name stringlengths 2 347 | module stringlengths 6 90 | deps listlengths 0 686 | allowCompletion bool 2
classes |
|---|---|---|---|
Set.preimage_const | Mathlib.Data.Set.Image | [
"Set.univ",
"_private.Mathlib.Data.Set.Image.0.Set.preimage_const._proof_1_1",
"Decidable",
"Membership.mem",
"Set.preimage",
"Set.instEmptyCollection",
"EmptyCollection.emptyCollection",
"Eq",
"Set.instMembership",
"ite",
"Set"
] | true |
Multiset.union_le_iff | Mathlib.Data.Multiset.UnionInter | [
"Lattice.toSemilatticeSup",
"PartialOrder.toPreorder",
"Multiset.instLattice",
"Preorder.toLE",
"Multiset",
"LE.le",
"sup_le_iff",
"And",
"Iff",
"Multiset.instUnion",
"Union.union",
"Multiset.instPartialOrder",
"DecidableEq"
] | true |
genericPoint_specializes | Mathlib.Topology.Sober | [
"Specializes",
"IsGenericPoint.specializes",
"IsIrreducible.genericPoint",
"congrArg",
"IsIrreducible.isGenericPoint_genericPoint_closure",
"Set.mem_univ._simp_1",
"Set.univ",
"IsClosed.closure_eq",
"Membership.mem",
"IrreducibleSpace.isIrreducible_univ",
"QuasiSober",
"IsClosed",
"Topologic... | true |
Mathlib.Meta.NormNum.Result.toSimpResult.match_1 | Mathlib.Tactic.NormNum.Result | [
"Lean.Expr.const",
"Lean.Expr.sort",
"Lean.Level",
"List.cons",
"Qq.Quoted",
"Lean.Expr.app",
"Sigma.mk",
"Sigma.casesOn",
"Lean.Level.succ",
"Lean.Name.mkStr1",
"Sigma",
"List.nil"
] | false |
PositiveLinearMap.gnsStarAlgHom._proof_13 | Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal | [
"InnerProductSpace.toNormedSpace",
"NormedCommRing.toSeminormedCommRing",
"CStarAlgebra.toNonUnitalCStarAlgebra",
"NonUnitalCStarAlgebra.toNonUnitalNormedRing",
"NormedRing.toRing",
"NormedSpace.toIsBoundedSMul",
"Complex.instNormedAddCommGroup",
"Complex.commRing",
"CommSemiring.toSemiring",
"Add... | false |
Filter.HasBasis.inf_neBot_iff | Mathlib.Order.Filter.Bases.Basic | [
"Filter.instMembership",
"Filter.HasBasis.inf_basis_neBot_iff",
"Filter.NeBot",
"Membership.mem",
"Set.instInter",
"Filter.instInf",
"Inter.inter",
"Filter.basis_sets",
"Filter.HasBasis",
"Iff",
"Set.Nonempty",
"Filter",
"Min.min",
"Set"
] | true |
BialgEquiv.ofAlgEquiv._proof_7 | Mathlib.RingTheory.Bialgebra.Equiv | [
"BialgEquiv.ofAlgEquiv._proof_4",
"AlgHom.toLinearMap",
"AlgEquiv.instEquivLike",
"Coalgebra.toCoalgebraStruct",
"Bialgebra.comulAlgHom",
"SemilinearMapClass.toMulActionSemiHomClass",
"BialgEquiv.ofAlgEquiv._proof_2",
"NonUnitalAlgHomClass.instLinearMapClass",
"Bialgebra.toCoalgebra",
"congrArg",
... | false |
CategoryTheory.Functor.PreservesRightHomologyOf.mk._flat_ctor | Mathlib.Algebra.Homology.ShortComplex.PreservesHomology | [
"CategoryTheory.Limits.HasZeroMorphisms",
"CategoryTheory.Functor",
"CategoryTheory.ShortComplex.RightHomologyData",
"CategoryTheory.Functor.PreservesRightHomologyOf.mk",
"CategoryTheory.ShortComplex",
"CategoryTheory.ShortComplex.RightHomologyData.IsPreservedBy",
"CategoryTheory.Functor.PreservesRightH... | false |
_private.Aesop.Forward.State.0.Aesop.VariableMap.modifyM.match_3 | Aesop.Forward.State | [
"Unit.unit",
"Aesop.InstMap",
"Option.casesOn",
"Option.some",
"Option.none",
"Unit",
"Option"
] | false |
Matroid.mapSetEmbedding_indep_iff' | Mathlib.Combinatorics.Matroid.Map | [
"Eq.mpr",
"congrArg",
"Matroid.E",
"Membership.mem",
"Exists",
"Eq.mp",
"Matroid.Indep",
"Set.Elem",
"id",
"Subtype",
"HasSubset.Subset",
"Matroid.mapSetEmbedding",
"_private.Mathlib.Combinatorics.Matroid.Map.0.Matroid.mapSetEmbedding._simp_5",
"Function.Embedding",
"And.casesOn",
"And... | true |
Topology.IsEmbedding.comapUniformSpace | Mathlib.Topology.UniformSpace.UniformEmbedding | [
"UniformSpace",
"Topology.IsEmbedding.comapUniformSpace._proof_1",
"UniformSpace.replaceTopology",
"TopologicalSpace",
"Topology.IsEmbedding",
"UniformSpace.comap",
"UniformSpace.toTopologicalSpace"
] | true |
_private.Mathlib.NumberTheory.DirichletCharacter.Orthogonality.0.DirichletCharacter.sum_char_inv_mul_char_eq._simp_1_1 | Mathlib.NumberTheory.DirichletCharacter.Orthogonality | [
"HMul.hMul",
"Mul",
"MulHomClass",
"map_mul",
"Eq.symm",
"Eq",
"DFunLike.coe",
"FunLike",
"instHMul"
] | false |
