basic_working.json

{
    "working_file_list": [
        "import Mathlib.MeasureTheory.Measure.GiryMonad\nimport Mathlib.Dynamics.Ergodic.MeasurePreserving\nimport Mathlib.MeasureTheory.Integral.Lebesgue\nimport Mathlib.MeasureTheory.Measure.OpenPos",
        "import Mathlib.Analysis.Normed.Group.Basic\nimport Mathlib.MeasureTheory.Function.AEMeasurableSequence\nimport Mathlib.MeasureTheory.Group.Arithmetic\nimport Mathlib.MeasureTheory.Order.Lattice\nimport Mathlib.Topology.Instances.EReal\nimport Mathlib.Topology.MetricSpace.Thickening\nimport Mathlib.Topology.GDelta\nimport Mathlib.Topology.Order.Lattice\nimport Mathlib.Topology.Semicontinuous",
        "import Mathlib.Analysis.SpecificLimits.Basic\nimport Mathlib.MeasureTheory.PiSystem\nimport Mathlib.Data.Countable.Basic\nimport Mathlib.Data.Fin.VecNotation",
        "import Mathlib.MeasureTheory.Measure.Content\nimport Mathlib.MeasureTheory.Group.Prod\nimport Mathlib.Topology.Algebra.Group.Compact",
        "import Mathlib.Dynamics.Ergodic.MeasurePreserving\nimport Mathlib.LinearAlgebra.Determinant\nimport Mathlib.LinearAlgebra.Matrix.Diagonal\nimport Mathlib.LinearAlgebra.Matrix.Transvection\nimport Mathlib.MeasureTheory.Constructions.Pi\nimport Mathlib.MeasureTheory.Measure.Stieltjes\nimport Mathlib.MeasureTheory.Measure.Haar.OfBasis",
        "import Mathlib.Data.Finset.Update\nimport Mathlib.Data.Prod.TProd\nimport Mathlib.GroupTheory.Coset\nimport Mathlib.Logic.Equiv.Fin\nimport Mathlib.MeasureTheory.MeasurableSpace.Defs\nimport Mathlib.Order.Filter.SmallSets\nimport Mathlib.Order.LiminfLimsup\nimport Mathlib.Data.Set.UnionLift",
        "import Mathlib.Analysis.NormedSpace.BoundedLinearMaps\nimport Mathlib.MeasureTheory.Measure.WithDensity\nimport Mathlib.MeasureTheory.Function.SimpleFuncDense\nimport Mathlib.Topology.Algebra.Module.FiniteDimension",
        "import Mathlib.MeasureTheory.Function.AEEqFun.DomAct\nimport Mathlib.MeasureTheory.Function.LpSpace",
        "import Mathlib.Analysis.SpecialFunctions.Pow.NNReal\nimport Mathlib.MeasureTheory.Constructions.BorelSpace.Complex",
        "import Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1",
        "import Mathlib.Analysis.NormedSpace.IndicatorFunction\nimport Mathlib.MeasureTheory.Function.EssSup\nimport Mathlib.MeasureTheory.Function.AEEqFun\nimport Mathlib.MeasureTheory.Function.SpecialFunctions.Basic",
        "import Mathlib.Topology.Instances.ENNReal\nimport Mathlib.MeasureTheory.Measure.Dirac",
        "import Mathlib.Probability.Notation\nimport Mathlib.Probability.Process.Stopping",
        "import Mathlib.Probability.Independence.Kernel",
        "import Mathlib.MeasureTheory.Integral.Bochner\nimport Mathlib.MeasureTheory.Measure.GiryMonad",
        "import Mathlib.Algebra.Module.Hom\nimport Mathlib.Algebra.Module.Prod\nimport Mathlib.Algebra.Module.Submodule.Ker\nimport Mathlib.Data.Set.Finite\nimport Mathlib.Order.ConditionallyCompleteLattice.Basic",
        "import Mathlib.LinearAlgebra.RootSystem.Defs",
        "import Mathlib.LinearAlgebra.Matrix.Adjugate\nimport Mathlib.RingTheory.PolynomialAlgebra",
        "import Mathlib.Algebra.AddTorsor",
        "import Mathlib.GroupTheory.Perm.Sign\nimport Mathlib.Data.Fintype.Perm\nimport Mathlib.LinearAlgebra.Multilinear.Basis",
        "import Mathlib.Data.Finsupp.Fintype\nimport Mathlib.LinearAlgebra.TensorProduct.Basis",
        "import Mathlib.RingTheory.Finiteness\nimport Mathlib.LinearAlgebra.FreeModule.Basic",
        "import Mathlib.Algebra.RingQuot\nimport Mathlib.LinearAlgebra.TensorAlgebra.Basic\nimport Mathlib.LinearAlgebra.QuadraticForm.Isometry\nimport Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv",
        "import Mathlib.Algebra.Module.Submodule.Bilinear\nimport Mathlib.GroupTheory.Congruence\nimport Mathlib.LinearAlgebra.Basic\nimport Mathlib.Tactic.SuppressCompilation",
        "import Mathlib.LinearAlgebra.Matrix.Determinant\nimport Mathlib.LinearAlgebra.Matrix.SesquilinearForm\nimport Mathlib.LinearAlgebra.Matrix.Symmetric",
        "import Mathlib.Algebra.Algebra.Basic\nimport Mathlib.Algebra.BigOperators.Order\nimport Mathlib.Data.Fintype.BigOperators\nimport Mathlib.Data.Fintype.Sort\nimport Mathlib.Data.List.FinRange\nimport Mathlib.LinearAlgebra.Pi",
        "import Mathlib.LinearAlgebra.CliffordAlgebra.Basic\nimport Mathlib.LinearAlgebra.Alternating.Basic",
        "import Mathlib.Algebra.Algebra.Spectrum\nimport Mathlib.LinearAlgebra.GeneralLinearGroup\nimport Mathlib.LinearAlgebra.FiniteDimensional",
        "import Mathlib.Algebra.FreeAlgebra\nimport Mathlib.Algebra.RingQuot\nimport Mathlib.Algebra.TrivSqZeroExt\nimport Mathlib.Algebra.Algebra.Operations\nimport Mathlib.LinearAlgebra.Multilinear.Basic",
        "import Mathlib.Algebra.Algebra.Tower",
        "import Mathlib.LinearAlgebra.FiniteDimensional",
        "import Mathlib.LinearAlgebra.LinearIndependent",
