Lean.Meta.Grind.Arith.Linear.Struct"
] | true |
Lean.Parser.Term.inferInstanceAs.formatter | Lean.Parser.Term | [
"Lean.PrettyPrinter.Formatter",
"Lean.PrettyPrinter.Formatter.orelse.formatter",
"Lean.ppSpace.formatter",
"Lean.Parser.withCache.formatter",
"Lean.Parser.leadingNode.formatter",
"instOfNatNat",
"Lean.PrettyPrinter.Formatter.withAntiquot.formatter",
"Lean.Parser.symbol.formatter",
"Bool.true",
"Na... | true |
Lean.Elab.Tactic.Do.ProofMode.Hyp.mk | Lean.Elab.Tactic.Do.ProofMode.MGoal | [
"Lean.Expr",
"Lean.Elab.Tactic.Do.ProofMode.Hyp",
"Lean.Name",
"Lean.Elab.Tactic.Do.ProofMode.Hyp.mk"
] | true |
Submodule.baseChangeOrderEmbedding_apply | Mathlib.RingTheory.Flat.FaithfullyFlat.Basic | [
"Submodule",
"CommRing",
"Algebra.to_smulCommClass",
"Semiring.toModule",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"TensorProduct.addCommMonoid",
"Submodule.baseChangeOrderEmbedding",
"PartialOrder.toPreorder",
"Algebra",
"Preorder.toLE",
"AddCommGrou... | true |
instSliceableSubarrayNat_6 | Init.Data.Slice.Array.Basic | [
"Std.Rco",
"Std.Rco.Sliceable.mkSlice",
"Subarray",
"Std.Ric.HasRcoIntersection.intersection",
"Std.Ric.Sliceable.mk",
"instSliceableArrayNatSubarray_1",
"instOfNatNat",
"Std.Ric",
"Array",
"Std.Rco.upper",
"instHAdd",
"HAdd.hAdd",
"Std.Slice.Internal.SubarrayData",
"Nat",
"Std.instHasRc... | true |
AdicCompletion.evalₐ_mkₐ | Mathlib.RingTheory.AdicCompletion.Algebra | [
"CommRing",
"Semiring.toModule",
"IsScalarTower.right",
"AdicCompletion.instAlgebraAdicCauchySequence",
"congrArg",
"CommSemiring.toSemiring",
"Ideal.Quotient.mk",
"AlgHom",
"AlgHom.funLike",
"AdicCompletion.instCommRingAdicCauchySequence",
"RingHom",
"Algebra.id",
"Ideal.instAlgebraQuotient... | true |
Height.mulHeight₁_ne_zero | Mathlib.NumberTheory.Height.Basic | [
"Real",
"Real.instZero",
"Height.AdmissibleAbsValues",
"Ne",
"Height.mulHeight₁_pos",
"LT.lt.ne'",
"Height.mulHeight₁",
"Zero.toOfNat0",
"OfNat.ofNat",
"Field",
"Real.instPreorder"
] | true |
Lean.NameGenerator.mkChild | Init.Meta.Defs | [
"Lean.Name.mkNum",
"Lean.NameGenerator.namePrefix",
"Prod.mk",
"instOfNatNat",
"Lean.NameGenerator.mk",
"instHAdd",
"HAdd.hAdd",
"Nat",
"Lean.NameGenerator.idx",
"instAddNat",
"Prod",
"OfNat.ofNat",
"Lean.NameGenerator"
] | true |
TopologicalSpace.Compacts.discreteUniformity_iff._simp_1 | Mathlib.Topology.UniformSpace.Closeds | [
"UniformSpace",
"TopologicalSpace.Compacts.uniformSpace",
"TopologicalSpace.Compacts.discreteUniformity_iff",
"propext",
"DiscreteUniformity",
"UniformSpace.toTopologicalSpace",
"Eq",
"TopologicalSpace.Compacts"
] | false |
Nat.instTrichotomousLt | Init.Data.Nat.Basic | [
"Std.Trichotomous.mk",
"Std.Trichotomous",
"Nat.ge_of_not_lt",
"Nat",
"LT.lt",
"Nat.le_antisymm",
"instLTNat",
"Not"
] | true |
Vector.scanlM.loop._unary._proof_1 | Batteries.Data.Vector.Basic | [
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"Vector.push",
"Int.natCast_add",
"of_decide_eq_true",
"le_of_le_of_eq",
"Vector",
"Lean.Omega.Constraint.mk",
"Lean.Omega.Constraint.combine_sat'",
"InvImage",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.ofNat_sub_dichotomy... | false |
_private.Init.Data.Int.DivMod.Lemmas.0.Int.neg_self_le_ediv_of_nonneg_of_nonpos._proof_1_3 | Init.Data.Int.DivMod.Lemmas | [
"Nat.lt_of_not_le",
"False",
"Lean.Omega.Constraint.not_sat'_of_isImpossible",
"of_decide_eq_true",
"le_of_le_of_eq",
"Lean.Omega.Constraint.mk",
"Int.add_one_le_of_lt",
"HSub.hSub",
"Lean.Omega.Int.add_congr",
"Lean.Omega.LinearCombo.eval",
"Option.some",
"id",
"instDecidableEqBool",
"Int... | false |
Nat.Partrec.Code.primrec₂_comp | Mathlib.Computability.PartrecCode | [
"Iff.mpr",
"Primrec.nat_double",
"Primrec.nat_add",
"HMul.hMul",
"Nat.Partrec.Code.encodeCode",
"Primrec.snd",
"Primcodable.ofDenumerable",
"Primrec₂.encode_iff",
"Nat.Partrec.Code",
"Primrec.fst",
"instMulNat",
"instOfNatNat",
"Prod.fst",
"Nat.pair",
"Primcodable.prod",