Nat.add_mod_add_ite | Mathlib.Data.Nat.ModEq | [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Nat.mod_zero",
"MulOne.toOne",
"Nat.ModEq.add",
"instHDiv",
"HMul.hMul",
"Nat.mod_modEq",
"congrArg",
"add_assoc",
"lt_of_not_ge",
"AddMonoid.toAddZeroClass",
"Nat.instAtLeastTwoHAddOfNat",
"AddCancelMonoid.toAddRightCancelMonoid",
"N... | true |
Algebra.idealMap._proof_1 | Mathlib.RingTheory.Ideal.Maps | [
"Semiring.toModule",
"CommSemiring.toSemiring",
"Ideal.mem_map_of_mem",
"Algebra",
"RingHom",
"Membership.mem",
"algebraMap",
"Ideal.map",
"Ideal",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"RingHom.instFunLike",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Submodule... | false |
_private.Mathlib.RingTheory.WittVector.TeichmullerSeries.0.WittVector._aux_Mathlib_RingTheory_WittVector_TeichmullerSeries___unexpand_WittVector_1 | Mathlib.RingTheory.WittVector.TeichmullerSeries | [
"Pure.pure",
"cond",
"Lean.TSyntax",
"Unit.unit",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.matchesIdent",
"Lean.Name.mkNum",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"Lean.PrettyPrinter.UnexpandM",
"MonadExcept.throw",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Sy... | false |
Finset.toRight_union | Mathlib.Data.Finset.Sum | [
"Finset.instUnion",
"congrArg",
"Finset",
"instDecidableEqSum",
"Finset.ext",
"Membership.mem",
"Sum",
"Finset.mem_toRight._simp_1",
"Finset.toRight",
"Finset.mem_union._simp_1",
"iff_self",
"Iff",
"Finset.instSetLike",
"Sum.inr",
"congr",
"True",
"of_eq_true",
"Or",
"Union.union... | true |
HasSum.mul_of_nonarchimedean | Mathlib.Topology.Algebra.InfiniteSum.Nonarchimedean | [
"UniformSpace",
"Eq.mpr",
"UniformSpace.Completion.coe'",
"HMul.hMul",
"UniformSpace.Completion.mul",
"Ring.toNonAssocRing",
"IsTopologicalRing.toIsTopologicalSemiring",
"AddGroupWithOne.toAddGroup",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"AddMonoid.toAddZeroClass",
"SummationFilter",
"... | true |
Asymptotics.isEquivalent_of_tendsto_one | Mathlib.Analysis.Asymptotics.AsymptoticEquivalent | [
"NormedCommRing.toNormedRing",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"NormedCommRing.toSeminormedCommRing",
"False",
"instHDiv",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
"NeZero.one",
"NormedRing.toRing",
"HMul.hMul",
"GroupWithZero.toDivInvMonoid",
"MulZeroClass.toMul",
"div_m... | true |
Lean.Compiler.LCNF.CSE.State.noConfusion | Lean.Compiler.LCNF.CSE | [
"Lean.Expr.instBEq",
"Lean.Compiler.LCNF.CSE.State.noConfusionType",
"Lean.PHashMap",
"Lean.Expr",
"Lean.FVarId",
"Lean.Compiler.LCNF.CSE.State.casesOn",
"Lean.Compiler.LCNF.Purity.pure",
"Lean.Compiler.LCNF.CSE.State",
"Eq.ndrec",
"Eq.refl",
"Lean.Expr.instHashable",
"Lean.Compiler.LCNF.FVarS... | false |
TopologicalSpace.Clopens.coe_inf | Mathlib.Topology.Sets.Closeds | [
"TopologicalSpace.Clopens.instMin",
"Set.instInter",
"Inter.inter",
"TopologicalSpace",
"SetLike.coe",
"TopologicalSpace.Clopens",
"Eq",
"Min.min",
"rfl",
"TopologicalSpace.Clopens.instSetLike",
"Set"
] | true |
Aesop.Queue.mk._flat_ctor | Aesop.Search.Queue.Class | [
"Aesop.Queue.mk",
"Array",
"Aesop.GoalRef",
"Aesop.Queue",
"Prod",
"BaseIO",
"Option"
] | false |
Lean.Elab.Term.StructInst.FieldLHS.fieldIndex.injEq | Lean.Elab.StructInst | [
"Eq.propIntro",
"Lean.Elab.Term.StructInst.FieldLHS",
"Lean.injEq_helper",
"Lean.Syntax",
"Lean.Elab.Term.StructInst.FieldLHS.fieldIndex.inj",
"Lean.Elab.Term.StructInst.FieldLHS.fieldIndex",
"And",
"Nat",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
SimpleGraph.center_top | Mathlib.Combinatorics.SimpleGraph.Diam | [
"Nontrivial",
"Eq.mpr",
"instAddMonoidWithOneENat",
"congrArg",
"Set.univ",
"Set.eq_univ_iff_forall",
"SimpleGraph.center_eq_univ_of_subsingleton",
"Membership.mem",
"id",
"subsingleton_or_nontrivial",
"SimpleGraph.center",
"SimpleGraph.mem_center_iff",
"Or.casesOn",
"SimpleGraph",
"AddM... | true |
CategoryTheory.RetractArrow.map_i_left | Mathlib.CategoryTheory.Retract | [
"CategoryTheory.Functor",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CategoryTheory.Comma.left",
"CategoryTheory.Functor.id",
"CategoryTheory.RetractArrow.map",
"CategoryTheory.Retract.i",