        "import Mathlib.LinearAlgebra.FreeModule.Finite.Basic\nimport Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff\nimport Mathlib.FieldTheory.Minpoly.Field",
        "import Mathlib.Init.Logic\nimport Mathlib.Init.Function\nimport Mathlib.Init.Algebra.Classes\nimport Std.Util.LibraryNote\nimport Std.Tactic.Lint.Basic",
        "import Mathlib.Init.Order.Defs\nimport Mathlib.Logic.Nontrivial.Defs\nimport Mathlib.Tactic.Attr.Register\nimport Mathlib.Data.Prod.Basic\nimport Mathlib.Data.Subtype\nimport Mathlib.Logic.Function.Basic\nimport Mathlib.Logic.Unique",
        "import Mathlib.Data.Bool.Basic\nimport Mathlib.Data.Option.Defs\nimport Mathlib.Data.Prod.Basic\nimport Mathlib.Data.Sigma.Basic\nimport Mathlib.Data.Subtype\nimport Mathlib.Data.Sum.Basic\nimport Mathlib.Init.Data.Sigma.Basic\nimport Mathlib.Logic.Equiv.Defs\nimport Mathlib.Logic.Function.Conjugate\nimport Mathlib.Tactic.Lift\nimport Mathlib.Tactic.Convert\nimport Mathlib.Tactic.Contrapose\nimport Mathlib.Tactic.GeneralizeProofs\nimport Mathlib.Tactic.SimpRw",
        "import Mathlib.Logic.Equiv.Nat\nimport Mathlib.Data.PNat.Basic\nimport Mathlib.Order.Directed\nimport Mathlib.Data.Countable.Defs\nimport Mathlib.Order.RelIso.Basic\nimport Mathlib.Data.Fin.Basic",
        "import Mathlib.Logic.Small.Defs\nimport Mathlib.Logic.Equiv.Set",
        "import Mathlib.Logic.Nonempty\nimport Mathlib.Init.Set\nimport Mathlib.Logic.Basic",
        "import Mathlib.Data.Option.Basic\nimport Mathlib.Data.Prod.PProd\nimport Mathlib.Logic.Equiv.Basic",
        "import Mathlib.Analysis.Calculus.TangentCone\nimport Mathlib.Analysis.NormedSpace.OperatorNorm.Asymptotics",
        "import Mathlib.Analysis.Calculus.Deriv.Add",
        "import Mathlib.Analysis.InnerProductSpace.Dual\nimport Mathlib.Analysis.Calculus.FDeriv.Basic\nimport Mathlib.Analysis.Calculus.Deriv.Basic",
        "import Mathlib.Analysis.Calculus.ContDiff.Basic\nimport Mathlib.Analysis.NormedSpace.FiniteDimension",
        "import Mathlib.Analysis.Calculus.Deriv.Comp\nimport Mathlib.Analysis.Calculus.Deriv.Add\nimport Mathlib.Analysis.Calculus.Deriv.Mul\nimport Mathlib.Analysis.Calculus.Deriv.Slope",
        "import Mathlib.Analysis.Calculus.FDeriv.Basic\nimport Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace",
        "import Mathlib.Analysis.Calculus.ContDiff.Defs\nimport Mathlib.Analysis.Calculus.FDeriv.Add\nimport Mathlib.Analysis.Calculus.FDeriv.Mul\nimport Mathlib.Analysis.Calculus.Deriv.Inverse",
        "import Mathlib.Algebra.DirectSum.Module\nimport Mathlib.Analysis.Complex.Basic\nimport Mathlib.Analysis.Convex.Uniform\nimport Mathlib.Analysis.NormedSpace.Completion\nimport Mathlib.Analysis.NormedSpace.BoundedLinearMaps",
        "import Mathlib.Algebra.Algebra.NonUnitalSubalgebra\nimport Mathlib.Algebra.Algebra.Subalgebra.Basic\nimport Mathlib.Analysis.Normed.Group.Basic\nimport Mathlib.GroupTheory.OrderOfElement\nimport Mathlib.Topology.Instances.NNReal\nimport Mathlib.Topology.MetricSpace.DilationEquiv",
        "import Mathlib.Algebra.Order.Group.TypeTags\nimport Mathlib.Analysis.Normed.Field.Basic",
        "import Mathlib.Analysis.Normed.Group.Seminorm\nimport Mathlib.Order.LiminfLimsup\nimport Mathlib.Topology.Instances.Rat\nimport Mathlib.Topology.MetricSpace.Algebra\nimport Mathlib.Topology.MetricSpace.IsometricSMul\nimport Mathlib.Topology.Sequences",
        "import Mathlib.Analysis.SpecialFunctions.Exp\nimport Mathlib.Data.Nat.Factorization.Basic\nimport Mathlib.Analysis.NormedSpace.Real",
        "import Mathlib.Analysis.SpecialFunctions.Exp\nimport Mathlib.Tactic.Positivity.Core",
        "import Mathlib.MeasureTheory.Integral.ExpDecay\nimport Mathlib.Analysis.SpecialFunctions.ImproperIntegrals\nimport Mathlib.Analysis.MellinTransform",
        "import Mathlib.Analysis.Convex.Basic\nimport Mathlib.Analysis.Convex.Hull\nimport Mathlib.Analysis.NormedSpace.Basic\nimport Mathlib.Topology.Bornology.Absorbs",
        "import Mathlib.Analysis.NormedSpace.Dual\nimport Mathlib.Analysis.NormedSpace.Star.Basic\nimport Mathlib.Analysis.Complex.Basic\nimport Mathlib.Analysis.InnerProductSpace.Adjoint\nimport Mathlib.Algebra.Star.Subalgebra",
        "import Mathlib.Analysis.BoxIntegral.Partition.Filter\nimport Mathlib.Analysis.BoxIntegral.Partition.Measure\nimport Mathlib.Topology.UniformSpace.Compact\nimport Mathlib.Init.Data.Bool.Lemmas",
        "import Mathlib.Algebra.BigOperators.Option\nimport Mathlib.Analysis.BoxIntegral.Box.Basic\nimport Mathlib.Data.Set.Pairwise.Lattice",
        "import Mathlib.Data.Set.Intervals.Monotone\nimport Mathlib.Topology.MetricSpace.Basic\nimport Mathlib.Topology.MetricSpace.Bounded\nimport Mathlib.Topology.Order.MonotoneConvergence",
        "import Mathlib.Data.Complex.Module\nimport Mathlib.Data.Complex.Order\nimport Mathlib.Data.Complex.Exponential\nimport Mathlib.Data.RCLike.Basic\nimport Mathlib.Topology.Algebra.InfiniteSum.Module\nimport Mathlib.Topology.Instances.RealVectorSpace",
        "import Mathlib.Analysis.Complex.Circle\nimport Mathlib.Analysis.NormedSpace.BallAction",
