name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 692 | allowCompletion bool 2
classes |
|---|---|---|---|
CompleteLatticeHom._sizeOf_1 | Mathlib.Order.Hom.CompleteLattice | [
"sInfHom.toFun",
"instOfNatNat",
"CompleteLattice.toCompleteSemilatticeInf",
"instHAdd",
"HAdd.hAdd",
"CompleteLatticeHom.rec",
"sInfHom._sizeOf_inst",
"Nat",
"sInfHom",
"SizeOf.sizeOf",
"CompleteSemilatticeSup.toSupSet",
"instAddNat",
"Set.image",
"CompleteLatticeHom",
"SizeOf",
"Comp... | false |
NonUnitalSubsemiring.instBot._proof_2 | Mathlib.RingTheory.NonUnitalSubsemiring.Defs | [
"HMul.hMul",
"congrArg",
"AddMonoid.toAddZeroClass",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Eq.mp",
"Set.instSingletonSet",
"id",
"MulZeroClass.mul_zero",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"AddZero.toZero",
"Distrib.toMul",
"cong... | false |
Finmap.union.eq_1 | Mathlib.Data.Finmap | [
"Finmap.union._proof_1",
"AList",
"Eq.refl",
"Finmap.liftOn₂",
"AList.instUnion",
"Finmap.union",
"Union.union",
"Eq",
"AList.toFinmap",
"Finmap",
"DecidableEq"
] | true |
instRingCorner._proof_14 | Mathlib.RingTheory.Idempotents | [
"NonUnitalSubring.instSetLike",
"NonAssocSemiring.toAddCommMonoidWithOne",
"HMul.hMul",
"AddMonoid.toAddSemigroup",
"SubNegMonoid.mk",
"Neg.mk",
"instRingCorner._proof_5",
"NonUnitalSubring",
"AddCommGroup.toAddGroup",
"NonUnitalSubring.toNonUnitalRing._proof_1",
"Sub.mk",
"SemigroupWithZero.t... | false |
IncidenceAlgebra.instRing._proof_6 | Mathlib.Combinatorics.Enumerative.IncidenceAlgebra | [
"AddGroup.toSubtractionMonoid",
"AddGroupWithOne.toAddGroup",
"Preorder.toLE",
"SubtractionMonoid.toSubNegZeroMonoid",
"Int",
"SubNegZeroMonoid.toNegZeroClass",
"Nat.cast",
"SubNegMonoid.zsmul",
"AddGroup.toSubNegMonoid",
"IncidenceAlgebra.instAddGroup",
"Nat",
"SubNegMonoid.toNeg",
"SubNegM... | false |
SSet.RelativeMorphism.ofSimplex₀._proof_2 | Mathlib.AlgebraicTopology.SimplicialSet.RelativeMorphism | [
"SSet.Subcomplex.toSSet",
"SSet.Subcomplex.ofSimplex",
"SSet.const",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.ConcreteCategory.hom",
"CategoryTheory.Functor.category",
"TypeCat.instFunLikeFun",
"Membership.mem",
"CategoryTheory.Subfunctor.... | false |
DFinsupp.hasAdd₂ | Mathlib.Data.DFinsupp.Defs | [
"AddZeroClass.toAddZero",
"inferInstance",
"DFinsupp.addZeroClass",
"AddZero.toZero",
"AddZeroClass",
"DFinsupp.instZero",
"DFinsupp.instAdd",
"DFinsupp",
"Add"
] | true |
_private.Init.Data.List.Find.0.List.head_flatten._simp_1_1 | Init.Data.List.Find | [
"List.head?",
"List.head",
"Option.some",
"Ne",
"List",
"List.head_eq_iff_head?_eq_some",
"propext",
"Eq",
"List.nil",
"Option"
] | false |
Sum.not_inr_le_inl._simp_1 | Mathlib.Data.Sum.Order | [
"False",
"eq_false",
"Sum",
"Sum.inl",
"LE.le",
"LE",
"Sum.not_inr_le_inl",
"Sum.inr",
"Sum.instLESum",
"Eq"
] | false |
CategoryTheory.op_epi_iff | Mathlib.CategoryTheory.EpiMono | [
"Opposite",
"CategoryTheory.Epi",
"CategoryTheory.Mono",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"Quiver.Hom.op",
"inferInstance",
"CategoryTheory.unop_mono_of_epi",
"Iff",
"Opposite.op",
"Iff.intro",
"CategoryTheory.op_epi_of_mono",
"CategoryTheory.Category.opposite",
"Cat... | true |
LLVM.DLLStorageClass | Lean.Compiler.IR.LLVMBindings | [
"_private.Lean.Compiler.IR.LLVMBindings.0.LLVM.DLLStorageClass.mk"
] | true |
_private.Batteries.Data.Array.Basic.0.Array.scanrMFast.loop._proof_1 | Batteries.Data.Array.Basic | [
"HSub.hSub",
"BitVec.toNat",
"LE.le",
"instLENat",
"Array",
"System.Platform.numBits",
"USize.toBitVec",
"instHSub",
"USize.toNat",
"Nat",
"LT.lt",
"instLTUSize",
"instLTNat",
"instSubUSize",
"OfNat.ofNat",
"Nat.lt_of_lt_of_le",
"Array.size",
"USize",
"USize.instOfNat"
] | false |
List.cyclicPermutations_ne_nil._simp_1 | Mathlib.Data.List.Rotate | [
"False",
"eq_false",
"List.cyclicPermutations_ne_nil",
"List.cyclicPermutations",
"List",
"Eq",
"List.nil"
] | false |
CategoryTheory.MorphismProperty.ext | Mathlib.CategoryTheory.MorphismProperty.Basic | [
"Eq.mpr",
"CategoryTheory.MorphismProperty",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"id",