"CategoryTheory.instCategoryArrow",
"CategoryTheory.Functor.map",
"CategoryTheory.CommaMorphism... | true |
_private.Mathlib.Data.Int.Interval.0.Finset.Ioc_succ_succ._simp_1_2 | Mathlib.Data.Int.Interval | [
"Finset",
"Membership.mem",
"Insert.insert",
"Finset.mem_insert",
"Finset.instInsert",
"Finset.instSetLike",
"propext",
"Or",
"Eq",
"SetLike.instMembership",
"DecidableEq"
] | false |
Finset.filter_subset._simp_1 | Mathlib.Data.Finset.Filter | [
"Finset",
"Finset.filter_subset",
"HasSubset.Subset",
"DecidablePred",
"True",
"eq_true",
"Finset.instHasSubset",
"Finset.filter",
"Eq"
] | false |
SheafOfModules.hom_ext_iff | Mathlib.Algebra.Category.ModuleCat.Sheaf | [
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"HEq.refl",
"CategoryTheory.Functor.category",
"SheafOfModules.val",
"PresheafOfModules.instCategory",
"Eq.casesOn",
"CategoryTheory.ObjectProperty.FullSubcategory.obj",
"RingCat",
"Iff",
"PresheafO... | true |
algebraMap_smul | Mathlib.Algebra.Algebra.Basic | [
"instHSMul",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"algebra_compatible_smul",
"IsScalarTower",
"AddMonoid.toAddZeroClass",
"Algebra",
"RingHom",
"Algebra.toSMul",
"algebraMap",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"AddCommMonoid",
"CommSemiring",
... | true |
pi_generateFrom_eq_finite | Mathlib.Topology.Constructions | [
"Iff.mpr",
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"False",
"Set.piecewise_eq_of_notMem",
"Finset.univ",
"Finset.coe_univ",
"eq_false",
"Pi.topologicalSpace",
"congrArg",
"and_self",
"Compl.compl",
"Finset",
"Set.univ",
"Finite",
"TopologicalSpace.GenerateOpen.basic",
"setOf",
"Set.sU... | true |
_private.Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper.0.AlgebraicGeometry.Proj.valuativeCriterion_existence_aux._simp_1_11 | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | [
"ValuationRing.mem_integer_iff",
"IsDomain",
"ValuationRing.linearOrderedCommGroupWithZero",
"CommRing",
"Subring.instSetLike",
"Ring.toNonAssocRing",
"CommSemiring.toSemiring",
"IsFractionRing",
"ValuationRing.ValueGroup",
"Algebra",
"RingHom",
"Membership.mem",
"Exists",
"Field.toDivisio... | false |
TwoSidedIdeal.asIdealOpposite | Mathlib.RingTheory.TwoSidedIdeal.Operations | [
"Submodule",
"Semiring.toModule",
"Ring.toNonAssocRing",
"TwoSidedIdeal.asIdeal",
"TwoSidedIdeal",
"MulOpposite",
"PartialOrder.toPreorder",
"Preorder.toLE",
"RingCon.op",
"Membership.mem",
"Distrib.toAdd",
"NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring",
"Submodule.instPartialOrder",
... | true |
Mathlib.Meta.NormNum.evalIsSquareRat | Mathlib.Tactic.NormNum.IsSquare | [
"Qq.QuotedDefEq",
"Pure.pure",
"Lean.instantiateMVars",
"Lean.MonadError.mk",
"Lean.instMonadExceptOfExceptionCoreM",
"Mathlib.Meta.NormNum.derive",
"Lean.MetavarKind.natural",
"_private.Mathlib.Tactic.NormNum.IsSquare.0.Mathlib.Meta.NormNum.evalIsSquareRat.match_100",
"ReaderT",
"instMonadControl... | true |
Std.MaxEqOr | Init.Data.Order.Classes | [
"Max",
"Std.MaxEqOr.mk"
] | true |
BitVec.ofInt_iSizeToInt | Init.Data.SInt.Lemmas | [
"instPowNat",
"ISize.toInt_bmod_two_pow_numBits",
"congrArg",
"BitVec",
"BitVec.ofInt",
"instOfNatNat",
"BitVec.toInt_ofInt",
"Int",
"BitVec.eq_of_toInt_eq",
"instNatPowNat",
"System.Platform.numBits",
"HPow.hPow",
"Int.bmod",
"Nat",
"congr",
"True",
"ISize.toBitVec",
"eq_self",
... | true |
Btw.rec | Mathlib.Order.Circular | [
"Btw",
"Btw.mk"
] | false |
MeasurableSpace.DynkinSystem.instPartialOrder._proof_3 | Mathlib.MeasureTheory.PiSystem | [
"Iff.mpr",
"Pi.preorder",
"Prop.le",
"PartialOrder.toPreorder",
"LE.le",
"Pi.hasLe",
"MeasurableSpace.DynkinSystem",
"MeasurableSpace.DynkinSystem.Has",
"MeasurableSpace.DynkinSystem.instLEDynkinSystem",
"Prop.partialOrder",
"MeasurableSpace.DynkinSystem.le_def",
"le_trans",
"Set"
] | false |
Std.DTreeMap.Internal.Impl.getKey._sunfold | Std.Data.DTreeMap.Internal.Queries | [
"Ordering.gt",
"Std.DTreeMap.Internal.Impl.getKey.match_1",
"Ord",
"Std.DTreeMap.Internal.Impl.getKey",
"Ordering",
"Ordering.eq",
"Std.DTreeMap.Internal.Impl.inner",
"Ord.compare",
"Bool.true",
"Std.DTreeMap.Internal.Impl.contains",
"Ordering.lt",
"Nat",