        "import Mathlib.Data.Fintype.Parity\nimport Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup\nimport Mathlib.Analysis.Complex.Basic\nimport Mathlib.GroupTheory.GroupAction.Defs\nimport Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup\nimport Mathlib.Tactic.LinearCombination",
        "import Mathlib.Algebra.GeomSum\nimport Mathlib.Order.Filter.Archimedean\nimport Mathlib.Order.Iterate\nimport Mathlib.Topology.Instances.ENNReal\nimport Mathlib.Topology.Algebra.Algebra",
        "import Mathlib.Algebra.Order.Module.OrderedSMul\nimport Mathlib.Analysis.Convex.Star\nimport Mathlib.LinearAlgebra.AffineSpace.AffineSubspace",
        "import Mathlib.Analysis.Convex.Hull\nimport Mathlib.LinearAlgebra.AffineSpace.Independent",
        "import Mathlib.Analysis.Convex.Hull",
        "import Mathlib.Analysis.Convex.Slope\nimport Mathlib.Analysis.SpecialFunctions.Pow.Real\nimport Mathlib.Tactic.LinearCombination",
        "import Mathlib.Algebra.Algebra.Pi\nimport Mathlib.Algebra.Algebra.RestrictScalars\nimport Mathlib.Analysis.Normed.Field.Basic\nimport Mathlib.Analysis.Normed.MulAction",
        "import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace\nimport Mathlib.Topology.Algebra.Module.Multilinear.Basic",
        "import Mathlib.Algebra.Algebra.Tower\nimport Mathlib.Analysis.LocallyConvex.WithSeminorms\nimport Mathlib.Topology.Algebra.Module.StrongTopology\nimport Mathlib.Analysis.NormedSpace.LinearIsometry\nimport Mathlib.Analysis.NormedSpace.ContinuousLinearMap\nimport Mathlib.Tactic.SuppressCompilation",
        "import Mathlib.Analysis.Normed.Group.Hom\nimport Mathlib.Analysis.NormedSpace.Basic\nimport Mathlib.Analysis.NormedSpace.LinearIsometry\nimport Mathlib.Algebra.Star.SelfAdjoint\nimport Mathlib.Algebra.Star.Subalgebra\nimport Mathlib.Algebra.Star.Unitary\nimport Mathlib.Topology.Algebra.Module.Star",
        "import Mathlib.Analysis.Calculus.FormalMultilinearSeries\nimport Mathlib.Analysis.SpecificLimits.Normed\nimport Mathlib.Logic.Equiv.Fin\nimport Mathlib.Topology.Algebra.InfiniteSum.Module",
        "import Mathlib.CategoryTheory.Sites.Sheaf\nimport Mathlib.Topology.Category.CompHaus.EffectiveEpi",
        "import Mathlib.Data.Fin.VecNotation\nimport Mathlib.SetTheory.Cardinal.Basic",
        "import Mathlib.ModelTheory.Syntax\nimport Mathlib.ModelTheory.Semantics\nimport Mathlib.ModelTheory.Algebra.Ring.Basic\nimport Mathlib.Algebra.Field.MinimalAxioms",
        "import Mathlib.ModelTheory.Syntax\nimport Mathlib.ModelTheory.Semantics\nimport Mathlib.Algebra.Ring.Equiv",
        "import Mathlib.Init.Control.Combinators\nimport Mathlib.Init.Function\nimport Mathlib.Tactic.CasesM\nimport Mathlib.Tactic.Attr.Core",
        "import Mathlib.Logic.Equiv.Defs",
        "import Mathlib.Data.Option.Defs\nimport Mathlib.Control.Functor",
        "import Mathlib.Control.Bifunctor\nimport Mathlib.Control.Traversable.Basic",
        "import Mathlib.Init.Order.LinearOrder\nimport Mathlib.Data.Prod.Basic\nimport Mathlib.Data.Subtype\nimport Mathlib.Tactic.Spread\nimport Mathlib.Tactic.Convert\nimport Mathlib.Tactic.SimpRw\nimport Mathlib.Tactic.Cases\nimport Mathlib.Order.Notation",
        "import Mathlib.Logic.Equiv.Option\nimport Mathlib.Order.RelIso.Basic\nimport Mathlib.Order.Disjoint\nimport Mathlib.Order.WithBot\nimport Mathlib.Tactic.Monotonicity.Attr\nimport Mathlib.Util.AssertExists",
        "import Mathlib.Data.SetLike.Basic\nimport Mathlib.Data.Set.Intervals.OrdConnected\nimport Mathlib.Data.Set.Intervals.OrderIso\nimport Mathlib.Data.Set.Lattice",
        "import Mathlib.Order.PropInstances",
        "import Mathlib.Data.Set.Finite",
        "import Mathlib.Logic.Function.Iterate\nimport Mathlib.Init.Data.Int.Order\nimport Mathlib.Order.Compare\nimport Mathlib.Order.Max\nimport Mathlib.Order.RelClasses\nimport Mathlib.Tactic.Choose",
        "import Mathlib.Order.CompleteLattice\nimport Mathlib.Order.Cover\nimport Mathlib.Order.Iterate",
        "import Mathlib.Init.Algebra.Classes\nimport Mathlib.Data.FunLike.Basic\nimport Mathlib.Logic.Embedding.Basic\nimport Mathlib.Order.RelClasses",
        "import Mathlib.Order.Atoms\nimport Mathlib.Order.OrderIsoNat\nimport Mathlib.Order.RelIso.Set\nimport Mathlib.Order.SupClosed\nimport Mathlib.Order.SupIndep\nimport Mathlib.Order.Zorn\nimport Mathlib.Data.Finset.Order\nimport Mathlib.Data.Set.Intervals.OrderIso\nimport Mathlib.Data.Finite.Set\nimport Mathlib.Tactic.TFAE",
        "import Mathlib.Order.Bounds.Basic\nimport Mathlib.Order.WellFounded\nimport Mathlib.Data.Set.Image\nimport Mathlib.Data.Set.Intervals.Basic\nimport Mathlib.Data.Set.Lattice",
        "import Mathlib.Data.Set.Intervals.Basic\nimport Mathlib.Data.Set.NAry\nimport Mathlib.Order.Directed",
        "import Mathlib.Data.Sum.Order\nimport Mathlib.Order.InitialSeg\nimport Mathlib.SetTheory.Cardinal.Basic\nimport Mathlib.Tactic.PPWithUniv",