"funext",
"Iff",
"propext",
"Eq.refl",
"CategoryTheory.CategoryStruct",
"Eq"
] | true |
measurable_from_prod_countable_left' | Mathlib.MeasureTheory.MeasurableSpace.Constructions | [
"Set.instSProd",
"Set.ext",
"Eq.mpr",
"MeasurableSet",
"mem_measurableAtom_self",
"SProd.sprod",
"congrArg",
"Measurable",
"Membership.mem",
"Exists",
"id",
"MeasurableSet.prod",
"Prod.mk",
"MeasurableSet.measurableAtom_of_countable",
"_private.Mathlib.MeasureTheory.MeasurableSpace.Const... | true |
CategoryTheory.Limits.SingleObj.Types.sections.equivFixedPoints._proof_2 | Mathlib.CategoryTheory.Limits.Shapes.SingleObj | [
"Monoid",
"CategoryTheory.Functor",
"Membership.mem",
"Set.Elem",
"CategoryTheory.SingleObj.star",
"Subtype.mk",
"CategoryTheory.SingleObj",
"Function.RightInverse",
"CategoryTheory.types",
"CategoryTheory.Limits.SingleObj.instMulActionObjSingleObjStar",
"Eq.refl",
"MulAction.fixedPoints",
"... | false |
Lean.Parser.withoutInfo | Lean.Parser.Basic | [
"Lean.Parser.ParserInfo.mk",
"Lean.Parser.FirstTokens.unknown",
"Lean.Parser.Parser",
"Lean.Parser.Parser.mk",
"Lean.Parser.Token",
"id",
"List",
"Lean.Parser.Parser.fn",
"Lean.Parser.SyntaxNodeKindSet"
] | true |
mem_irreducibleComponent | Mathlib.Topology.Irreducible | [
"IsPreirreducible",
"Set.singleton_subset_iff",
"Membership.mem",
"Set.instSingletonSet",
"HasSubset.Subset",
"TopologicalSpace",
"And",
"And.right",
"And.left",
"Iff.mp",
"irreducibleComponent_property",
"Singleton.singleton",
"Eq",
"Set.instMembership",
"irreducibleComponent",
"Set.i... | true |
Besicovitch.SatelliteConfig.inter | Mathlib.MeasureTheory.Covering.Besicovitch | [
"Besicovitch.SatelliteConfig",
"Real.instLE",
"Real",
"Besicovitch.SatelliteConfig.c",
"instOfNatNat",
"LE.le",
"Real.instAdd",
"instHAdd",
"Besicovitch.SatelliteConfig.r",
"MetricSpace",
"HAdd.hAdd",
"Nat",
"Fin.last",
"LT.lt",
"instLTFin",
"instAddNat",
"MetricSpace.toPseudoMetricS... | true |
CategoryTheory.ProjectiveResolution.π_f_succ | Mathlib.CategoryTheory.Preadditive.Projective.Resolution | [
"CategoryTheory.ProjectiveResolution.π",
"HomologicalComplex.isZero_single_obj_X",
"CategoryTheory.Limits.HasZeroMorphisms",
"False",
"Nat.instMulZeroClass",
"ChainComplex",
"HomologicalComplex.instCategory",
"Nat.instOne",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Q... | true |
Algebra.Generators.CotangentSpace.compEquiv._proof_6 | Mathlib.RingTheory.Kaehler.JacobiZariski | [
"CommRing",
"Algebra.to_smulCommClass",
"Algebra.Extension.commRing",
"instSMulOfMul",
"CommSemiring.toSemiring",
"Algebra",
"Algebra.toSMul",
"Algebra.Extension.Ring",
"Algebra.Generators",
"instDistribOfSemiring",
"CommRing.toCommSemiring",
"Distrib.toMul",
"Algebra.Generators.toExtension"... | false |
Finset.Ico_union_Ico' | Mathlib.Order.Interval.Finset.Basic | [
"Eq.mpr",
"Finset.coe_Ico",
"Lattice.toSemilatticeSup",
"LinearOrder.toDecidableEq",
"Finset.instUnion",
"congrArg",
"Finset",
"LinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"Set.instUnion",
"SemilatticeSup.toMax",
"Finset.coe_inj",
"DistribLa... | true |
_private.Lean.PrettyPrinter.0.Lean.PrettyPrinter.ppConstNameWithInfos._sparseCasesOn_1 | Lean.PrettyPrinter | [
"Nat.ne_of_beq_eq_false",
"Option.ctorIdx",
"Nat.shiftRight",
"Option.some",
"Nat.hasNotBit",
"Option.rec",
"instOfNatNat",
"Nat.land",
"Option.none",
"Nat",
"Bool",
"Eq.refl",
"OfNat.ofNat",
"Bool.false",
"Option"
] | false |
PUnit.sub_eq | Mathlib.Algebra.Group.PUnit | [
"HSub.hSub",
"instHSub",
"PUnit",
"PUnit.unit",
"Eq",
"rfl",
"PUnit.instSub_mathlib"
] | true |
Subgroup.FiniteIndex | Mathlib.GroupTheory.Index | [
"Group",
"Subgroup",
"Subgroup.FiniteIndex.mk"
] | true |
CategoryTheory.Presieve.instHasPullbacksSingletonOfHasPullback | Mathlib.CategoryTheory.Sites.Sieves | [
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"inferInstance",
"CategoryTheory.Limits.HasPullback",
"CategoryTheory.Presieve.HasPullbacks.mk",
"Unit",
"CategoryTheory.Presieve.HasPullbacks",
"CategoryTheory.Presieve.singleton",
"CategoryTheory.Category.toCategoryStruct",