"Bool",
"Std.DTreeMap.Internal.Imp... | false |
Lean.Meta.Grind.AC.DiseqCnstrProof.erase_dup | Lean.Meta.Tactic.Grind.AC.Types | [
"Lean.Meta.Grind.AC.DiseqCnstr",
"Lean.Meta.Grind.AC.DiseqCnstrProof",
"Lean.Meta.Grind.AC.DiseqCnstrProof.erase_dup"
] | true |
Sum.swap_swap_eq | Init.Data.Sum.Lemmas | [
"Sum.swap",
"Sum.swap_swap",
"Function.comp",
"Sum",
"id",
"funext",
"Eq"
] | true |
_private.Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.0._auto_382 | Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
UniformSpace.hausdorff | Mathlib.Topology.UniformSpace.Closeds | [
"UniformSpace",
"UniformSpace.ofCore",
"uniformity",
"Filter.lift'",
"UniformSpace.hausdorff._proof_4",
"UniformSpace.Core.mk",
"Prod",
"UniformSpace.hausdorff._proof_1",
"hausdorffEntourage",
"UniformSpace.hausdorff._proof_3",
"Set"
] | true |
CovariantDerivative.difference | Mathlib.Geometry.Manifold.VectorBundle.CovariantDerivative.Basic | [
"NormedCommRing.toSeminormedCommRing",
"CompleteSpace",
"instAddMonoidWithOneENat",
"NormedSpace",
"ContinuousSMul",
"CovariantDerivative.toFun",
"FiberBundle",
"ContinuousLinearMap.topologicalSpace",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"IsCovariantDerivativeOn.diff... | true |
Sum.getRight_eq_getRight? | Mathlib.Data.Sum.Basic | [
"Sum.isRight",
"Sum.getRight?",
"Sum",
"Bool.true",
"Sum.getRight",
"Option.get",
"Bool",
"_private.Mathlib.Data.Sum.Basic.0.Sum.getRight_eq_getRight?._proof_1_5",
"Option.isSome",
"Eq"
] | true |
Lean.Meta.Sym.getInt16Value? | Lean.Meta.Sym.LitValues | [
"Pure.pure",
"OptionT.instMonad",
"OptionT",
"Int16",
"Int16.ofInt",
"Lean.Expr",
"Lean.Meta.Sym.getIntValue?",
"Int",
"Id",
"Applicative.toPure",
"Alternative.toApplicative",
"Monad.toBind",
"Bind.bind",
"Id.instMonad",
"OptionT.instAlternative"
] | true |
Submodule.instDiv._proof_1 | Mathlib.Algebra.Algebra.Operations | [
"add_mul",
"Eq.mpr",
"Submodule",
"HMul.hMul",
"congrArg",
"CommSemiring.toSemiring",
"AddMonoid.toAddZeroClass",
"setOf",
"Algebra",
"Distrib.rightDistribClass",
"Membership.mem",
"AddZeroClass.toAddZero",
"Algebra.toModule",
"id",
"CommSemiring",
"NonUnitalNonAssocSemiring.toAddCommM... | false |
SeminormedCommGroup | Mathlib.Analysis.Normed.Group.Defs | [
"SeminormedCommGroup.mk"
] | true |
Topology.IsQuotientMap.trivializationOfVAddDisjoint._proof_8 | Mathlib.Topology.Covering.Quotient | [
"AddGroup.toSubtractionMonoid",
"NegZeroClass.toNeg",
"AddMonoid.toAddSemigroup",
"Membership.mem",
"SubtractionMonoid.toSubNegZeroMonoid",
"SubNegZeroMonoid.toNegZeroClass",
"HVAdd.hVAdd",
"And.casesOn",
"AddAction",
"AddAction.toAddSemigroupAction",
"Topology.IsQuotientMap.trivializationOfVAdd... | false |
Computability.«term_≡ᵀ_» | Mathlib.Computability.TuringDegree | [
"Lean.ParserDescr.trailingNode",
"instOfNatNat",
"Lean.ParserDescr.binary",
"Nat",
"Lean.ParserDescr.symbol",
"Lean.Name.mkStr2",
"Lean.ParserDescr.cat",
"OfNat.ofNat",
"Lean.Name.mkStr1",
"Lean.TrailingParserDescr"
] | true |
Vector.push_inj_left | Init.Data.Vector.Lemmas | [
"Vector.pop_eq_of_push_eq",
"Vector.push",
"Vector",
"congrArg",
"instOfNatNat",
"instHAdd",
"Iff",
"HAdd.hAdd",
"Nat",
"True",
"Iff.intro",
"eq_self",
"of_eq_true",
"instAddNat",
"congrFun'",
"OfNat.ofNat",
"Eq",
"Eq.trans"
] | true |
Lean.mkPtrSet | Lean.Util.PtrSet | [
"Lean.instBEqPtr",
"Lean.PtrSet",
"instOfNatNat",
"Lean.Ptr",
"Nat",
"Lean.instHashablePtr",
"optParam",
"OfNat.ofNat",
"Std.HashSet.emptyWithCapacity"
] | true |
Subtype.forall_set_subtype | Mathlib.Data.Set.Image | [
"Eq.mpr",
"congrArg",
"Set.forall_subset_range_iff",
"Iff.rfl",
"Membership.mem",
"Set.Elem",
"id",
"Subtype",
"HasSubset.Subset",
"Subtype.range_coe",
"Iff",
"propext",
"Set.image",
"Set.range",
"Eq.symm",
"Subtype.val",
"Eq",
"Set.instMembership",
"Set.instHasSubset",
"Set"
] | true |
Lean.Widget.GetGoToLocationParams.noConfusionType | Lean.Server.FileWorker.WidgetRequests | [
"Lean.Widget.GetGoToLocationParams.casesOn",
"Lean.Server.WithRpcRef",
"Lean.Widget.GetGoToLocationParams",
"Lean.Elab.InfoWithCtx",
"Lean.Server.GoToKind",
"Eq"
] | false |
SimpleGraph.Subgraph.botIso._proof_2 | Mathlib.Combinatorics.SimpleGraph.Subgraph | [