        "import Mathlib.Data.Set.Lattice\nimport Mathlib.Logic.Small.Basic\nimport Mathlib.Logic.Function.OfArity\nimport Mathlib.Order.WellFounded",
        "import Mathlib.Data.Int.Basic\nimport Mathlib.SetTheory.Game.PGame\nimport Mathlib.Tactic.Abel",
        "import Mathlib.Algebra.Order.Hom.Monoid\nimport Mathlib.SetTheory.Game.Ordinal",
        "import Mathlib.Algebra.Module.Basic\nimport Mathlib.Data.Fintype.BigOperators\nimport Mathlib.Data.Finsupp.Defs\nimport Mathlib.Data.Set.Countable\nimport Mathlib.Logic.Small.Set\nimport Mathlib.Order.ConditionallyCompleteLattice.Basic\nimport Mathlib.Order.SuccPred.CompleteLinearOrder\nimport Mathlib.SetTheory.Cardinal.SchroederBernstein\nimport Mathlib.Tactic.PPWithUniv",
        "import Mathlib.Algebra.Group.Equiv.TypeTags\nimport Mathlib.Algebra.Module.Basic\nimport Mathlib.Algebra.Module.LinearMap.Basic\nimport Mathlib.Algebra.MonoidAlgebra.Basic\nimport Mathlib.LinearAlgebra.Dual\nimport Mathlib.LinearAlgebra.Contraction\nimport Mathlib.RingTheory.TensorProduct.Basic",
        "import Mathlib.Algebra.Category.GroupCat.Basic\nimport Mathlib.CategoryTheory.SingleObj\nimport Mathlib.CategoryTheory.Limits.FunctorCategory\nimport Mathlib.CategoryTheory.Limits.Preserves.Basic\nimport Mathlib.CategoryTheory.Adjunction.Limits\nimport Mathlib.CategoryTheory.Conj",
        "import Mathlib.Algebra.Homology.Opposite\nimport Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex\nimport Mathlib.RepresentationTheory.GroupCohomology.Resolution",
        "import Mathlib.CategoryTheory.Limits.HasLimits",
        "import Mathlib.CategoryTheory.Limits.Connected\nimport Mathlib.CategoryTheory.Limits.Constructions.Over.Products\nimport Mathlib.CategoryTheory.Limits.Constructions.Over.Connected\nimport Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers\nimport Mathlib.CategoryTheory.Limits.Constructions.Equalizers",
        "import Mathlib.CategoryTheory.Limits.Shapes.RegularMono\nimport Mathlib.CategoryTheory.Limits.Shapes.Kernels\nimport Mathlib.CategoryTheory.Limits.Preserves.Basic",
        "import Mathlib.CategoryTheory.NatIso",
        "import Mathlib.CategoryTheory.Limits.Constructions.Pullbacks\nimport Mathlib.CategoryTheory.Preadditive.Biproducts\nimport Mathlib.CategoryTheory.Limits.Shapes.Images\nimport Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers\nimport Mathlib.CategoryTheory.Abelian.NonPreadditive",
        "import Mathlib.CategoryTheory.Subobject.MonoOver\nimport Mathlib.CategoryTheory.Skeletal\nimport Mathlib.CategoryTheory.ConcreteCategory.Basic\nimport Mathlib.Tactic.ApplyFun\nimport Mathlib.Tactic.CategoryTheory.Elementwise",
        "import Mathlib.CategoryTheory.EqToHom\nimport Mathlib.CategoryTheory.Functor.Const\nimport Mathlib.CategoryTheory.Opposites\nimport Mathlib.Data.Prod.Basic",
        "import Mathlib.CategoryTheory.CommSq",
        "import Mathlib.Algebra.BigOperators.Basic\nimport Mathlib.Algebra.Group.Hom.Defs\nimport Mathlib.Algebra.Module.Basic\nimport Mathlib.CategoryTheory.Endomorphism\nimport Mathlib.CategoryTheory.Limits.Shapes.Kernels",
        "import Mathlib.CategoryTheory.Preadditive.Opposite\nimport Mathlib.Algebra.Category.ModuleCat.Basic\nimport Mathlib.Algebra.Category.GroupCat.Preadditive",
        "import Mathlib.CategoryTheory.Functor.Category\nimport Mathlib.CategoryTheory.Functor.FullyFaithful\nimport Mathlib.CategoryTheory.Functor.ReflectsIso",
        "import Mathlib.CategoryTheory.EqToHom\nimport Mathlib.CategoryTheory.NatIso\nimport Mathlib.CategoryTheory.Products.Basic",
        "import Mathlib.Algebra.Group.Basic\nimport Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero\nimport Mathlib.CategoryTheory.Monoidal.End\nimport Mathlib.CategoryTheory.Monoidal.Discrete",
        "import Mathlib.CategoryTheory.Equivalence",
        "import Mathlib.CategoryTheory.FinCategory.Basic\nimport Mathlib.CategoryTheory.Limits.Cones\nimport Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits\nimport Mathlib.CategoryTheory.Adjunction.Basic\nimport Mathlib.CategoryTheory.Category.Preorder\nimport Mathlib.CategoryTheory.Category.ULift\nimport Mathlib.CategoryTheory.PEmpty",
        "import Mathlib.CategoryTheory.Monoidal.Types.Symmetric\nimport Mathlib.CategoryTheory.Monoidal.Types.Coyoneda\nimport Mathlib.CategoryTheory.Monoidal.Center\nimport Mathlib.Tactic.ApplyFun",
        "import Mathlib.CategoryTheory.Abelian.Basic",
        "import Mathlib.CategoryTheory.EqToHom",
        "import Mathlib.CategoryTheory.Iso\nimport Mathlib.CategoryTheory.Functor.Category\nimport Mathlib.CategoryTheory.EqToHom",
        "import Mathlib.CategoryTheory.Whiskering\nimport Mathlib.CategoryTheory.Functor.FullyFaithful\nimport Mathlib.CategoryTheory.NatIso",
        "import Mathlib.CategoryTheory.Extensive\nimport Mathlib.CategoryTheory.Sites.Coverage\nimport Mathlib.CategoryTheory.EffectiveEpi.Basic",
        "import Mathlib.CategoryTheory.Adjunction.Limits\nimport Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products\nimport Mathlib.CategoryTheory.Limits.Shapes.Biproducts\nimport Mathlib.CategoryTheory.Shift.Basic",