"_private.Mathli... | true |
Nat.toArray_rcc_eq_singleton_iff | Init.Data.Range.Polymorphic.NatLemmas | [
"Nat.toArray_rcc_eq_toArray_rco",
"Std.Rcc.toArray",
"Std.Rco.toArray",
"congrArg",
"Nat.toArray_rco_eq_singleton_iff._simp_1",
"Std.PRange.instIsAlwaysFiniteNat_1",
"instOfNatNat",
"instLENat",
"List.toArray",
"List.cons",
"Array",
"iff_self",
"instHAdd",
"And",
"Iff",
"HAdd.hAdd",
... | true |
FirstOrder.Language.age.fg_substructure | Mathlib.ModelTheory.Fraisse | [
"FirstOrder.Language.age",
"FirstOrder.Language.Substructure.fg_iff_structure_fg",
"FirstOrder.Language.Substructure.inducedStructure",
"Membership.mem",
"FirstOrder.Language.Substructure.instSetLike",
"inferInstance",
"Subtype",
"CategoryTheory.Bundled.structure",
"FirstOrder.Language.Embedding",
... | true |
Std.Tactic.BVDecide.BVPred.noConfusionType | Std.Tactic.BVDecide.Bitblast.BVExpr.Basic | [
"Std.Tactic.BVDecide.BVPred.casesOn",
"Nat",
"HEq",
"Std.Tactic.BVDecide.BVBinPred",
"Std.Tactic.BVDecide.BVExpr",
"Eq",
"Std.Tactic.BVDecide.BVPred"
] | false |
Function.Injective.completeBooleanAlgebra._proof_4 | Mathlib.Order.CompleteBooleanAlgebra | [
"Function.Injective.completeBooleanAlgebra._proof_1",
"Preorder.toLT",
"Lattice.toSemilatticeSup",
"CompleteLattice.toLattice",
"DistribLattice.le_sup_inf",
"Compl.compl",
"HImp",
"PartialOrder.toPreorder",
"Preorder.toLE",
"BooleanAlgebra.toCompl",
"SemilatticeSup.toMax",
"Max",
"DistribLat... | false |
Filter.mem_pi_of_mem | Mathlib.Order.Filter.Pi | [
"Filter.instMembership",
"Membership.mem",
"Function.eval",
"Filter.mem_iInf_of_mem",
"Set.preimage",
"Filter.preimage_mem_comap",
"Filter.pi",
"Filter",
"Filter.comap",
"Set"
] | true |
CategoryTheory.ShortComplex.cyclesFunctor_obj | Mathlib.Algebra.Homology.ShortComplex.LeftHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.cyclesFunctor",
"CategoryTheory.ShortComplex.instCategory",
"CategoryTheory.Limits.HasCokernels",
"CategoryTheory.Limits.HasKernels",
"Eq.refl",
"CategoryTheory.ShortComplex.leftHomologyFunctor._proof... | true |
String.Slice.pos!_eq_pos | Init.Data.String.Lemmas.Basic | [
"dite_cond_eq_true",
"String.Slice.pos",
"congrArg",
"panicWithPosWithDecl",
"String.Slice",
"instDecidableEqBool",
"instOfNatNat",
"String.Pos.Raw",
"String.Pos.Raw.IsValidForSlice",
"String.Slice.pos?._proof_1",
"Bool.true",
"String.Pos.Raw.isValidForSlice",
"String.Slice.pos!",
"Nat",
... | true |
InverseSystem.pEquivOnLim._proof_2 | Mathlib.Order.DirectedInverseSystem | [
"Eq.mpr",
"Preorder.toLT",
"InverseSystem.invLimEquiv",
"Equiv.instEquivLike",
"Order.succ",
"Order.IsSuccPrelimit",
"LinearOrder.toDecidableEq",
"InverseSystem.PEquivOn.equiv",
"congrArg",
"Equiv.trans",
"LinearOrder",
"InverseSystem.piEquivLim.eq_1",
"WellFoundedLT",
"PartialOrder.toPreo... | false |
_private.Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme.0.AlgebraicGeometry.termSbo_ | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1"
] | true |
EReal.div_zero | Mathlib.Data.EReal.Inv | [
"Eq.mpr",
"EReal.instDivInvMonoid",
"instHDiv",
"HMul.hMul",
"EReal.instMulZeroOneClass",
"MulZeroClass.toMul",
"congrArg",
"EReal",
"EReal.instInv",
"id",
"HDiv.hDiv",
"instZeroEReal",
"MulZeroClass.mul_zero",
"Inv.inv",
"DivInvMonoid.toDiv",
"Zero.toOfNat0",
"Eq.refl",
"MulZeroOn... | true |
Aesop.EMap.mk.sizeOf_spec | Aesop.EMap | [
"Aesop.EMap._sizeOf_inst",
"Option._sizeOf_inst",
"Lean.PArray",
"Lean.PersistentArray._sizeOf_inst",
"Lean.Expr",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"SizeOf.sizeOf",
"Lean.Meta.DiscrTree",
"Aesop.EMap",
"instAddNat",
"Eq.refl",
"instSizeOfNat",
"SizeOf",
"Lean.Meta.Disc... | true |
ProbabilityTheory.indepSets_singleton_iff | Mathlib.Probability.Independence.Basic | [
"Pure.pure",
"MeasureTheory.ae",
"Unit.unit",
"_private.Mathlib.Probability.Independence.Basic.0.ProbabilityTheory.indepSets_singleton_iff._simp_1_2",
"MeasureTheory.Measure",
"instCountablePUnit",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"Filter.Eventually",
"standardBorelSpace_of_di... | true |