"Primrec",
"... | true |
Std.Do.SVal.curry_nil | Std.Do.SPred.SVal | [
"Std.Do.SVal.StateTuple",
"Std.Do.SVal",
"PUnit.unit",
"Std.Do.SVal.curry",
"Eq",
"rfl",
"List.nil"
] | true |
AlgebraicGeometry.IsZariskiLocalAtTarget.of_range_subset_iSup | Mathlib.AlgebraicGeometry.Morphisms.Basic | [
"AlgebraicGeometry.Scheme.Hom.opensFunctor",
"AlgebraicGeometry.PresheafedSpace.Hom",
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.Category.assoc",
"CategoryTheory.MorphismProperty.IsLocalAtTarget.toRespects",
"TopologicalSpace.Opens.coe_iSup",
"CategoryTheory.Functor",
"AlgebraicGeo... | true |
PresheafOfModules.Derivation.mk.noConfusion | Mathlib.Algebra.Category.ModuleCat.Differentials.Presheaf | [
"PresheafOfModules.map",
"CategoryTheory.Functor.op",
"CategoryTheory.Functor",
"instHSMul",
"Opposite",
"HMul.hMul",
"CommRingCat.carrier",
"Quiver.opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"PresheafOfModules.instModuleCarrierObjOppositeCommRingCatCarrierCarrierRingCatCompForget₂RingHo... | false |
Std.Internal.instLawfulMonadLiftBindFunctionIdRunOfLawfulMonad | Init.Data.Iterators.Internal.LawfulMonadLiftFunction | [
"LawfulMonad",
"Id.run",
"Id",
"Std.Internal.LawfulMonadLiftBindFunction",
"Std.Internal.LawfulMonadLiftBindFunction.mk",
"True",
"eq_self",
"of_eq_true",
"Id.instMonad",
"implies_true",
"Monad",
"Eq",
"Eq.trans",
"forall_congr"
] | true |
PSet.Subset.congr_right | Mathlib.SetTheory.ZFC.PSet | [
"PSet.instHasSubset",
"_private.Mathlib.SetTheory.ZFC.PSet.0.PSet.Subset.congr_right.match_1_5",
"PSet.Func",
"Exists",
"_private.Mathlib.SetTheory.ZFC.PSet.0.PSet.Subset.congr_right.match_1_3",
"HasSubset.Subset",
"PSet.mk",
"PSet",
"PSet.Equiv.symm",
"Iff",
"PSet.Equiv.trans",
"_private.Math... | true |
_private.Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups.0.Subgroup.hasDetPlusMinusOne_adjoinNegOne_iff._simp_1_2 | Mathlib.NumberTheory.ModularForms.ArithmeticSubgroups | [
"neg_eq_iff_eq_neg",
"InvolutiveNeg",
"propext",
"InvolutiveNeg.toNeg",
"Eq",
"Neg.neg"
] | false |
IsConformalMap.injective | Mathlib.Analysis.Normed.Operator.Conformal | [
"LinearIsometry",
"instHSMul",
"SeminormedAddCommGroup",
"Field.isDomain",
"NormedSpace",
"instIsTorsionFreeOfIsDomainOfNoZeroSMulDivisors",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousLinearMap.funLike",
"NormedSpace.toModule",
"AddMonoid.toAddZeroClass",
"Lin... | true |
OpenPartialHomeomorph.toStructomorph._proof_2 | Mathlib.Geometry.Manifold.HasGroupoid | [
"chartedSpaceSelf",
"OpenPartialHomeomorph.open_source",
"HasGroupoid",
"TopologicalSpace.Opens.instChartedSpace",
"PartialEquiv.target",
"TopologicalSpace.Opens.instHasGroupoid",
"OpenPartialHomeomorph.trans",
"TopologicalSpace.Opens",
"Membership.mem",
"Set.Elem",
"StructureGroupoid",
"Struc... | false |
Batteries.HashMap.empty | Batteries.Data.HashMap.Basic | [
"Batteries.mkHashMap",
"instOfNatNat",
"Nat",
"Hashable",
"OfNat.ofNat",
"BEq",
"Batteries.HashMap"
] | true |
LinearIsometry.extend._proof_3 | Mathlib.Analysis.InnerProductSpace.PiL2 | [
"InnerProductSpace.toNormedSpace",
"Submodule",
"Nat.instOrderedSub",
"Nat.instIsOrderedAddMonoid",
"AddLeftCancelSemigroup.toIsLeftCancelAdd",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Submodule.addCommMonoid",
"NormedSpace.toModule",
"HSub.hSub",
"NormedDivisionRing.toDivisionRing",
"Memb... | false |
PointwiseConvergenceCLM.piEquivL._proof_9 | Mathlib.Topology.Algebra.Module.Spaces.PointwiseConvergenceCLM | [
"Pi.addCommMonoid",
"LinearEquiv.right_inv",
"Pi.topologicalSpace",
"UniformConvergenceCLM.instAddCommGroup",
"ContinuousLinearEquiv.toLinearEquiv",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"PointwiseConvergenceCLM.piEquivL._proof_1",
"PointwiseConvergenceCLM.piEquivL._proof... | false |
ENNReal.add_biSup' | Mathlib.Data.ENNReal.Operations | [
"Iff.mpr",
"ENNReal.instAdd",
"congrArg",
"iSup",
"CompletelyDistribLattice.toCompleteLattice",