        "import Mathlib.CategoryTheory.Types\nimport Mathlib.CategoryTheory.Functor.EpiMono\nimport Mathlib.CategoryTheory.Limits.Constructions.EpiMono",
        "import Mathlib.CategoryTheory.Monoidal.Free.Coherence\nimport Mathlib.CategoryTheory.Monoidal.Discrete\nimport Mathlib.CategoryTheory.Monoidal.NaturalTransformation\nimport Mathlib.CategoryTheory.Monoidal.Opposite\nimport Mathlib.Tactic.CategoryTheory.Coherence\nimport Mathlib.CategoryTheory.CommSq",
        "import Mathlib.CategoryTheory.Monoidal.Functor\nimport Mathlib.CategoryTheory.ChosenFiniteProducts\nimport Mathlib.CategoryTheory.Limits.Shapes.Types\nimport Mathlib.Logic.Equiv.Fin",
        "import Mathlib.CategoryTheory.Monoidal.Functor",
        "import Mathlib.CategoryTheory.Monoidal.Free.Coherence\nimport Mathlib.Tactic.CategoryTheory.Coherence\nimport Mathlib.CategoryTheory.Closed.Monoidal\nimport Mathlib.Tactic.ApplyFun",
        "import Mathlib.CategoryTheory.Monoidal.Category\nimport Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts\nimport Mathlib.CategoryTheory.PEmpty",
        "import Mathlib.CategoryTheory.Preadditive.Basic\nimport Mathlib.Algebra.Module.LinearMap.Basic\nimport Mathlib.Algebra.Algebra.Basic",
        "import Mathlib.CategoryTheory.Category.Init\nimport Mathlib.Combinatorics.Quiver.Basic\nimport Mathlib.Tactic.PPWithUniv\nimport Mathlib.Tactic.Common",
        "import Mathlib.CategoryTheory.Limits.Shapes.Products",
        "import Mathlib.Data.Fintype.Basic\nimport Mathlib.CategoryTheory.DiscreteCategory\nimport Mathlib.CategoryTheory.Opposites\nimport Mathlib.CategoryTheory.Category.ULift",
        "import Mathlib.CategoryTheory.Category.Basic",
        "import Mathlib.CategoryTheory.Comma.StructuredArrow\nimport Mathlib.CategoryTheory.Limits.Shapes.Equivalence",
        "import Mathlib.CategoryTheory.FintypeCat\nimport Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers\nimport Mathlib.CategoryTheory.Limits.FintypeCat\nimport Mathlib.CategoryTheory.Limits.MonoCoprod\nimport Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal\nimport Mathlib.CategoryTheory.Limits.Shapes.Types\nimport Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory\nimport Mathlib.CategoryTheory.Limits.Shapes.Diagonal\nimport Mathlib.CategoryTheory.SingleObj\nimport Mathlib.Data.Finite.Card",
        "import Mathlib.CategoryTheory.Groupoid\nimport Mathlib.Combinatorics.Quiver.Basic",
        "import Mathlib.LinearAlgebra.StdBasis\nimport Mathlib.Tactic.Linarith\nimport Mathlib.Data.Finset.PiAntidiagonal\nimport Mathlib.Data.MvPolynomial.Basic",
        "import Mathlib.Tactic.FinCases\nimport Mathlib.Data.Nat.Choose.Sum\nimport Mathlib.LinearAlgebra.Finsupp",
        "import Mathlib.Algebra.GroupPower.Order\nimport Mathlib.RingTheory.Ideal.Operations\nimport Mathlib.Tactic.TFAE",
        "import Mathlib.RingTheory.Adjoin.Basic",
        "import Mathlib.Algebra.Ring.Equiv\nimport Mathlib.Algebra.Ring.Prod\nimport Mathlib.Data.Set.Finite\nimport Mathlib.GroupTheory.Submonoid.Membership\nimport Mathlib.GroupTheory.Subsemigroup.Membership\nimport Mathlib.GroupTheory.Subsemigroup.Centralizer",
        "import Mathlib.Algebra.EuclideanDomain.Basic\nimport Mathlib.Data.Nat.Factors\nimport Mathlib.RingTheory.Coprime.Basic\nimport Mathlib.RingTheory.PrincipalIdealDomain",
        "import Mathlib.Algebra.CharP.ExpChar\nimport Mathlib.Algebra.GeomSum\nimport Mathlib.Data.MvPolynomial.CommRing\nimport Mathlib.Data.MvPolynomial.Equiv\nimport Mathlib.RingTheory.Polynomial.Content\nimport Mathlib.RingTheory.UniqueFactorizationDomain",
        "import Mathlib.Algebra.NeZero\nimport Mathlib.Algebra.Polynomial.BigOperators\nimport Mathlib.RingTheory.RootsOfUnity.Complex\nimport Mathlib.Data.Polynomial.Lifts\nimport Mathlib.Data.Polynomial.Splits\nimport Mathlib.FieldTheory.RatFunc\nimport Mathlib.NumberTheory.ArithmeticFunction\nimport Mathlib.RingTheory.RootsOfUnity.Basic",
        "import Mathlib.Data.Polynomial.Derivative\nimport Mathlib.Data.Nat.Parity\nimport Mathlib.Data.Nat.Factorial.DoubleFactorial",
        "import Mathlib.RingTheory.EisensteinCriterion\nimport Mathlib.RingTheory.Polynomial.ScaleRoots",
        "import Mathlib.Algebra.GroupPower.Ring\nimport Mathlib.Algebra.Ring.Divisibility.Basic\nimport Mathlib.Algebra.Ring.Hom.Defs\nimport Mathlib.GroupTheory.GroupAction.Units\nimport Mathlib.Logic.Basic\nimport Mathlib.Tactic.Ring",
        "import Mathlib.RingTheory.Noetherian\nimport Mathlib.Algebra.DirectSum.Module\nimport Mathlib.Algebra.DirectSum.Finsupp\nimport Mathlib.Algebra.Module.Projective\nimport Mathlib.Algebra.Module.Injective\nimport Mathlib.Algebra.Module.CharacterModule\nimport Mathlib.LinearAlgebra.DirectSum.TensorProduct\nimport Mathlib.LinearAlgebra.FreeModule.Basic\nimport Mathlib.Algebra.Module.Projective",
        "import Mathlib.GroupTheory.Subgroup.Basic\nimport Mathlib.RingTheory.Subsemiring.Basic",