Set.Pairwise.insert_of_symmetric | Mathlib.Data.Set.Pairwise.Basic | [
"Iff.mpr",
"Symmetric",
"Membership.mem",
"Insert.insert",
"Ne",
"Set.Pairwise",
"And",
"Set.pairwise_insert_of_symmetric",
"Set.instInsert",
"And.intro",
"Set.instMembership",
"Set"
] | true |
_private.Mathlib.NumberTheory.FLT.Three.0.FermatLastTheoremForThreeGen.Solution.lambda_not_dvd_y | Mathlib.NumberTheory.FLT.Three | [
"IsPrimitiveRoot.toInteger_isPrimitiveRoot",
"_private.Mathlib.NumberTheory.FLT.Three.0.FermatLastTheoremForThreeGen.Solution'.b",
"_private.Mathlib.NumberTheory.FLT.Three.0.FermatLastTheoremForThreeGen.Solution.toSolution'",
"Units.val",
"instDecidableNot",
"Semigroup.toMul",
"Dvd.dvd",
"HMul.hMul",
... | true |
_private.Mathlib.Tactic.Tauto.0.Mathlib.Tactic.Tauto.distribNotAt.match_1 | Mathlib.Tactic.Tauto | [
"Lean.Expr",
"instOfNatNat",
"List.cons",
"List",
"Nat",
"List.casesOn",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn",
"List.nil"
] | false |
Colex.exists._simp_1 | Mathlib.Order.Lex | [
"Equiv.instEquivLike",
"Colex",
"Exists",
"Equiv",
"propext",
"Colex.exists",
"toColex",
"Eq",
"DFunLike.coe",
"EquivLike.toFunLike"
] | false |
CategoryTheory.Limits.splitMonoOfIdempotentOfIsLimitFork_retraction | Mathlib.CategoryTheory.Limits.Shapes.Equalizers | [
"CategoryTheory.Limits.splitMonoOfIdempotentOfIsLimitFork",
"CategoryTheory.Limits.Fork.ofι",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Limits.WalkingParallelPair",
"CategoryTheory.CategoryStruct.id",
"CategoryTheory.Limits.walkingParallelPairHomCategory",
"CategoryTheory... | true |
MeasureTheory.AEEqFun.coeFn_add | Mathlib.MeasureTheory.Function.AEEqFun | [
"MeasureTheory.ae",
"MeasureTheory.Measure",
"MeasureTheory.AEEqFun.coeFn_comp₂",
"MeasureTheory.AEEqFun.cast",
"Filter.EventuallyEq",
"MeasureTheory.AEEqFun",
"MeasurableSpace",
"TopologicalSpace",
"instHAdd",
"Pi.instAdd",
"HAdd.hAdd",
"continuous_add",
"ContinuousAdd",
"MeasureTheory.AE... | true |
AlgebraicGeometry.Scheme.Modules.fromTildeΓNatTrans | Mathlib.AlgebraicGeometry.Modules.Tilde | [
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme.Modules.fromTildeΓ",
"CategoryTheory.Functor",
"AlgebraicGeometry.Scheme.Modules.instCategory",
"CommRingCat.carrier",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"ModuleCat",
"CommRingCat",
"CategoryTheory.Functor.category",
"Categ... | true |
derivWithin_intCast | Mathlib.Analysis.Calculus.Deriv.Basic | [
"Int.cast",
"derivWithin_const",
"NormedSpace",
"NormedSpace.toModule",
"Pi.instIntCast",
"PseudoMetricSpace.toUniformSpace",
"IntCast",
"Pi.instZero",
"SubtractionMonoid.toSubNegZeroMonoid",
"Int",
"SubNegZeroMonoid.toNegZeroClass",
"SubtractionCommMonoid.toSubtractionMonoid",
"derivWithin"... | true |
ProofWidgets.LayoutKind.inline | ProofWidgets.Data.Html | [
"ProofWidgets.LayoutKind.inline",
"ProofWidgets.LayoutKind"
] | true |
ContinuousLinearMap.flip_smul | Mathlib.Analysis.Normed.Operator.Bilinear | [
"NormedCommRing.toSeminormedCommRing",
"instHSMul",
"SeminormedAddCommGroup",
"NormedSpace.toIsBoundedSMul",
"UniformContinuousConstSMul.to_continuousConstSMul",
"NormedSpace",
"ContinuousLinearMap.topologicalSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"ContinuousLine... | true |
AddSubgroup.Commensurable.discreteTopology_iff | Mathlib.Topology.Algebra.IsUniformGroup.DiscreteSubgroup | [
"AddSubgroup.instCompleteLattice",
"Trans.trans",
"AddSubgroup.discreteTopology_iff_of_isFiniteRelIndex",
"DiscreteTopology",
"AddSubgroup.Commensurable",
"Membership.mem",
"inf_le_right",
"CompleteLattice.toConditionallyCompleteLattice",
"Eq.rec",
"Subtype",
"Ne",
"instOfNatNat",
"Semilatti... | true |
_private.Mathlib.Logic.Basic.0.exists_and_exists_comm.match_1_3 | Mathlib.Logic.Basic | [
"Exists",
"And.casesOn",
"And",
"Exists.casesOn",
"And.intro",
"Exists.intro"
] | false |
IsPrimitiveRoot.neg_one | Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots | [
"Nontrivial",
"Iff.mpr",
"Eq.mpr",
"NegZeroClass.toNeg",
"NonAssocSemiring.toAddCommMonoidWithOne",
"CommRing",
"IsPrimitiveRoot.orderOf",
"congrArg",
"CommSemiring.toSemiring",