"iSup_subtype'",
"Exists",
"Subtype",
"ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice",
"ENNReal.add_iSup",
"instHAdd",
"nonempty_subtype",
"CompleteLinearOrder.toConditionallyCom... | true |
CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_fst | Mathlib.CategoryTheory.LocallyCartesianClosed.Over | [
"CategoryTheory.Over",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Over.Hom.left",
"CategoryTheory.Comma.left",
"CategoryTheory.ChosenPullbacksAlong.snd",
"CategoryTheory.Functor.id",
"CategoryTheory.instCategoryOver",
"CategoryTheory.ChosenPullbacksAlong.pullbackObj",
... | true |
Lean.Meta.Grind.AC.MonadGetStruct.mk._flat_ctor | Lean.Meta.Tactic.Grind.AC.Util | [
"Lean.Meta.Grind.AC.MonadGetStruct",
"Lean.Meta.Grind.AC.Struct",
"Lean.Meta.Grind.AC.MonadGetStruct.mk"
] | false |
Real.cos_add_int_mul_two_pi | Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic | [
"Int.cast",
"Function.Periodic.int_mul",
"Real",
"Real.pi",
"HMul.hMul",
"Real.cos",
"Nat.instAtLeastTwoHAddOfNat",
"instOfNatNat",
"Int",
"Real.commRing",
"CommRing.toNonAssocCommRing",
"Real.instAdd",
"instHAdd",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"Real.instMul",
"Real.cos... | true |
Matrix.instFintypeOfDecidableEq._aux_1 | Mathlib.Data.Matrix.Basic | [
"Finset.univ",
"Matrix",
"Finset",
"Pi.instFintype",
"Fintype.piFinset",
"Fintype",
"DecidableEq"
] | false |
Subalgebra.map_comap_eq_self | Mathlib.Algebra.Algebra.Subalgebra.Lattice | [
"congrArg",
"inf_of_le_left",
"AlgHom",
"PartialOrder.toPreorder",
"Algebra.instCompleteLatticeSubalgebra",
"Algebra",
"Preorder.toLE",
"CompleteLattice.toConditionallyCompleteLattice",
"Eq.mp",
"SemilatticeInf.toMin",
"LE.le",
"CommSemiring",
"Subalgebra.map",
"Subalgebra.instPartialOrder... | true |
_private.Mathlib.Topology.Algebra.InfiniteSum.SummationFilter.0.SummationFilter.support_map._proof_1_3 | Mathlib.Topology.Algebra.InfiniteSum.SummationFilter | [
"of_eq_false",
"False",
"Set.mem_range",
"forall_not_of_not_exists",
"eq_false",
"Lean.Grind.iff_eq",
"Classical.byContradiction",
"SummationFilter",
"Set.mem_image",
"Membership.mem",
"Exists",
"Eq.mp",
"id",
"Function.Embedding",
"And.casesOn",
"And",
"Iff",
"Exists.casesOn",
"... | false |
Finsupp.mapDomain_comapDomain | Mathlib.Data.Finsupp.Basic | [
"Eq.mpr",
"congrArg",
"Function.Injective.injOn",
"Finset",
"Finsupp.mapDomain",
"AddMonoid.toAddZeroClass",
"Finsupp.support",
"Function.Embedding.mk",
"Eq.rec",
"AddZeroClass.toAddZero",
"id",
"Finsupp.embDomain_comapDomain",
"HasSubset.Subset",
"AddCommMonoid",
"Function.Embedding",
... | true |
Diffeology.DSmooth.eq_1 | Mathlib.Geometry.Diffeology.Basic | [
"Real",
"Function.comp",
"Diffeology.IsPlot",
"EuclideanSpace",
"DiffeologicalSpace",
"Nat",
"Diffeology.DSmooth",
"Eq.refl",
"Fin",
"Eq"
] | true |
Std.Http.Body.Length.fixed.sizeOf_spec | Std.Internal.Http.Data.Body.Length | [
"Std.Http.Body.Length.fixed",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Std.Http.Body.Length",
"instAddNat",
"Eq.refl",
"instSizeOfNat",
"OfNat.ofNat",
"Std.Http.Body.Length._sizeOf_inst",
"Eq"
] | true |
_private.Std.Data.Iterators.Lemmas.Combinators.Monadic.Zip.0.Std.Iterators.Types.Zip.instIterator.match_5.eq_2 | Std.Data.Iterators.Lemmas.Combinators.Monadic.Zip | [
"Std.IterM.IsPlausibleOutput",
"Option.some",
"Exists",
"Subtype",
"Std.Iterator",
"Option.none",
"Eq.refl",
"Std.IterM",
"Eq",
"Std.Iterators.Types.Zip.instIterator.match_5",
"Option"
] | true |
AddAction.not_addCommute_of_disjoint_movedBy_preimage | Mathlib.GroupTheory.GroupAction.FixedPoints | [
"AddGroup.toSubtractionMonoid",
"AddMonoid.toAddSemigroup",
"CompleteBooleanAlgebra.toCompleteDistribLattice",
"congrArg",
"AddAction.movedBy_mem_fixedBy_of_addCommute",
"Compl.compl",
"Set.univ",
"OrderBot.toBot",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Set.addActionSet",
"Add... | true |