"SimpleGraph.Subgraph.botIso.match_1",
"Empty.elim",
"SimpleGraph.Subgraph",
"False.elim",
"Membership.mem",
"Set.Elem",
"Bot.bot",
"Subtype.mk",
"SimpleGraph",
"Empty",
"SimpleGraph.Subgraph.instBot",
"Eq",
"Set.instMembership",
"SimpleGraph.Subgraph.verts",
"Subtype.property",
"Simpl... | false |
CategoryTheory.Grothendieck.map._proof_2 | Mathlib.CategoryTheory.Grothendieck | [
"CategoryTheory.Cat.category",
"Eq.mpr",
"CategoryTheory.Functor",
"CategoryTheory.Grothendieck.fiber",
"CategoryTheory.Cat.Hom₂.eqToHom_toNatTrans",
"CategoryTheory.Grothendieck.base",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.eqToHom_map",
"CategoryThe... | false |
_private.Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper.0.AlgebraicGeometry.Proj.isSeparated._simp_5 | Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper | [
"AlgebraicGeometry.Spec",
"AlgebraicGeometry.Scheme",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"CommRingCat",
"AlgebraicGeometry.Spec.map",
"CommRingCat.instCategory",
"AlgebraicGeometry.Spec.map_comp",
"CategoryTheory.CategoryStruct.comp",
"CategoryTheory.Category.toCategoryStruct"... | false |
Turing.TM1to0.trAux._sunfold | Mathlib.Computability.TuringMachine.PostTuringMachine | [
"cond",
"Option.some",
"Prod.mk",
"Turing.TM1to0.Λ'",
"Turing.TM1to0.trAux",
"Option.none",
"Turing.TM0.Stmt.move",
"Bool",
"Prod",
"Turing.TM1to0.trAux.match_1",
"Turing.TM0.Stmt",
"Turing.TM1.Stmt",
"Turing.Dir",
"Turing.TM0.Stmt.write",
"Option"
] | false |
ContinuousAlternatingMap.piLIE._proof_6 | Mathlib.Analysis.Normed.Module.Alternating.Basic | [
"SeminormedAddGroup.toAddGroup",
"SeminormedAddCommGroup",
"NormedSpace",
"AddCommGroup.toAddCommMonoid",
"NormedSpace.toModule",
"NormedField.toField",
"Field.toSemifield",
"Field.toCommRing",
"smulCommClass_self",
"SeminormedAddCommGroup.toSeminormedAddGroup",
"Semifield.toDivisionSemiring",
... | false |
Function.IsFixedPt.eq_1 | Mathlib.Order.OmegaCompletePartialOrder | [
"Eq.refl",
"Function.IsFixedPt",
"Eq"
] | true |
Dvd.noConfusion | Init.Prelude | [
"HEq.refl",
"Dvd.noConfusionType",
"Dvd",
"Dvd.casesOn",
"eq_of_heq",
"Eq.ndrec",
"HEq",
"Eq"
] | false |
Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.cooper₁.elim | Lean.Meta.Tactic.Grind.Arith.Cutsat.Types | [
"PULift.up",
"Lean.Meta.Grind.Arith.Cutsat.CooperSplit",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.ctorElim",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof",
"Nat",
"Eq.symm",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.ctorIdx",
"Eq",
"Lean.Meta.Grind.Arith.Cutsat.DvdCnstrProof.cooper₁"
] | false |
Algebra.WeaklyQuasiFiniteAt.of_quasiFiniteAt_residueField | Mathlib.RingTheory.QuasiFinite.Weakly | [
"IsUnit.mul_iff",
"Ideal.Quotient.isScalarTower",
"NonUnitalNonAssocCommRing.toNonUnitalNonAssocCommSemiring",
"Ideal.Quotient.commSemiring",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"RingHom.instRingHomClass",
"Algebra.QuasiFinite.of_surjective_algHom",
"CommRing",
"Algebra.to_smulCom... | true |
Std.TreeSet.Raw.maxD_eq_iff_mem_and_forall | Std.Data.TreeSet.Raw.Lemmas | [
"Std.TreeSet.Raw.WF.out",
"Membership.mem",
"Ordering",
"Std.TreeSet.Raw.instMembership",
"Std.TransCmp",
"Std.TreeMap.Raw.maxKeyD_eq_iff_mem_and_forall",
"Bool.true",
"And",
"Std.TreeSet.Raw",
"Unit",
"Iff",
"Std.LawfulEqCmp",
"Bool",
"Std.TreeSet.Raw.isEmpty",
"Ordering.isLE",
"Std.T... | true |
CompactlySupportedContinuousMap.instInf._proof_2 | Mathlib.Topology.ContinuousMap.CompactlySupported | [
"CompactlySupportedContinuousMap.hasCompactSupport",
"CompactlySupportedContinuousMap",
"Pi.instMinForall_mathlib",
"SemilatticeInf.toMin",
"TopologicalSpace",
"SemilatticeInf",
"CompactlySupportedContinuousMap.instFunLike",
"DFunLike.coe",
"HasCompactSupport.inf",
"Min.min",
"HasCompactSupport"... | false |
_private.Mathlib.Algebra.Algebra.Bilinear.0.LinearMap.pow_mulLeft.match_1_1 | Mathlib.Algebra.Algebra.Bilinear | [
"Unit.unit",
"instOfNatNat",
"Unit",
"Nat",
"OfNat.ofNat",
"Nat.succ",
"Nat.casesOn"
] | false |
CategoryTheory.ComposableArrows.fourδ₁Toδ₀_app_zero | Mathlib.CategoryTheory.ComposableArrows.Four | [