"HEq.refl",
"AddGroupWithOne.toAddMonoidWithOne",
"Eq.casesOn",
"id",
"Ne",
"SubtractionMonoid.toSubNegZeroMon... | true |
AddLocalization.liftOn.eq_1 | Mathlib.GroupTheory.MonoidLocalization.Basic | [
"AddCon.instFunLikeForallProp",
"AddCon",
"Prod.instAdd",
"AddMonoid.toAddZeroClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"AddLocalization.liftOn._proof_1",
"Subtype",
"AddLocalization.liftOn",
"AddSubmonoid.add",
"Prod.mk",
"AddSubmonoid",
"AddCommMonoid",
"AddLocalization.rec",
... | true |
ContinuousLinearMapWOT.ext_dual_iff | Mathlib.Analysis.LocallyConvex.WeakOperatorTopology | [
"NormedCommRing.toNormedRing",
"NormedCommRing.toSeminormedCommRing",
"Semiring.toModule",
"NormedRing.toRing",
"AddCommGroup.toAddCommMonoid",
"HEq.refl",
"ContinuousLinearMap.funLike",
"ContinuousLinearMapWOT.instFunLike",
"PseudoMetricSpace.toUniformSpace",
"ContinuousLinearMapWOT",
"RingHom"... | true |
_private.Mathlib.RingTheory.TwoSidedIdeal.Operations.0.TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure_absorbing._simp_1_1 | Mathlib.RingTheory.TwoSidedIdeal.Operations | [
"NonUnitalNonAssocRing",
"NegZeroClass.toNeg",
"HMul.hMul",
"TwoSidedIdeal",
"NonUnitalNonAssocRing.toAddCommGroup",
"NonUnitalNonAssocSemiring.toMulZeroClass",
"Membership.mem",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNeg... | false |
Turing.PartrecToTM2.move₂_ok | Mathlib.Computability.TuringMachine.ToPartrec | [
"Eq.mpr",
"Inhabited.default",
"Function.update_eq_self",
"Turing.PartrecToTM2.tr",
"Turing.TM2.stepAux",
"Function.update",
"Turing.PartrecToTM2.K'.rev",
"Turing.PartrecToTM2.instDecidableEqK'",
"Turing.PartrecToTM2.Γ'",
"Turing.PartrecToTM2.Λ'.push",
"congrArg",
"Option.instMembership",
"H... | true |
Lean.Elab.Tactic.RCases.RCasesPatt.noConfusion | Lean.Elab.Tactic.RCases | [
"Lean.Elab.Tactic.RCases.RCasesPatt",
"Lean.Syntax",
"Lean.Syntax.Term",
"List",
"Eq.ndrec",
"Lean.Elab.Tactic.RCases.RCasesPatt.noConfusionType",
"Lean.Name",
"Eq.refl",
"Lean.Elab.Tactic.RCases.RCasesPatt.casesOn",
"Eq"
] | false |
Filter.HasBasis.cauchySeq_iff | Mathlib.Topology.UniformSpace.Cauchy | [
"Set.instSProd",
"UniformSpace",
"Eq.mpr",
"Filter.atTop_basis",
"Set.Ici",
"CauchySeq",
"SetRel",
"SProd.sprod",
"congrArg",
"Filter.HasBasis.tendsto_iff",
"Filter.HasBasis.prod_self",
"uniformity",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"Exists",
"forall_comm... | true |
TypeVec.toSubtype._unsafe_rec | Mathlib.Data.TypeVec | [
"TypeVec.toSubtype.match_1",
"TypeVec.toSubtype._unsafe_rec",
"Fin2.fz",
"TypeVec.ofRepeat",
"Subtype",
"Fin2.fs",
"Nat",
"TypeVec.repeat",
"TypeVec.Subtype_",
"TypeVec.drop",
"TypeVec.Arrow",
"Nat.succ",
"TypeVec.dropFun",
"Fin2",
"TypeVec"
] | false |
Lean.Compiler.LCNF.Code.return.noConfusion | Lean.Compiler.LCNF.Basic | [
"id",
"Lean.FVarId",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Code.noConfusion",
"Lean.Compiler.LCNF.Code",
"heq_of_eq",
"Lean.Compiler.LCNF.Code.return",
"Eq.refl",
"Eq"
] | false |
_private.Mathlib.SetTheory.ZFC.Rank.0.PSet.rank_insert._simp_1_2 | Mathlib.SetTheory.ZFC.Rank | [
"PSet.instMembership",
"Membership.mem",
"Insert.insert",
"PSet",
"propext",
"PSet.instInsert",
"Or",
"Eq",
"PSet.mem_insert_iff",
"PSet.Equiv"
] | false |
Lean.Lsp.RpcWireFormat.recOn | Lean.Server.Rpc.Basic | [
"Lean.Lsp.RpcWireFormat.rec",
"Lean.Lsp.RpcWireFormat.v1",
"Lean.Lsp.RpcWireFormat",
"Lean.Lsp.RpcWireFormat.v0"
] | false |
Equiv.Perm.IsThreeCycle | Mathlib.GroupTheory.Perm.Cycle.Type | [
"Equiv.Perm.cycleType",
"Multiset",
"instOfNatNat",
"Multiset.instSingleton",
"Fintype",
"Equiv.Perm",
"Nat",
"Singleton.singleton",
"OfNat.ofNat",
"Eq",
"DecidableEq"
] | true |
WittVector.idIsPolyI' | Mathlib.RingTheory.WittVector.IsPoly | [
"CommRing",
"WittVector.IsPoly",
"WittVector.idIsPoly",
"WittVector",
"Nat"
] | true |
Nat.Partrec.Code.pappAck.match_1 | Mathlib.Computability.Ackermann | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
PosPart.noConfusionType | Mathlib.Algebra.Notation | [
"PosPart",
"PosPart.casesOn",
"HEq"
] | false |