Lean.Linter.UnusedVariables.FVarDefinition.rec | Lean.Linter.UnusedVariables | [
"Lean.Syntax",
"Lean.FVarId",
"Array",
"Lean.Linter.UnusedVariables.FVarDefinition.mk",
"Lean.Name",
"Lean.Options",
"Lean.Linter.UnusedVariables.FVarDefinition"
] | false |
Lean.Parser.Term.let.formatter | Lean.Parser.Term | [
"Lean.PrettyPrinter.Formatter",
"Lean.Parser.withCache.formatter",
"Lean.Parser.Term.optSemicolon.formatter",
"Lean.Parser.leadingNode.formatter",
"instOfNatNat",
"Lean.PrettyPrinter.Formatter.withAntiquot.formatter",
"Lean.Parser.symbol.formatter",
"Lean.Parser.Term.letConfig.formatter",
"Bool.true... | true |
Submodule.ker_liftQ_eq_bot' | Mathlib.LinearAlgebra.Quotient.Basic | [
"Submodule",
"Submodule.Quotient.addCommMonoid",
"Eq.ge",
"AddCommGroup.toAddCommMonoid",
"PartialOrder.toPreorder",
"LinearMap.ker",
"RingHom",
"Submodule.hasQuotient",
"AddCommGroup",
"Eq.le",
"Submodule.instPartialOrder",
"Bot.bot",
"Submodule.Quotient.module",
"LinearMap",
"Submodule... | true |
BitVec.zero_or | Init.Data.BitVec.Lemmas | [
"instHOrOfOrOp",
"BitVec.getElem_or",
"congrArg",
"BitVec.instOrOp",
"BitVec",
"instOfNatNat",
"Bool.false_or",
"BitVec.ofNat",
"GetElem.getElem",
"HOr.hOr",
"Nat",
"LT.lt",
"True",
"eq_self",
"BitVec.getElem_zero",
"Bool",
"of_eq_true",
"Bool.or",
"BitVec.instGetElemNatBoolLt",
... | true |
Complex.ofReal_mem_slitPlane | Mathlib.Analysis.Complex.Basic | [
"False",
"Real",
"_private.Mathlib.Analysis.Complex.Basic.0.Complex.ofReal_mem_slitPlane._simp_1_1",
"Real.instZero",
"congrArg",
"Complex.im",
"Real.instLT",
"Membership.mem",
"not_true_eq_false",
"Ne",
"Complex.ofReal",
"Complex.re",
"iff_self",
"Iff",
"LT.lt",
"True",
"eq_self",
... | true |
_private.Batteries.Data.BitVec.Lemmas.0.BitVec.getMsb_ofFnLE._proof_1_2 | Batteries.Data.BitVec.Lemmas | [
"Lean.RArray.leaf",
"False",
"_private.Batteries.Data.BitVec.Lemmas.0.BitVec.getMsb_ofFnLE._proof_1_1",
"Lean.Grind.nestedProof",
"eq_false",
"congrArg",
"HEq.refl",
"Classical.byContradiction",
"HSub.hSub",
"Eq.mp",
"Fin.mk",
"id",
"Nat.sub_sub",
"instSubNat",
"instOfNatNat",
"Nat.Lin... | false |
GradedAlgHom.toEnd._proof_2 | Mathlib.RingTheory.GradedAlgebra.AlgHom | [
"Submodule",
"HMul.hMul",
"Monoid.toMulOneClass",
"CommSemiring.toSemiring",
"GradedAlgHom",
"GradedAlgHom.toAlgHom",
"AlgHom",
"Algebra",
"Algebra.toModule",
"MulOne.toMul",
"GradedAlgHom.instMonoid",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"MulOneClass.toMulOne",
"... | false |
ContMDiffWithinAt.div | Mathlib.Geometry.Manifold.Algebra.LieGroup | [
"Eq.mpr",
"DivInvMonoid.toInv",
"instHDiv",
"HMul.hMul",
"ContMDiffWithinAt",
"NormedSpace",
"Monoid.toMulOneClass",
"congrArg",
"Group",
"ContMDiffWithinAt.inv",
"id",
"MulOne.toMul",
"HDiv.hDiv",
"DivInvMonoid.toMonoid",
"div_eq_mul_inv",
"Group.toDivInvMonoid",
"TopologicalSpace",... | true |
_private.Init.Data.String.Lemmas.Splits.0.String.Pos.splits_next_right._simp_1_1 | Init.Data.String.Lemmas.Splits | [
"String",
"instAppendString",
"instHAppendOfAppend",
"Eq.symm",
"Eq",
"HAppend.hAppend",
"String.append_assoc"
] | false |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getKey?_inter_of_contains_right._simp_1_1 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Ordering",
"Ordering.eq",
"Ord.compare",
"Bool.true",
"BEq.beq",
"propext",
"Bool",
"Std.LawfulBEqOrd",
"BEq",
"Eq",
"Std.LawfulBEqOrd.compare_eq_iff_beq"
] | false |
Prod.Lex.instIsWellFounded | Mathlib.Order.RelClasses | [
"IsWellFounded.mk",
"Prod.Lex",
"IsWellFounded.wf",
"Prod",
"IsWellFounded",
"WellFounded.prod_lex"
] | true |
Polynomial.Sequence.ctorIdx | Mathlib.Algebra.Polynomial.Sequence | [
"Polynomial.Sequence",
"Nat",
"Semiring"
] | false |
Submodule.Quotient.smulCommClass | Mathlib.LinearAlgebra.Quotient.Defs | [
"Submodule",
"instHSMul",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsScalarTower",
"Submodule.Quotient.mk",
"SMul",
"AddMonoid.toAddZeroClass",
"AddCommGroup.toAddGroup",