"instNeZeroNatHAdd_1",
"CategoryTheory.ComposableArrows.fourδ₁Toδ₀",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"PartialOrder.toPreorder",
"Fin.instOfNat",
"Preorder.smallCategory",
"instOfNatNat",
"instHAdd",
"Fin.instPartialOrder",
"HAdd.hAdd",
"Nat.instNeZeroSucc",
"Nat",
"... | true |
FiniteArchimedeanClass.lift_mk | Mathlib.Algebra.Order.Archimedean.Class | [
"of_eq_false",
"dite_congr",
"WithTop.untop.congr_simp",
"eq_false",
"LinearOrder.toDecidableEq",
"congrArg",
"AddCommGroup.toAddCommMonoid",
"ArchimedeanClass.lift_mk",
"LinearOrder",
"ArchimedeanClass.instLinearOrder",
"PartialOrder.toPreorder",
"Preorder.toLE",
"SemilatticeInf.toPartialOr... | true |
FirstOrder.Language.Sentence.cardGe.eq_1 | Mathlib.ModelTheory.Semantics | [
"instDecidableNot",
"SProd.sprod",
"FirstOrder.Language.BoundedFormula.instTop",
"List.map",
"FirstOrder.Language.BoundedFormula.exs",
"instDecidableEqFin",
"FirstOrder.Language.Term.bdEqual",
"Function.comp",
"FirstOrder.Language.Term",
"FirstOrder.Language.BoundedFormula.not",
"Sum",
"Ne",
... | true |
Subsemigroup.instCompleteLattice._proof_14 | Mathlib.Algebra.Group.Subsemigroup.Basic | [
"Subsemigroup.instBot",
"False.elim",
"Subsemigroup.notMem_bot",
"Mul",
"Membership.mem",
"Bot.bot",
"Subsemigroup",
"Subsemigroup.instSetLike",
"SetLike.instMembership"
] | false |
_private.Mathlib.Tactic.DeriveEncodable.0.Mathlib.Deriving.Encodable.instEncodableS | Mathlib.Tactic.DeriveEncodable | [
"Nat.encodable",
"Encodable.ofEquiv",
"Nat",
"_private.Mathlib.Tactic.DeriveEncodable.0.Mathlib.Deriving.Encodable.S_equiv",
"Encodable",
"_private.Mathlib.Tactic.DeriveEncodable.0.Mathlib.Deriving.Encodable.S"
] | true |
_private.Std.Data.DTreeMap.Internal.Model.0.Std.DTreeMap.Internal.Impl.entryAtIdx?.match_1.eq_1 | Std.Data.DTreeMap.Internal.Model | [
"Ordering.gt",
"Unit.unit",
"Ordering",
"Ordering.eq",
"Unit",
"Ordering.lt",
"Std.DTreeMap.Internal.Impl.entryAtIdx?.match_1",
"Eq.refl",
"Eq"
] | true |
Turing.PartrecToTM2.move₂ | Mathlib.Computability.TuringMachine.ToPartrec | [
"Turing.PartrecToTM2.K'.rev",
"Turing.PartrecToTM2.Γ'",
"Turing.PartrecToTM2.Λ'",
"Turing.PartrecToTM2.Λ'.move",
"Bool",
"Turing.PartrecToTM2.K'",
"Bool.false",
"Turing.PartrecToTM2.moveExcl"
] | true |
Mathlib.Notation3.mkScopedMatcher | Mathlib.Util.Notation3 | [
"Pure.pure",
"OptionT.instMonad",
"Lean.TSyntax",
"OptionT",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Syntax.ident",
"Lean.Elab.Term.instMonadMacroAdapterTermElabM",
"Lean.Quote.quote",
"Array.push",
"Lean.Elab.Term.instMonadTermElabM",
"String",
"Lean.SourceInfo",
"Lean.TSyntax.mk",
"Lean.... | true |
_private.Mathlib.Algebra.Lie.Weights.Cartan.0.LieAlgebra.mem_zeroRootSubalgebra._simp_1_1 | Mathlib.Algebra.Lie.Weights.Cartan | [
"LieHom",
"Module.End.instRing",
"LieSubmodule.instSetLike",
"CommRing",
"instHSMul",
"Module.End.instMonoid",
"CommSemiring.toSemiring",
"DistribMulAction.toDistribSMul",
"AddCommGroup.toAddCommMonoid",
"LieRing.IsNilpotent",
"LieModule.mem_genWeightSpace",
"LinearMap.instFunLike",
"HSub.hS... | false |
Ideal.map_sup_comap_of_surjective | Mathlib.RingTheory.Ideal.Maps | [
"GaloisInsertion.l_sup_u",
"Lattice.toSemilatticeSup",
"Semiring.toModule",
"Submodule.completeLattice",
"Ideal.giMapComap",
"CompleteLattice.toConditionallyCompleteLattice",
"SemilatticeSup.toMax",
"Ideal.map",
"Ideal",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Max.max",
"NonAssocSemiring... | true |
Lean.Parser.Term.subst.parenthesizer | Lean.Parser.Term | [
"Lean.PrettyPrinter.Parenthesizer",
"instOfNatNat",
"Lean.PrettyPrinter.Parenthesizer.andthen.parenthesizer",
"Lean.Parser.symbol.parenthesizer",
"Nat",
"Lean.Parser.termParser.parenthesizer",
"Lean.PrettyPrinter.Parenthesizer.trailingNode.parenthesizer",
"OfNat.ofNat",
"Bool.false",
"Lean.Name.mk... | true |
Homeomorph.mulRight | Mathlib.Topology.Algebra.Group.Basic | [
"Homeomorph.mk",
"Homeomorph.mulRight._proof_2",
"Monoid.toMulOneClass",
"Homeomorph.mulRight._proof_1",
"Group",
"MulOne.toMul",
"DivInvMonoid.toMonoid",
"Group.toDivInvMonoid",
"TopologicalSpace",
"MulOneClass.toMulOne",
"Equiv.Perm",