Lean.Meta.Grind.NormalizePattern.State.recOn | Lean.Meta.Tactic.Grind.EMatchTheorem | [
"Lean.Meta.Grind.NormalizePattern.State.mk",
"Lean.instBEqHeadIndex",
"Std.HashSet",
"instHashableNat",
"Lean.Meta.Grind.NormalizePattern.State.rec",
"instBEqOfDecidableEq",
"Array",
"Lean.instHashableHeadIndex",
"Nat",
"instDecidableEqNat",
"Lean.Meta.Grind.NormalizePattern.State",
"Lean.Head... | false |
Std.ExtDHashMap.Const.get_modify_self | Std.Data.ExtDHashMap.Lemmas | [
"Std.ExtDHashMap.inner",
"Std.ExtDHashMap.instMembershipOfEquivBEqOfLawfulHashable",
"Std.ExtDHashMap.Const.mem_modify",
"Quot.pliftOn._proof_2",
"Membership.mem",
"Std.ExtDHashMap.Const.modify",
"Std.ExtDHashMap.inductionOn",
"Std.DHashMap.Const.get_modify_self",
"Std.ExtDHashMap.mk",
"LawfulHash... | true |
Module.Relations.Solution.IsPresentation.desc.congr_simp | Mathlib.Algebra.Module.Presentation.Basic | [
"Module.Relations.Solution.IsPresentation",
"AddCommGroup.toAddCommMonoid",
"Eq.rec",
"AddCommGroup",
"Module.Relations.Solution",
"LinearMap",
"Eq.ndrec",
"Eq.refl",
"Module.Relations",
"Module.Relations.Solution.IsPresentation.desc",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring",
... | true |
Std.DTreeMap.Internal.Impl.Const.maxKeyD_alter!_eq_self | Std.Data.DTreeMap.Internal.Lemmas | [
"Std.DTreeMap.Internal.Impl.maxKeyD",
"Std.DTreeMap.Internal.Impl.SizedBalancedTree.impl",
"Ord",
"congrArg",
"Std.TransOrd",
"HSub.hSub",
"Membership.mem",
"Eq.mp",
"Std.DTreeMap.Internal.Impl.size",
"instSubNat",
"instOfNatNat",
"Std.DTreeMap.Internal.Impl.Const.maxKeyD_alter_eq_self",
"St... | true |
_private.Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal.0.IsCyclotomicExtension.Rat.«term𝒑» | Mathlib.NumberTheory.NumberField.Cyclotomic.Ideal | [
"Lean.Name.mkNum",
"Lean.Name.mkStr",
"instOfNatNat",
"Lean.Name.anonymous",
"Lean.ParserDescr",
"Lean.ParserDescr.node",
"Nat",
"Lean.ParserDescr.symbol",
"OfNat.ofNat"
] | true |
FloatArray.map | Batteries.Data.FloatArray | [
"FloatArray",
"Float",
"FloatArray.mapM",
"Id",
"Id.instMonad"
] | true |
_private.Mathlib.Algebra.Module.ZLattice.Summable.0.ZLattice.sum_piFinset_Icc_rpow_le._simp_1_9 | Mathlib.Algebra.Module.ZLattice.Summable | [
"zpow_natCast",
"DivInvMonoid.toZPow",
"DivInvMonoid.toMonoid",
"Int",
"Nat.cast",
"DivInvMonoid",
"Monoid.toPow",
"HPow.hPow",
"Nat",
"instNatCastInt",
"instHPow",
"Eq.symm",
"Eq"
] | false |
CategoryTheory.Mod.Hom.mk | Mathlib.CategoryTheory.Monoidal.Mod | [
"CategoryTheory.Mod.mod",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.Mod.X",
"CategoryTheory.Mod.Hom",
"CategoryTheory.MonoidalCategory.MonoidalLeftAction",
"CategoryTheory.Mod",
"CategoryTheory.Category.toCategoryStruct",
"CategoryTh... | true |
AddGroup.residuallyFinite_of_forall_exists_finite_addMonoidHom | Mathlib.GroupTheory.ResiduallyFinite | [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"AddSubgroup.FiniteIndex",
"congrArg",
"Subtype.finite",
"Finite",
"AddMonoid.toAddZeroClass",
"AddMonoidHom.range",
"Membership.mem",
"Exists",
"AddZeroClass.toAddZero",
"id",
"Ne",
"SubtractionMonoid.toSubNegZeroMonoid",
"AddGroup.residuallyFin... | true |
_aux_Mathlib_Data_Fintype_Sets___elabRules_finsetStx_1 | Mathlib.Data.Fintype.Sets | [
"Pure.pure",
"Lean.TSyntax",
"Lean.Elab.Term.TermElab",
"Lean.instMonadExceptOfExceptionCoreM",
"Lean.Meta.mkFreshLevelMVar",
"Lean.MetavarKind.natural",
"Lean.Elab.Term.elabTerm",
"Lean.Expr.isAppOfArity",
"Lean.mkSort",
"Lean.Elab.Term.instMonadTermElabM",
"ReaderT",
"Lean.Meta.State",
"Le... | false |
isOpen_iff_generate_intervals._to_dual_1 | Mathlib.Topology.Order.Basic | [
"Preorder.topology",
"Eq.mpr",
"OrderTopology",
"Set.Ioi",
"congrArg",
"Iff.rfl",
"setOf",
"Exists",
"Eq.mp",
"id",
"TopologicalSpace.generateFrom",
"TopologicalSpace",
"Preorder.topology._to_dual_cast_4",
"Iff",
"implies_congr",
"congr",
"TopologicalSpace.GenerateOpen",
"Eq.refl",... | false |
CategoryTheory.Subobject.instLattice._proof_1 | Mathlib.CategoryTheory.Subobject.Lattice | [
"SemilatticeSup.le_sup_left",
"CategoryTheory.Limits.HasImages",
"PartialOrder.toPreorder",