"Submodule.hasQuotient",
"AddZeroClass.toAddZero",
"AddCommGroup",
"DistribSMul.toSMulZeroClass... | true |
Std.Time.instHAddOffset | Std.Time.Date.Basic | [
"Rat.instOfNat",
"instHDiv",
"Rat",
"HDiv.hDiv",
"HAdd",
"Std.Time.Internal.UnitVal.add",
"Std.Time.Nanosecond.Offset",
"OfNat.ofNat",
"HAdd.mk",
"Rat.instDiv"
] | true |
MonoidAlgebra.tensorEquiv | Mathlib.RingTheory.TensorProduct.MonoidAlgebra | [
"MonoidAlgebra.semiring",
"MonoidAlgebra.addCommMonoid",
"AddMonoidAlgebra.tensorEquiv.invFun._proof_1",
"Algebra.to_smulCommClass",
"CommSemiring.toSemiring",
"MonoidAlgebra.tensorEquiv._proof_5",
"IsScalarTower.toAlgHom",
"Algebra.TensorProduct.lift",
"Algebra",
"Algebra.TensorProduct.instCommSe... | true |
Aesop.Options.useDefaultSimpSet._default | Aesop.Options.Public | [
"id",
"Bool.true",
"Bool"
] | false |
R_mul | Mathlib.Geometry.Manifold.Algebra.Monoid | [
"ContMDiffMul",
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"NormedSpace",
"instTopENat",
"congrArg",
"mul_assoc",
"ContMDiffMap.ext",
"WithTop.some",
"TopologicalSpace",
"ModelWithCorners",
"ContMDiffMap",
"ENat",
"True",
"eq_self",
"of_eq_true",
"NontriviallyNormedField",
"Non... | true |
LieModule.trivial_iff_lower_central_eq_bot | Mathlib.Algebra.Lie.Nilpotent | [
"LieAlgebra.toModule",
"LieSubmodule.instSetLike",
"Eq.mpr",
"CommRing",
"LieSubmodule.instBot",
"LieRing.toAddCommGroup",
"Iff.of_eq",
"LieSubmodule.instTop",
"congrArg",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"Bracket.bracket",
"setOf",
"LieSubmodule",
"Membership.m... | true |
Complex.sqrt_neg_I | Mathlib.Analysis.RCLike.Sqrt | [
"AddGroup.toSubtractionMonoid",
"Norm.norm",
"SeminormedAddGroup.toNorm",
"Eq.mpr",
"NegZeroClass.toNeg",
"NormedCommRing.toSeminormedCommRing",
"Real.partialOrder",
"Real",
"DivInvMonoid.toInv",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"SeminormedAddGroup.toAddGroup",
"H... | true |
SaturatedAddSubmonoid.instSetLike.eq_1 | Mathlib.Algebra.Group.Submonoid.Saturation | [
"SetLike",
"SaturatedAddSubmonoid.toAddSubmonoid",
"AddSubsemigroup.carrier",
"AddZeroClass.toAddZero",
"AddSubmonoid.toAddSubsemigroup",
"SetLike.mk",
"AddZeroClass",
"SaturatedAddSubmonoid.instSetLike._proof_1",
"AddZero.toAdd",
"Eq.refl",
"Eq",
"SaturatedAddSubmonoid",
"SaturatedAddSubmon... | true |
IntermediateField.instMulActionSubtypeMem | Mathlib.FieldTheory.IntermediateField.Basic | [
"IntermediateField",
"IntermediateField.toField",
"Algebra",
"Membership.mem",
"Subtype",
"IntermediateField.instMulActionSubtypeMem._proof_1",
"Field.toSemifield",
"Field.toCommRing",
"Semifield.toDivisionSemiring",
"MulAction",
"Semiring.toMonoid",
"DivisionSemiring.toSemiring",
"Intermedi... | true |
Set.mem_toFinset | Mathlib.Data.Fintype.Sets | [
"Finset.univ",
"Iff.of_eq",
"congrArg",
"Finset",
"Finset.map",
"Membership.mem",
"Exists",
"Set.Elem",
"Subtype",
"Set.toFinset",
"Subtype.exists._simp_1",
"Function.Embedding",
"Subtype.mk",
"iff_self",
"funext",
"And",
"Iff",
"Fintype",
"Finset.instSetLike",
"exists_prop_con... | true |
instLipschitzMulMultiplicativeOfLipschitzAdd | Mathlib.Topology.MetricSpace.Algebra | [
"LipschitzAdd",
"Multiplicative.monoid",
"LipschitzMul",
"instPseudoMetricSpaceMultiplicative",
"Multiplicative",
"PseudoMetricSpace",
"LipschitzMul.mk",
"AddMonoid",
"LipschitzAdd.lipschitz_add"
] | true |
Complex.instIsComplete | Mathlib.Analysis.Complex.Norm | [
"Norm.norm",
"Real",
"Complex.instNorm",
"HasEquiv.Equiv",
"Complex.limAux",
"instHasEquivOfSetoid",
"CauSeq",
"Exists.intro",
"CauSeq.equiv",
"CauSeq.IsComplete",
"Complex.equiv_limAux",
"CauSeq.const",
"Complex",
"Complex.instRing",
"Complex.isAbsoluteValueNorm",
"Real.instField",
... | true |
AddCommGrpCat.addCommGroupObj.eq_1 | Mathlib.Algebra.Category.Grp.Limits | [
"CategoryTheory.Functor",
"AddCommGrpCat.addCommGroupObj._proof_19",
"AddCommGrpCat.instCategory",
"AddCommGrpCat.addCommGroupObj._proof_21",