        "import Mathlib.Algebra.Algebra.Operations\nimport Mathlib.Algebra.Algebra.Subalgebra.Tower\nimport Mathlib.LinearAlgebra.Prod\nimport Mathlib.LinearAlgebra.Finsupp",
        "import Mathlib.Algebra.Module.Basic\nimport Mathlib.Algebra.Ring.Equiv\nimport Mathlib.Algebra.Ring.Prod\nimport Mathlib.Algebra.GroupRingAction.Subobjects\nimport Mathlib.Data.Set.Finite\nimport Mathlib.GroupTheory.Submonoid.Centralizer\nimport Mathlib.GroupTheory.Submonoid.Membership\nimport Mathlib.RingTheory.NonUnitalSubsemiring.Basic",
        "import Mathlib.GroupTheory.MonoidLocalization\nimport Mathlib.Algebra.GroupWithZero.NonZeroDivisors\nimport Mathlib.RingTheory.OreLocalization.OreSet\nimport Mathlib.Tactic.NoncommRing",
        "import Mathlib.Algebra.Function.Support\nimport Mathlib.Order.WellFoundedSet",
        "import Mathlib.RingTheory.Ideal.Over\nimport Mathlib.RingTheory.Polynomial.RationalRoot",
        "import Mathlib.Algebra.CharP.Basic\nimport Mathlib.Data.Polynomial.AlgebraMap\nimport Mathlib.Data.MvPolynomial.Degrees\nimport Mathlib.LinearAlgebra.FinsuppVectorSpace\nimport Mathlib.LinearAlgebra.FreeModule.Finite.Basic",
        "import Mathlib.Algebra.DirectSum.Algebra\nimport Mathlib.Algebra.DirectSum.Decomposition\nimport Mathlib.Algebra.DirectSum.Internal\nimport Mathlib.Algebra.DirectSum.Ring",
        "import Mathlib.Algebra.Algebra.Tower\nimport Mathlib.Algebra.GroupWithZero.NonZeroDivisors\nimport Mathlib.GroupTheory.MonoidLocalization\nimport Mathlib.RingTheory.Ideal.Basic\nimport Mathlib.GroupTheory.GroupAction.Ring",
        "import Mathlib.Init.Data.Int.CompLemmas\nimport Mathlib.RingTheory.UniqueFactorizationDomain\nimport Mathlib.RingTheory.Localization.Basic",
        "import Mathlib.Algebra.CharP.Two\nimport Mathlib.Algebra.CharP.Reduced\nimport Mathlib.Algebra.NeZero\nimport Mathlib.Data.Polynomial.RingDivision\nimport Mathlib.GroupTheory.SpecificGroups.Cyclic\nimport Mathlib.NumberTheory.Divisors\nimport Mathlib.RingTheory.IntegralDomain\nimport Mathlib.Tactic.Zify",
        "import Mathlib.LinearAlgebra.FiniteDimensional\nimport Mathlib.LinearAlgebra.TensorProduct.Tower\nimport Mathlib.RingTheory.Adjoin.Basic\nimport Mathlib.LinearAlgebra.DirectSum.Finsupp",
        "import Mathlib.Data.MvPolynomial.Counit\nimport Mathlib.Data.MvPolynomial.Invertible\nimport Mathlib.RingTheory.WittVector.Defs",
        "import Mathlib.RingTheory.MvPowerSeries.Basic\nimport Mathlib.Data.Polynomial.Basic\nimport Mathlib.Data.Polynomial.AlgebraMap",
        "import Mathlib.RingTheory.PrincipalIdealDomain\nimport Mathlib.RingTheory.Ideal.LocalRing\nimport Mathlib.RingTheory.Valuation.PrimeMultiplicity\nimport Mathlib.LinearAlgebra.AdicCompletion",
        "import Mathlib.GroupTheory.Subgroup.Basic\nimport Mathlib.RingTheory.NonUnitalSubsemiring.Basic",
        "import Mathlib.RingTheory.Localization.Integer\nimport Mathlib.RingTheory.Localization.Submodule",
        "import Mathlib.Algebra.Group.Conj\nimport Mathlib.Algebra.Group.Pi.Lemmas\nimport Mathlib.Data.Set.Image\nimport Mathlib.GroupTheory.Submonoid.Centralizer\nimport Mathlib.Order.Atoms\nimport Mathlib.Tactic.ApplyFun",
        "import Mathlib.Algebra.Group.Prod\nimport Mathlib.Algebra.Group.Units.Equiv\nimport Mathlib.Algebra.GroupPower.IterateHom\nimport Mathlib.Logic.Equiv.Set",
        "import Mathlib.Algebra.Module.BigOperators\nimport Mathlib.Data.Fintype.Perm\nimport Mathlib.GroupTheory.Perm.Finite\nimport Mathlib.GroupTheory.Perm.List",
        "import Mathlib.Algebra.Group.Hom.Defs\nimport Mathlib.Algebra.Group.Units\nimport Mathlib.GroupTheory.Subsemigroup.Basic",
        "import Mathlib.Algebra.PUnitInstances\nimport Mathlib.GroupTheory.Subgroup.Basic\nimport Mathlib.GroupTheory.Congruence\nimport Mathlib.GroupTheory.Submonoid.Membership",
        "import Mathlib.Data.Fintype.Card\nimport Mathlib.GroupTheory.GroupAction.Defs\nimport Mathlib.GroupTheory.GroupAction.Group\nimport Mathlib.Data.Setoid.Basic\nimport Mathlib.Data.Set.Pointwise.SMul\nimport Mathlib.GroupTheory.Subgroup.Basic",
        "import Mathlib.Algebra.Group.Opposite\nimport Mathlib.Algebra.Group.Pi.Lemmas\nimport Mathlib.GroupTheory.GroupAction.Defs",
        "import Mathlib.Algebra.Group.Hom.Defs\nimport Mathlib.Data.Set.Lattice\nimport Mathlib.Data.SetLike.Basic",
        "import Mathlib.Data.Fintype.Basic\nimport Mathlib.Data.List.Sublists\nimport Mathlib.Data.List.InsertNth\nimport Mathlib.GroupTheory.Subgroup.Basic",
        "import Mathlib.Algebra.Group.TypeTags\nimport Mathlib.Algebra.Ring.Defs\nimport Mathlib.Data.Int.Cast.Basic\nimport Mathlib.Order.Monotone.Basic",
        "import Mathlib.Data.Nat.Order.Basic\nimport Mathlib.Data.Int.Basic\nimport Mathlib.Algebra.Order.Group.Abs\nimport Mathlib.Algebra.Order.Ring.CharZero\nimport Mathlib.Algebra.Divisibility.Basic",
        "import Mathlib.Init.Data.Nat.Lemmas\nimport Mathlib.Data.Int.Cast.Defs\nimport Mathlib.Algebra.Group.Basic",