"Preorder.toLE",
"CategoryTheory.Subobject.semilatticeSup",
"LE.le",
"SemilatticeSup.toPartialOrder",
"CategoryTheory.Limits.HasBinaryCoproducts",
"CategoryTheory.Subobject",
"CategoryTheory.Category",
"S... | false |
CategoryTheory.CatEnrichedOrdinary.instCategoryHom._proof_2 | Mathlib.CategoryTheory.Bicategory.CatEnriched | [
"CategoryTheory.Cat.category",
"Equiv.instEquivLike",
"CategoryTheory.EnrichedOrdinaryCategory",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.CatEnrichedOrdinary.Hom.ext",
"CategoryTheory.CatEnrichedOrdinary",
"congrArg",
"CategoryTheory.EnrichedOrdinaryCategory.toEnriched... | false |
CategoryTheory.Abelian.LeftResolution.karoubi.π | Mathlib.Algebra.Homology.LeftResolution.Reduced | [
"CategoryTheory.Idempotents.whiskeringLeftObjToKaroubiFullyFaithful",
"CategoryTheory.Abelian.LeftResolution.karoubi.F",
"CategoryTheory.Functor",
"CategoryTheory.Idempotents.Karoubi",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Functor.Additive",
"CategoryTheory.Functor.ca... | true |
HomologicalComplex.eval._proof_1 | Mathlib.Algebra.Homology.HomologicalComplex | [
"CategoryTheory.Limits.HasZeroMorphisms",
"HomologicalComplex.instCategory",
"HomologicalComplex.Hom.f",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HomologicalComplex",
"CategoryTheory.CategoryStruct.id",
"id",
"ComplexShape",
"Eq.refl",
"CategoryTheory.Category.toCategoryStruct",
... | false |
SimpleGraph.not_isCompleteMultipartite_iff_exists_isPathGraph3Compl | Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite | [
"congrArg",
"SimpleGraph.Adj",
"Exists",
"Eq.mp",
"IsTrans.trans",
"SimpleGraph.IsPathGraph3Compl",
"SimpleGraph.IsCompleteMultipartite",
"SimpleGraph.exists_isPathGraph3Compl_of_not_isCompleteMultipartite",
"SimpleGraph",
"Iff",
"_private.Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite.0... | true |
Set.Subsingleton.countable | Mathlib.Data.Set.Countable | [
"Set.Subsingleton",
"Set.Countable",
"Set.Subsingleton.finite",
"Set.Finite.countable",
"Set"
] | true |
Submodule.range_projectionL | Mathlib.Topology.Algebra.Module.Complement | [
"Submodule",
"RingHomSurjective.ids",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"Submodule.projectionL",
"LinearMap.range",
"AddCommGroup",
"ContinuousLinearMap.toLinearMap",
"Submodule.IsTopCompl.isCompl",
"Submodule.IsTopCompl",
"TopologicalSpace",
"True",
"eq_self",
"Submodule.range_p... | true |
QuadraticMap.Isometry.ofEq | Mathlib.LinearAlgebra.QuadraticForm.Isometry | [
"LinearMap.id",
"CommSemiring.toSemiring",
"QuadraticMap.Isometry.ofEq._proof_1",
"LinearMap",
"AddCommMonoid",
"CommSemiring",
"QuadraticMap.Isometry.mk",
"Module",
"RingHom.id",
"Semiring.toNonAssocSemiring",
"Eq",
"QuadraticMap.Isometry",
"QuadraticMap"
] | true |
Equiv.Perm.apply_mem_support | Mathlib.GroupTheory.Perm.Support | [
"Eq.mpr",
"Equiv.Perm.support",
"Equiv.instEquivLike",
"congrArg",
"Finset",
"Iff.rfl",
"Equiv.Perm.mem_support",
"Membership.mem",
"id",
"Equiv",
"Ne",
"Iff",
"Fintype",
"Finset.instSetLike",
"Equiv.Perm",
"Ne.eq_1",
"propext",
"Equiv.apply_eq_iff_eq",
"Eq",
"DFunLike.coe",
... | true |
PeriodPair.derivWeierstrassPExcept_def | Mathlib.Analysis.SpecialFunctions.Elliptic.Weierstrass | [
"Eq.mpr",
"Submodule",
"PeriodPair.derivWeierstrassPExcept_sub",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddMonoid.toAddZeroClass",
"Nat.instAtLeastTwoHAddOfNat",
"Complex.instNormedField",
"HSub.hSub",
"Membership.mem",
"Comple... | true |
_private.Std.Data.DTreeMap.Internal.Lemmas.0.Std.DTreeMap.Internal.Impl.get!_empty._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 |
FreeAddMagma.length | Mathlib.Algebra.Free | [
"FreeAddMagma.brecOn",
"FreeAddMagma.length._f",
"Nat",
"FreeAddMagma"
] | true |
ContDiffWithinAt.mul | Mathlib.Analysis.Calculus.ContDiff.Operations | [
"ContDiff.comp_contDiffWithinAt",
"Prod.normedSpace",
"NormedRing.toRing",
"HMul.hMul",
"Prod.normedAddCommGroup",
"NormedSpace",
"NormedRing.toNonUnitalNormedRing",
"Prod.mk",
"Prod.fst",
"instDistribOfSemiring",
"NonUnitalNormedRing.toNormedAddCommGroup",