"AddCommGrpCat.addCommGroupObj._proof_16",
"AddCommGrpCat.addCommGroupObj._proof_3",
"SubNegMonoid.mk",
"AddMonoid.toAddZeroClass",
"CategoryTheory.Functor.co... | true |
List.toJson | Lean.Data.Json.FromToJson.Basic | [
"Lean.Json",
"Lean.ToJson.toJson",
"List.toArray",
"Array",
"List",
"Lean.instToJsonArray",
"Lean.ToJson"
] | true |
Polynomial.smeval_X | Mathlib.Algebra.Polynomial.Smeval | [
"NonAssocSemiring.toAddCommMonoidWithOne",
"Pow",
"congrArg",
"AddMonoid.toAddZeroClass",
"Polynomial.sum",
"Polynomial.sum_X_index",
"AddZeroClass.toAddZero",
"instOfNatNat",
"AddCommMonoidWithOne.toAddMonoidWithOne",
"MulActionWithZero",
"Polynomial.smul_pow",
"AddCommMonoid",
"one_smul",
... | true |
_private.Batteries.Data.MLList.Basic.0.MLList.fix?.match_1 | Batteries.Data.MLList.Basic | [
"Unit.unit",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Option"
] | false |
Lean.Grind.Linarith.eq_normN | Init.Grind.Module.NatModuleNorm | [
"Eq.mpr",
"Lean.Grind.Linarith.Expr",
"Lean.Grind.Linarith.Poly.denoteN",
"congrArg",
"Lean.Grind.Linarith.Context",
"Lean.Grind.Linarith.Expr.denoteN",
"Eq.mp",
"id",
"Lean.Grind.Linarith.eq_normN_cert",
"Bool.true",
"BEq.beq",
"implies_congr",
"Lean.Grind.Linarith.Expr.toPolyN",
"Lean.Gr... | true |
CliffordAlgebra.range_ι_le_evenOdd_one | Mathlib.LinearAlgebra.CliffordAlgebra.Grading | [
"Submodule",
"CliffordAlgebra.ι",
"RingHomSurjective.ids",
"CommRing",
"Eq.ge",
"ZMod.commRing",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"AddCommGroup.toAddCommMonoid",
"CliffordAlgebra",
"instAlgebraCliffordAlgebra",
"Submodule.completeLattice",
"PartialOrder.toPreorder",
"Cliff... | true |
FixedDetMatrices.reduce | Mathlib.LinearAlgebra.Matrix.FixedDetMatrices | [
"Int.instDiv",
"instHSMul",
"Matrix.SpecialLinearGroup",
"instHDiv",
"FixedDetMatrices.reduce._proof_2",
"Matrix",
"InvImage",
"FixedDetMatrices.instSMulSpecialLinearGroupFixedDetMatrix",
"instDecidableEqFin",
"DivInvMonoid.toZPow",
"WellFounded.Nat.fix",
"Int.instDecidableEq",
"ModularGroup... | true |
ContractibleSpace.recOn | Mathlib.Topology.Homotopy.Contractible | [
"ContractibleSpace.mk",
"ContractibleSpace.rec",
"ContractibleSpace",
"TopologicalSpace",
"Unit",
"ContinuousMap.HomotopyEquiv",
"Nonempty",
"instTopologicalSpacePUnit"
] | false |
_private.Lean.Elab.Tactic.Do.VCGen.SuggestInvariant.0.Lean.Elab.Tactic.Do.classifyInvariantUse | Lean.Elab.Tactic.Do.VCGen.SuggestInvariant | [
"Pure.pure",
"Unit.unit",
"bne",
"Subarray",
"Bool.not",
"Lean.Expr.isAppOfArity",
"Lean.Expr.isApp",
"Array.push",
"Monad.toApplicative",
"Lean.Expr.instBEq",
"Lean.Expr.isAppOf",
"Lean.Expr.cleanupAnnotations",
"_private.Lean.Elab.Tactic.Do.VCGen.SuggestInvariant.0.Lean.Elab.Tactic.Do.Clas... | true |
CategoryTheory.Endofunctor.Algebra.equivOfNatIso._proof_1 | Mathlib.CategoryTheory.Endofunctor.Algebra | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.category",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Iso.hom_inv_id",
"CategoryTheory.Iso",
"True",
"eq_self",
"CategoryTheory.CategoryStruct.comp",
"of_eq_true",
"... | false |
LieSubmodule.instSupSet._proof_1 | Mathlib.Algebra.Lie.Submodule | [
"Eq.mpr",
"Submodule",
"False",
"Submodule.addSubmonoidClass",
"CommRing",
"Lattice.toSemilatticeSup",
"AddSubmonoidClass.toAddMemClass",
"Finset.mem_insert_self",
"CompleteLattice.toLattice",
"Iff.of_eq",
"Submodule.toAddSubmonoid",
"congrArg",
"CommSemiring.toSemiring",
"Set.Subset.trans... | false |
Std.StreamMap.toArray | Std.Sync.StreamMap | [
"IO",
"Array.map",
"Prod.mk",
"Std.Internal.IO.Async.Selector",
"Array",
"_private.Std.Sync.StreamMap.0.Std.StreamMap.streams",
"Unit",
"Std.StreamMap",
"Prod",
"_private.Std.Sync.StreamMap.0.Std.StreamMap.toArray.match_1"
] | true |
Lean.Parser.Term.sufficesDecl.parenthesizer | Lean.Parser.Term | [
"Lean.Parser.Term.showRhs.parenthesizer",
"Lean.Parser.withCache.parenthesizer",
"Lean.Parser.mkAntiquot.parenthesizer",