        "import Mathlib.Data.Int.Order.Basic\nimport Mathlib.Data.Nat.Cast.Order\nimport Mathlib.Algebra.Ring.Divisibility.Basic",
        "import Mathlib.Data.DList.Defs\nimport Mathlib.Tactic.TypeStar",
        "import Mathlib.Mathport.Rename",
        "import Mathlib.Data.Nat.SuccPred\nimport Mathlib.Algebra.CharZero.Lemmas\nimport Mathlib.Algebra.Order.Sub.WithTop\nimport Mathlib.Algebra.Order.Ring.WithTop",
        "import Mathlib.Data.Real.Sqrt\nimport Mathlib.Analysis.NormedSpace.Star.Basic\nimport Mathlib.Analysis.NormedSpace.ContinuousLinearMap\nimport Mathlib.Analysis.NormedSpace.Basic",
        "import Mathlib.Init.ZeroOne\nimport Mathlib.Data.Set.Defs\nimport Mathlib.Order.Basic\nimport Mathlib.Order.SymmDiff\nimport Mathlib.Tactic.Tauto\nimport Mathlib.Tactic.ByContra\nimport Mathlib.Util.Delaborators",
        "import Mathlib.Data.Set.Function\nimport Mathlib.Logic.Relation\nimport Mathlib.Logic.Pairwise",
        "import Mathlib.Algebra.Group.Equiv.Basic\nimport Mathlib.Algebra.Group.Units.Hom\nimport Mathlib.Algebra.GroupPower.Basic\nimport Mathlib.Algebra.GroupWithZero.Basic\nimport Mathlib.Algebra.Opposites\nimport Mathlib.Data.Nat.Order.Basic\nimport Mathlib.Data.Set.Lattice\nimport Mathlib.Tactic.Common",
        "import Mathlib.Order.MinMax\nimport Mathlib.Data.Set.Basic\nimport Mathlib.Tactic.Says",
        "import Mathlib.Data.List.Lex\nimport Mathlib.Data.Char",
        "import Mathlib.Logic.Function.Basic\nimport Mathlib.Tactic.MkIffOfInductiveProp",
        "import Mathlib.Data.PNat.Defs\nimport Mathlib.Data.Nat.Bits\nimport Mathlib.Data.Nat.Order.Basic\nimport Mathlib.Data.Set.Basic\nimport Mathlib.Algebra.GroupWithZero.Divisibility\nimport Mathlib.Algebra.Order.Positive.Ring\nimport Mathlib.Order.Hom.Basic",
        "import Mathlib.Data.W.Basic",
        "import Mathlib.Control.Functor.Multivariate\nimport Mathlib.Data.PFunctor.Univariate.Basic",
        "import Mathlib.Init.Function\nimport Mathlib.Logic.Function.Basic\nimport Mathlib.Tactic.Inhabit",
        "import Mathlib.Algebra.Module.LinearMap.Basic\nimport Mathlib.Algebra.BigOperators.Basic\nimport Mathlib.Data.Set.Finite\nimport Mathlib.GroupTheory.Submonoid.Membership\nimport Mathlib.GroupTheory.GroupAction.BigOperators\nimport Mathlib.Data.Finset.Preimage",
        "import Lean.Linter.Deprecated\nimport Mathlib.Mathport.Rename\nimport Mathlib.Init.Data.Nat.Bitwise\nimport Mathlib.Init.Data.Int.Basic\nimport Mathlib.Init.ZeroOne",
        "import Mathlib.Logic.Equiv.List",
        "import Mathlib.Init.Function\nimport Mathlib.Logic.Function.Basic",
        "import Mathlib.Algebra.Algebra.Tower\nimport Mathlib.Algebra.GroupPower.Ring\nimport Mathlib.Algebra.Regular.Pow\nimport Mathlib.Algebra.MonoidAlgebra.Support\nimport Mathlib.Data.Finsupp.Antidiagonal\nimport Mathlib.Order.SymmDiff\nimport Mathlib.RingTheory.Adjoin.Basic",
        "import Mathlib.Control.Traversable.Equiv\nimport Mathlib.Control.Traversable.Instances\nimport Std.Data.LazyList\nimport Mathlib.Lean.Thunk",
        "import Mathlib.Logic.Relation\nimport Mathlib.Order.GaloisConnection",
        "import Mathlib.Data.Vector\nimport Mathlib.Data.List.Nodup\nimport Mathlib.Data.List.OfFn\nimport Mathlib.Data.List.InsertNth\nimport Mathlib.Control.Applicative\nimport Mathlib.Control.Traversable.Basic",
        "import Mathlib.Algebra.GroupPower.Ring\nimport Mathlib.Algebra.MonoidAlgebra.Basic\nimport Mathlib.Data.Finset.Sort",
        "import Mathlib.RingTheory.Finiteness\nimport Mathlib.Data.Polynomial.AlgebraMap",
        "import Std.Tactic.Alias",
        "import Mathlib.Algebra.BigOperators.Finsupp\nimport Mathlib.Algebra.Regular.SMul\nimport Mathlib.Data.Finset.Preimage\nimport Mathlib.Data.Rat.BigOperators\nimport Mathlib.GroupTheory.GroupAction.Hom\nimport Mathlib.Data.Set.Basic",
        "import Mathlib.Data.Finset.Attr\nimport Mathlib.Data.Multiset.Bind\nimport Mathlib.Data.Multiset.FinsetOps\nimport Mathlib.Data.Set.Lattice",
        "import Mathlib.Order.Cover\nimport Mathlib.Order.LocallyFinite\nimport Mathlib.Data.Set.Intervals.Monoid",
        "import Mathlib.Algebra.Group.TypeTags\nimport Mathlib.Algebra.Ring.Defs\nimport Mathlib.Algebra.GroupWithZero.Defs",
        "import Mathlib.Algebra.Order.Monoid.WithZero\nimport Mathlib.Algebra.Order.Ring.Canonical\nimport Mathlib.Data.Nat.Basic",
        "import Mathlib.Data.Nat.Defs\nimport Mathlib.Tactic.GCongr.Core\nimport Mathlib.Tactic.Common\nimport Mathlib.Tactic.Monotonicity.Attr",
        "import Mathlib.Algebra.GroupPower.Basic\nimport Mathlib.Algebra.GroupWithZero.Divisibility\nimport Mathlib.Data.Nat.Order.Lemmas\nimport Mathlib.Tactic.NthRewrite",
        "import Mathlib.Algebra.Divisibility.Basic\nimport Mathlib.Algebra.Group.Equiv.Basic\nimport Mathlib.Algebra.Group.TypeTags\nimport Mathlib.Algebra.Ring.Hom.Defs\nimport Mathlib.Data.Nat.Basic",