"Equiv.mulRight",
"Homeomorph",
"SeparatelyContinuous... | true |
Turing.TM2to1.trStmts₁.eq_3 | Mathlib.Computability.TuringMachine.StackTuringMachine | [
"Finset.instUnion",
"Finset",
"Turing.TM2to1.StAct.pop",
"Classical.propDecidable",
"Turing.TM2.Stmt.pop",
"Insert.insert",
"Finset.instInsert",
"Turing.TM2to1.Λ'",
"Turing.TM2to1.Λ'.ret",
"Turing.TM2to1.Λ'.go",
"Eq.refl",
"Union.union",
"Finset.instSingleton",
"Singleton.singleton",
"Tu... | true |
Module.DirectLimit.of._proof_3 | Mathlib.Algebra.Colimit.Module | [
"instHSMul",
"AddCon.addZeroClass",
"instAddCommMonoidDirectSum",
"ZeroHom.toFun",
"DirectSum.instModule",
"DistribMulAction.toDistribSMul",
"AddMonoid.toAddZeroClass",
"Preorder.toLE",
"AddMonoidHom.toZeroHom",
"AddZeroClass.toAddZero",
"DistribSMul.toSMulZeroClass",
"LE.le",
"LinearMap",
... | false |
Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave'_1 | Init.Tactics | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"instMonadExceptOfMonadExceptOf",
"Lean.SourceInfo",
"MonadExcept.throw",
"Lean.Syntax.node5",
"Lean.Syntax.isOfKind",
"EStateM.instMonad",
"Lean.Macro.Exception",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.Syntax",
"ReaderT.... | false |
Real.analyticOn_cos | Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv | [
"Real",
"AnalyticOn",
"ContDiff.contDiffOn",
"Real.denselyNormedField",
"Real.cos",
"Real.normedAddCommGroup",
"Real.contDiff_cos",
"ContDiffOn.analyticOn",
"WithTop.top",
"ENat",
"NontriviallyNormedField.toNormedField",
"DenselyNormedField.toNontriviallyNormedField",
"NormedField.toNormedSp... | true |
Subgroup.rightCosetEquivSubgroup | Mathlib.GroupTheory.Coset.Basic | [
"instHSMul",
"HMul.hMul",
"DivInvOneMonoid.toInvOneClass",
"Monoid.toMulOneClass",
"MulOpposite",
"Group",
"Group.toDivisionMonoid",
"Membership.mem",
"DivisionMonoid.toDivInvOneMonoid",
"Equiv.mk",
"Set.Elem",
"Equiv",
"MulOne.toMul",
"Subtype",
"DivInvMonoid.toMonoid",
"Subgroup",
... | true |
Batteries.RBNode.Balanced.below.black | Batteries.Data.RBMap.Basic | [
"Batteries.RBNode",
"instOfNatNat",
"Batteries.RBNode.Balanced.black",
"instHAdd",
"HAdd.hAdd",
"Batteries.RBColor",
"Nat",
"Batteries.RBNode.Balanced.below.black",
"instAddNat",
"Batteries.RBColor.black",
"Batteries.RBNode.Balanced.below",
"OfNat.ofNat",
"Batteries.RBNode.node",
"Batterie... | true |
RatFunc.instCommRing._proof_5 | Mathlib.FieldTheory.RatFunc.Basic | [
"CommRing",
"One.mk",
"AddMonoid.toAddSemigroup",
"Zero.zero",
"Add.mk",
"AddMonoid.toZero",
"AddCommGroup.toAddGroup",
"Add.add",
"instOfNatNat",
"One.one",
"AddSemigroup.toAdd",
"RatFunc",
"AddGroup.toSubNegMonoid",
"CommMonoid.toMonoid",
"Nat",
"Zero.mk",
"Zero.toOfNat0",
"Eq.re... | false |
Set.pi.eq_1 | Mathlib.Data.Set.Prod | [
"setOf",
"Membership.mem",
"Eq.refl",
"Set.pi",
"Eq",
"Set.instMembership",
"Set"
] | true |
_private.Mathlib.RingTheory.Ideal.Height.0.Ideal.sup_primeHeight_of_maximal_eq_ringKrullDim._proof_1_2 | Mathlib.RingTheory.Ideal.Height | [
"Submodule",
"CommRing",
"Semiring.toModule",
"CommSemiring.toSemiring",
"Bot.bot",
"NonUnitalNonAssocSemiring.toAddCommMonoid",
"Submodule.instBot",
"CommRing.toCommSemiring",
"NonAssocSemiring.toNonUnitalNonAssocSemiring",
"Ideal.IsPrime",
"Ideal.IsMaximal",
"Semiring.toNonAssocSemiring",
... | false |
_private.Init.Data.List.Lemmas.0.List.map_eq_nil_iff.match_1_1 | Init.Data.List.Lemmas | [
"False",
"HEq.refl",
"List.map",
"False.elim",
"noConfusion_of_Nat",
"Eq.casesOn",
"List.cons",
"List",
"List.casesOn",
"Eq.refl",
"HEq",
"Eq",
"List.ctorIdx",
"List.nil"
] | false |
CategoryTheory.Abelian.SpectralObject.d_d._auto_5 | Mathlib.Algebra.Homology.SpectralObject.Differentials | [
"Lean.Syntax.node",
"Array.push",
"Lean.Syntax",
"Array.empty",
"Lean.SourceInfo.none",
"Lean.Name.mkStr1",
"Lean.Name.mkStr4",
"Lean.mkAtom"
] | false |
Complex.HadamardThreeLines.norm_invInterpStrip | Mathlib.Analysis.Complex.Hadamard | [
"Norm.norm",
"Eq.mpr",
"Real.instPow",
"Real",
"HMul.hMul",
"Real.instZero",
"congrArg",
"Complex.HadamardThreeLines.invInterpStrip",
"Real.instSub",
"NormedDivisionRing.toNormMulClass",
"Complex.instNormedField",
"HSub.hSub",