"Lean.Parser.group.parenthesizer",
"Lean.Parser.hygieneInfo.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.Parser.Term.binderIdent.parenthesizer",
"Lean... | true |
_private.Mathlib.Data.Set.Order.0.Set.not_monotoneOn_not_antitoneOn_iff_exists_le_le._simp_1_3 | Mathlib.Data.Set.Order | [
"And",
"and_assoc",
"propext",
"Eq"
] | false |
AlgebraicGeometry.Spec.basicOpen_hom_ext | Mathlib.AlgebraicGeometry.Spec | [
"CategoryTheory.Functor.op",
"Eq.mpr",
"CategoryTheory.Category.assoc",
"CategoryTheory.Epi.left_cancellation",
"CategoryTheory.Functor",
"Semiring.toModule",
"Opposite",
"AlgebraicGeometry.SheafedSpace",
"CommRingCat.carrier",
"AlgebraicGeometry.PresheafedSpace.carrier",
"PrimeSpectrum.basicOpe... | true |
subtypeOrEquiv.congr_simp | Mathlib.Logic.Embedding.Set | [
"Prop.le",
"Prop.instHeytingAlgebra",
"subtypeOrEquiv",
"Disjoint",
"Pi.instOrderBot",
"Sum",
"Equiv",
"Subtype",
"DecidablePred",
"Pi.partialOrder",
"Eq.refl",
"Or",
"Prop.partialOrder",
"HeytingAlgebra.toOrderBot",
"Eq"
] | true |
InnerProductSpace.toInnerProductSpaceable_ofReal | Mathlib.Analysis.InnerProductSpace.OfNorm | [
"parallelogram_law_with_norm_mul",
"Real",
"Real.instRCLike",
"InnerProductSpaceable.mk",
"InnerProductSpaceable",
"NormedAddCommGroup.toSeminormedAddCommGroup",
"InnerProductSpace",
"NormedAddCommGroup"
] | true |
String.Pos.next._proof_1 | Init.Data.String.Basic | [
"String.toSlice",
"Eq.mpr",
"String.Pos.ofToSlice_toSlice",
"String.endPos_toSlice",
"congrArg",
"String",
"String.Pos.toSlice",
"id",
"Ne",
"String.Slice.endPos",
"String.Pos.ofToSlice",
"congr",
"String.endPos",
"String.Pos",
"String.Slice.Pos",
"Eq",
"Not",
"Eq.trans"
] | false |
Submodule.comapSubtypeEquivOfLe._proof_1 | Mathlib.Algebra.Module.Submodule.Map | [
"Submodule",
"Submodule.addCommMonoid",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Subtype",
"Submodule.instPartialOrder",
"Submodule.module",
"LE.le",
"AddCommMonoid",
"Subtype.mk",
"Submodule.comap",
"Submodule.setLike",
"eq_self",
"Submodule.subtype",
"of_eq_true... | false |
String.Slice.Pattern.Model.IsLongestRevMatchAt.recOn | Init.Data.String.Lemmas.Pattern.Basic | [
"String.instLEPos_1",
"String.Slice",
"String.Slice.Pattern.Model.IsLongestRevMatchAt.mk",
"LE.le",
"String.Slice.Pos.sliceTo",
"String.Slice.Pattern.Model.IsLongestRevMatchAt.rec",
"String.Slice.Pattern.Model.PatternModel",
"String.Slice.Pos",
"String.Slice.Pattern.Model.IsLongestRevMatch",
"Stri... | false |
Subgroup.coe_center | Mathlib.GroupTheory.Subgroup.Center | [
"Monoid.toMulOneClass",
"Group",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Set.center",
"Subgroup",
"Subgroup.center",
"Group.toDivInvMonoid",
"MulOneClass.toMulOne",
"SetLike.coe",
"Eq",
"Subgroup.instSetLike",
"rfl",
"Set"
] | true |
_private.Mathlib.Analysis.Meromorphic.Divisor.0.MeromorphicOn.divisor_const._simp_1_1 | Mathlib.Analysis.Meromorphic.Divisor | [
"False",
"LinearOrderedAddCommGroupWithTop",
"eq_false",
"AddMonoid.toAddZeroClass",
"PartialOrder.toPreorder",
"Preorder.toLE",
"AddZeroClass.toAddZero",
"LinearOrderedAddCommGroupWithTop.toOrderTop",
"LinearOrderedAddCommGroupWithTop.toSubNegMonoid",
"AddZero.toZero",
"OrderTop.toTop",
"Line... | false |
UpperSet.symm_map | Mathlib.Order.UpperLower.CompleteLattice | [
"Set.ext",
"SetLike.mem_coe._simp_1",
"UpperSet",
"congrArg",
"UpperSet.instSetLike",
"OrderIso.ext",
"Set.mem_image._simp_1",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"OrderIso",
"UpperSet.map",
"OrderIso.symm",
"Set.mem_preimage._simp_1",
"iff_self",
... | true |
Lean.Lsp.LeanStaleDependencyParams.mk.sizeOf_spec | Lean.Data.Lsp.Internal | [
"instOfNatNat",
"Lean.Lsp.DocumentUri",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Lean.Lsp.LeanStaleDependencyParams",
"instAddNat",
"String._sizeOf_inst",
"Eq.refl",
"OfNat.ofNat",
"Lean.Lsp.LeanStaleDependencyParams.mk",
"Eq",
"Lean.Lsp.LeanStaleDependencyParams._sizeOf_inst"