"Distrib.toMul",
"NormedAlgebra.to... | true |
Finset.mem_attachFin._simp_1 | Mathlib.Data.Finset.Fin | [
"Finset",
"Membership.mem",
"Fin.val",
"Finset.instSetLike",
"Nat",
"LT.lt",
"propext",
"instLTNat",
"Fin",
"Finset.attachFin",
"Eq",
"SetLike.instMembership",
"Finset.mem_attachFin"
] | false |
Lean.Compiler.LCNF.Code.isDecl | Lean.Compiler.LCNF.Basic | [
"Lean.Compiler.LCNF.FunDecl",
"Lean.Compiler.LCNF.Purity",
"Lean.Compiler.LCNF.Purity.pure",
"autoParam",
"Bool.true",
"Lean.Compiler.LCNF.Code",
"_private.Lean.Compiler.LCNF.Basic.0.Lean.Compiler.LCNF.Code.isDecl.match_1",
"Bool",
"Lean.Compiler.LCNF.Alt._auto_5",
"Lean.Compiler.LCNF.LetDecl",
... | true |
CategoryTheory.Limits.CoproductsFromFiniteFiltered.liftToFinsetColimIso._proof_1 | Mathlib.CategoryTheory.Limits.Constructions.Filtered | [
"CategoryTheory.Functor",
"CategoryTheory.Limits.hasColimitOfHasColimitsOfShape",
"CategoryTheory.Limits.HasColimitsOfShape",
"CategoryTheory.discreteCategory",
"CategoryTheory.Limits.HasColimit",
"CategoryTheory.Category",
"CategoryTheory.Discrete"
] | false |
CategoryTheory.Sieve.functorPullback_monotone | Mathlib.CategoryTheory.Sites.Sieves | [
"GaloisConnection.monotone_u",
"CategoryTheory.Functor",
"PartialOrder.toPreorder",
"Monotone",
"CategoryTheory.Sieve",
"CompleteLattice.toCompleteSemilatticeInf",
"CompleteSemilatticeInf.toPartialOrder",
"CategoryTheory.Sieve.functorPushforward",
"CategoryTheory.Sieve.functor_galoisConnection",
"... | true |
exists_orderEmbedding_covby_of_forall_covby_finite | Mathlib.Order.KonigLemma | [
"Preorder.toLT",
"Set.Ici",
"strictMono_nat_of_lt_succ",
"IsStronglyAtomic",
"CovBy",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Set.Finite",
"Exists",
"PartialOrder",
"exists_seq_covby_of_forall_covby_finite",
"instOfNatNat",
"instLENat",
"instHAdd",
"And",
"Exists.casesO... | true |
_private.Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable.0.aestronglyMeasurable_union_iff._simp_1_1 | Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable | [
"Bool.forall_bool",
"Bool.true",
"And",
"propext",
"Bool",
"Bool.false",
"Eq"
] | false |
himp_inf_le | Mathlib.Order.Heyting.Basic | [
"le_rfl",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOrder",
"GeneralizedHeytingAlgebra.toHImp",
"SemilatticeInf.toMin",
"LE.le",
"le_himp_iff",
"GeneralizedHeytingAlgebra.toLattice",
"Iff.mp",
"GeneralizedHeytingAlgebra",
"Min.min",
"HImp.himp",
"Lattice.toSemila... | true |
isMulTorsionFree_iff_not_isOfFinOrder | Mathlib.GroupTheory.OrderOfElement | [
"Eq.mpr",
"MulOne.toOne",
"not_isOfFinOrder_of_isMulTorsionFree",
"instHDiv",
"InvOneClass.toOne",
"DivisionCommMonoid.toDivisionMonoid",
"IsMulTorsionFree",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"congrArg",
"DivInvOneMonoid.toDivInvMonoid",
"_private.Mathlib.GroupTheory.Ord... | true |
_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_58 | Mathlib.Data.List.Induction | [
"List.getLast",
"False",
"Lean.Grind.nestedProof",
"eq_false",
"congrArg",
"False.elim",
"Lean.Grind.Bool.ne_of_eq_false_of_eq_true",
"noConfusion_of_Nat",
"Lean.Grind.imp_false_eq",
"cast",
"Eq.mp",
"_private.Mathlib.Data.List.Induction.0.List.reverseRec_concat._proof_1_10",
"instDecidableE... | false |
Topology.IsLocallyConstructible.preimage_of_isOpenEmbedding | Mathlib.Topology.Constructible | [
"Set.restrictPreimage",
"Filter.instMembership",
"ContinuousAt.preimage_mem_nhds",
"Topology.IsConstructible.preimage_of_isOpenEmbedding",
"Membership.mem",
"Exists",
"nhds",
"Set.Elem",
"Topology.IsOpenEmbedding.continuous",
"Topology.IsOpenEmbedding.restrictPreimage",
"And.casesOn",
"Continu... | true |
CoalgCat.forget₂_obj | Mathlib.Algebra.Category.CoalgCat.Basic | [
"CoalgCat.toModuleCat",
"CommRing",
"Coalgebra.toCoalgebraStruct",
"CoalgCat",
"CoalgCat.category",
"ModuleCat",
"CoalgHom",
"CoalgCat.hasForgetToModule",
"AddCommGroup.toAddCommMonoid",
"LinearMap.instFunLike",
"ModuleCat.instConcreteCategoryLinearMapIdCarrier",
"LinearMap",
"CoalgCat.concr... | true |
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