"Real.instLT",
"Complex.instPow",
"Complex.instMul",
"Compl... | true |
_private.Init.Meta.Defs.0.Lean.Syntax.getTailInfo?.match_1 | Init.Meta.Defs | [
"Lean.Syntax.node",
"Lean.Syntax.ident",
"Lean.SourceInfo.ctorIdx",
"Lean.Syntax.ctorIdx",
"String",
"Lean.SourceInfo",
"Lean.Syntax.atom",
"Lean.Syntax",
"_private.Init.Meta.Defs.0.Lean.Syntax.getTailInfo?._sparseCasesOn_1",
"Nat.hasNotBit",
"Substring.Raw",
"Array",
"List",
"Lean.Syntax.... | false |
Set.ncard_lt_card | Mathlib.Data.Set.Card | [
"Iff.mpr",
"Subtype.finite",
"Set.univ",
"Finite",
"HasSSubset.SSubset",
"Set.instHasSSubset",
"Membership.mem",
"Eq.rec",
"Nat.card",
"Ne",
"Set.toFinite",
"Nat",
"LT.lt",
"Set.ncard_lt_ncard",
"Set.ssubset_univ_iff",
"instLTNat",
"Set.ncard_univ",
"Set.ncard",
"Eq",
"Set.inst... | true |
_private.Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra.0.IntermediateField.algebraAdjoinAdjoin.instIsFractionRingSubtypeMemSubalgebraAdjoinAdjoin.match_3 | Mathlib.FieldTheory.IntermediateField.Adjoin.Algebra | [
"IntermediateField",
"Algebra",
"Subtype.casesOn",
"Membership.mem",
"Subtype",
"Field.toSemifield",
"Subtype.mk",
"Semifield.toDivisionSemiring",
"IntermediateField.adjoin",
"DivisionSemiring.toSemiring",
"IntermediateField.instSetLike",
"Semifield.toCommSemiring",
"Field",
"SetLike.instM... | false |
CompHausLike.LocallyConstant.counitAppAppImage | Mathlib.Condensed.Discrete.LocallyConstant | [
"CategoryTheory.Limits.IsTerminal.from",
"CategoryTheory.Functor",
"Opposite",
"CategoryTheory.CategoryStruct.toQuiver",
"instMetricSpacePUnit",
"Quiver.Hom.op",
"instIndiscreteTopologyPUnit",
"EMetricSpace.metrizableSpace",
"instDiscreteTopologyPUnit",
"DiscreteTopology.toT2Space",
"CompHausLik... | true |
Finsupp.optionElim | Mathlib.Data.Finsupp.Option | [
"Finsupp.optionEquiv",
"Prod.mk",
"Prod",
"Finsupp",
"Equiv.invFun",
"Option",
"Zero"
] | true |
Lean.Meta.Grind.Order.modify' | Lean.Meta.Tactic.Grind.Order.Types | [
"Lean.Meta.Grind.Order.orderExt",
"Lean.Meta.Grind.Order.State",
"Unit",
"Lean.Meta.Grind.SolverExtension.modifyState",
"Lean.Meta.Grind.GoalM"
] | true |
CategoryTheory.WideSubcategory.instMonoidalCategory._proof_6 | Mathlib.CategoryTheory.Monoidal.Widesubcategory | [
"CategoryTheory.MorphismProperty",
"CategoryTheory.WideSubcategory.obj",
"CategoryTheory.WideSubcategory.instMonoidalCategoryStruct._proof_1",
"CategoryTheory.CategoryStruct.toQuiver",
"Quiver.Hom",
"congrArg",
"CategoryTheory.MonoidalCategory",
"CategoryTheory.WideSubcategory",
"CategoryTheory.Morp... | false |
_private.Lean.Meta.Tactic.Grind.Split.0.Lean.Meta.Grind.Action.mkAndThenSeq._sunfold | Lean.Meta.Tactic.Grind.Split | [
"Pure.pure",
"Lean.TSyntax",
"Lean.MonadRef.mkInfoFromRefPos",
"Lean.Core.instMonadRefCoreM",
"Lean.SourceInfo",
"Lean.Name.mkStr5",
"_private.Lean.Meta.Tactic.Grind.Split.0.Lean.Meta.Grind.Action.mkAndThenSeq",
"Lean.Syntax.atom",
"Lean.TSyntax.mk",
"Lean.TSyntax.raw",
"IO.RealWorld",
"EIO",
... | false |
Lean.Level.imax.injEq | Lean.Level | [
"Eq.propIntro",
"Lean.injEq_helper",
"Lean.Level.imax",
"Lean.Level",
"Lean.Level.imax.inj",
"And",
"Eq.ndrec",
"Eq.refl",
"Eq"
] | true |
FreeAddMonoid.lift_restrict | Mathlib.Algebra.FreeMonoid.Basic | [
"Equiv.apply_symm_apply",
"Equiv.instEquivLike",
"FreeAddMonoid.of",
"AddMonoid.toAddZeroClass",
"FreeAddMonoid.instAddCancelMonoid",
"AddCancelMonoid.toAddRightCancelMonoid",
"Function.comp",
"AddZeroClass.toAddZero",
"Equiv",
"FreeAddMonoid.lift",
"AddRightCancelMonoid.toAddMonoid",
"AddMono... | true |
mul_isLeftRegular_iff._simp_2 | Mathlib.Algebra.Regular.Basic | [
"Semigroup",
"Semigroup.toMul",
"HMul.hMul",
"IsLeftRegular",
"propext",
"mul_isLeftRegular_iff",
"Eq",
"instHMul"
] | false |
Nat.map_add_toList_ric | Init.Data.Range.Polymorphic.NatLemmas | [
"Std.Rco",
"Std.Rco.toList.congr_simp",
"congrArg",
"List.map",
"Nat.toList_rcc_eq_toList_rco",
"Std.PRange.instIsAlwaysFiniteNat_1",
"Std.Ric.toList",
"instOfNatNat",
"instLENat",
"Nat.map_add_toList_rco",
"Std.Ric.mk",
"_private.Init.Data.Range.Polymorphic.NatLemmas.0.Nat.map_add_toList_ric.... | true |
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