] | true |
MeasureTheory.hasFiniteIntegral_neg_iff | Mathlib.MeasureTheory.Function.L1Space.HasFiniteIntegral | [
"NegZeroClass.toNeg",
"SubtractionMonoid.toInvolutiveNeg",
"MeasureTheory.Measure",
"Pi.instNeg",
"Pi.involutiveNeg",
"PseudoMetricSpace.toUniformSpace",
"Eq.rec",
"SeminormedAddGroup.toContinuousENorm",
"neg_neg",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"Sub... | true |
_private.Init.Data.Range.Lemmas.0.Std.Legacy.Range.forIn'.eq_1 | Init.Data.Range.Lemmas | [
"_private.Init.Data.Range.Basic.0.Std.Legacy.Range.forIn'._proof_1",
"Membership.mem",
"_private.Init.Data.Range.Basic.0.Std.Legacy.Range.forIn'.loop",
"Std.Legacy.Range.start",
"ForInStep",
"Std.Legacy.Range.forIn'",
"Nat",
"Std.Legacy.Range",
"Std.Legacy.instMembershipNatRange",
"Eq.refl",
"Mo... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.getD_inter_of_contains_eq_false_left._simp_1_3 | Std.Data.DTreeMap.Internal.Lemmas | [
"Ord",
"Membership.mem",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"propext",
"Bool",
"Std.DTreeMap.Internal.Impl.mem_iff_contains",
"Eq",
"Std.DTreeMap.Internal.Impl",
"Std.DTreeMap.Internal.Impl.instMembershipOfOrd"
] | false |
iteratedFDeriv_eq_equiv_comp | Mathlib.Analysis.Calculus.IteratedDeriv.Defs | [
"LinearIsometryEquiv.instEquivLike",
"Eq.mpr",
"NormedCommRing.toSeminormedCommRing",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"Semiring.toModule",
"NormedSpace.toIsBoundedSMul",
"LinearIsometryEquiv.symm",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"congrArg",
"... | true |
CategoryTheory.ReflQuiver.recOn | Mathlib.Combinatorics.Quiver.ReflQuiver | [
"Quiver.Hom",
"Quiver",
"CategoryTheory.ReflQuiver",
"CategoryTheory.ReflQuiver.mk",
"CategoryTheory.ReflQuiver.rec"
] | false |
CategoryTheory.Limits.coconeOfDiagramInitial._proof_1 | Mathlib.CategoryTheory.Limits.Shapes.IsTerminal | [
"CategoryTheory.Limits.IsInitial.hom_ext",
"CategoryTheory.Functor",
"CategoryTheory.IsIso",
"_private.Mathlib.CategoryTheory.Limits.Shapes.IsTerminal.0.CategoryTheory.Limits.coneOfDiagramTerminal._simp_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.Functor.cat... | false |
Lean.TraceData.tag | Lean.Message | [
"String",
"Lean.TraceData"
] | true |
Nat.length_toList_ric | Init.Data.Range.Polymorphic.NatLemmas | [
"congrArg",
"Std.Ric.toList",
"instOfNatNat",
"instLENat",
"Std.Ric.mk",
"Std.PRange.instLawfulUpwardEnumerableLENat",
"Nat.size_ric",
"instHAdd",
"Std.Ric.size",
"HAdd.hAdd",
"Std.PRange.instUpwardEnumerableNat",
"Nat",
"Std.PRange.instHasSizeNat",
"True",
"eq_self",
"Std.PRange.instL... | true |
_private.Mathlib.Topology.Compactness.CountablyCompact.0.isCountablyCompact_iff_infinite_subset_has_accPt._proof_1_2 | Mathlib.Topology.Compactness.CountablyCompact | [
"Lean.Grind.of_eq_eq_true",
"Lean.Grind.eq_false_of_not_eq_true",
"Inhabited.default",
"of_eq_false",
"False",
"Set.mem_range",
"Lean.Grind.and_eq_of_eq_true_right",
"forall_not_of_not_exists",
"Lean.Grind.not_not",
"Lean.Grind.not_false",
"Lean.Grind.not_and",
"eq_false",
"Lean.Grind.iff_eq... | false |
uniformContinuous_sInf_rng | Mathlib.Topology.UniformSpace.Basic | [
"UniformContinuous",
"UniformSpace",
"Eq.mpr",
"iInf",
"congrArg",
"Filter.instInfSet",
"Iff.rfl",
"uniformity",
"Membership.mem",
"Set.Elem",
"id",
"Prod.mk",
"iInf_uniformity",
"Prod.fst",
"Subtype.mk",
"sInf_eq_iInf'",
"Iff",
"Filter.Tendsto",
"propext",
"Filter.tendsto_iInf... | true |
MeasureTheory.Measure.haveLebesgueDecomposition_of_sigmaFinite | Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue | [
"Iff.mpr",
"Eq.mpr",
"MeasureTheory.Measure.withDensity",
"lt_of_le_of_lt",
"Trans.trans",
"MeasureTheory.Measure",
"Preorder.toLT",
"TopologicalSpace.MetrizableSpace.toPseudoMetrizableSpace",
"Pi.addCommMonoid",
"MeasureTheory.instSFiniteOfSigmaFinite",
"MeasurableSet",
"compl_compl",
"Pi.t... | true |
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