        "import Mathlib.Init.Data.Nat.Lemmas\nimport Mathlib.Init.Data.Nat.Bitwise\nimport Mathlib.Data.Nat.GCD.Basic\nimport Mathlib.Logic.Function.Iterate\nimport Mathlib.Data.Finset.NatAntidiagonal\nimport Mathlib.Algebra.BigOperators.Basic\nimport Mathlib.Tactic.Ring\nimport Mathlib.Tactic.Zify",
        "import Mathlib.Data.Nat.Factorial.Basic\nimport Mathlib.Order.Monotone.Basic",
        "import Mathlib.Algebra.BigOperators.Finsupp\nimport Mathlib.Data.Finsupp.Multiset\nimport Mathlib.Data.Nat.PrimeFin\nimport Mathlib.NumberTheory.Padics.PadicVal\nimport Mathlib.Data.Nat.GCD.BigOperators\nimport Mathlib.Data.Nat.Interval\nimport Mathlib.Tactic.IntervalCases\nimport Mathlib.Algebra.GroupPower.Order",
        "import Mathlib.Data.Set.Basic\nimport Mathlib.Tactic.Monotonicity.Attr\nimport Mathlib.Tactic.SetLike",
        "import Mathlib.Algebra.NeZero\nimport Mathlib.Order.RelIso.Basic\nimport Mathlib.Data.Nat.Order.Basic\nimport Mathlib.Order.Hom.Set\nimport Std.Data.Fin.Lemmas",
        "import Mathlib.Data.Fin.OrderHom\nimport Mathlib.Data.Pi.Lex\nimport Mathlib.Data.Set.Intervals.Basic",
        "import Mathlib.Algebra.Star.Basic\nimport Mathlib.Algebra.Order.CauSeq.Completion",
        "import Mathlib.Algebra.CharP.Basic\nimport Mathlib.RingTheory.Ideal.Operations\nimport Mathlib.Data.Fintype.Units\nimport Mathlib.Data.Nat.Parity\nimport Mathlib.Tactic.FinCases",
        "import Mathlib.Logic.Function.Basic\nimport Mathlib.Util.CompileInductive",
        "import Mathlib.Algebra.Algebra.Opposite\nimport Mathlib.Algebra.Algebra.Pi\nimport Mathlib.Algebra.BigOperators.Pi\nimport Mathlib.Algebra.BigOperators.Ring\nimport Mathlib.Algebra.BigOperators.RingEquiv\nimport Mathlib.Algebra.Module.LinearMap.Basic\nimport Mathlib.Algebra.Module.Pi\nimport Mathlib.Algebra.Star.BigOperators\nimport Mathlib.Algebra.Star.Module\nimport Mathlib.Algebra.Star.Pi\nimport Mathlib.Data.Fintype.BigOperators\nimport Mathlib.GroupTheory.GroupAction.BigOperators",
        "import Mathlib.Init.Data.Nat.Lemmas\nimport Mathlib.Init.Function",
        "import Mathlib.Data.Semiquot\nimport Mathlib.Data.Nat.Size\nimport Mathlib.Tactic.Ring.RingNF",
        "import Mathlib.Data.Set.Card\nimport Mathlib.Order.Minimal\nimport Mathlib.Data.Matroid.Init",
        "import Mathlib.Data.Set.List\nimport Mathlib.Data.List.Perm\nimport Mathlib.Init.Quot -- Porting note: added import\nimport Mathlib.Order.Hom.Basic",
        "import Mathlib.Mathport.Rename",
        "import Mathlib.Data.PFunctor.Univariate.M",
        "import Mathlib.Data.PFunctor.Multivariate.Basic",
        "import Mathlib.Init.Control.Combinators\nimport Mathlib.Data.Option.Defs\nimport Mathlib.Logic.IsEmpty\nimport Mathlib.Logic.Relator\nimport Mathlib.Util.CompileInductive\nimport Aesop",
        "import Mathlib.Algebra.Order.Ring.WithTop\nimport Mathlib.Algebra.Order.Sub.WithTop\nimport Mathlib.Data.Real.NNReal\nimport Mathlib.Data.Set.Intervals.WithBotTop",
        "import Mathlib.Data.Bool.Basic\nimport Mathlib.Data.Nat.Defs\nimport Mathlib.Data.Option.Basic\nimport Mathlib.Data.List.Defs\nimport Mathlib.Init.Data.List.Basic\nimport Mathlib.Init.Data.List.Instances\nimport Mathlib.Init.Data.List.Lemmas\nimport Mathlib.Logic.Unique\nimport Mathlib.Order.Basic\nimport Std.Data.List.Lemmas\nimport Mathlib.Tactic.Common",
        "import Mathlib.Logic.Equiv.Nat\nimport Mathlib.Logic.Equiv.Fin\nimport Mathlib.Data.Countable.Defs",
        "import Mathlib.Data.Multiset.Basic\nimport Mathlib.Data.Vector.Basic\nimport Mathlib.Data.Setoid.Basic\nimport Mathlib.Tactic.ApplyFun",
        "import Mathlib.Init.Align",
        "import Mathlib.Data.Fintype.Powerset\nimport Mathlib.Data.Fintype.Prod\nimport Mathlib.Data.Fintype.Sigma\nimport Mathlib.Data.Fintype.Sum\nimport Mathlib.Data.Fintype.Vector",
        "import Mathlib.Algebra.CharZero.Lemmas\nimport Mathlib.Algebra.GroupPower.Ring\nimport Mathlib.Algebra.GroupWithZero.Bitwise\nimport Mathlib.Data.Real.Basic\nimport Mathlib.Data.Set.Image",
        "import Mathlib.Algebra.Ring.Hom.Defs -- FIXME: This import is bogus\nimport Mathlib.Data.Finset.Image\nimport Mathlib.Data.Fin.OrderHom",
        "import Mathlib.Algebra.Category.Ring.FilteredColimits\nimport Mathlib.Geometry.RingedSpace.SheafedSpace\nimport Mathlib.Topology.Sheaves.Stalks\nimport Mathlib.Algebra.Category.Ring.Colimits\nimport Mathlib.Algebra.Category.Ring.Limits",
        "import Mathlib.Analysis.InnerProductSpace.Projection\nimport Mathlib.Geometry.Euclidean.PerpBisector\nimport Mathlib.Algebra.QuadraticDiscriminant",
        "import Mathlib.Analysis.Convex.StrictConvexBetween\nimport Mathlib.Geometry.Euclidean.Basic",
        "import Mathlib.Analysis.InnerProductSpace.Basic\nimport Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse",
        "import Mathlib.Analysis.InnerProductSpace.TwoDim\nimport Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic",
        "import Mathlib.Analysis.Normed.Group.AddTorsor\nimport Mathlib.Analysis.InnerProductSpace.Basic",
        "import Mathlib.Geometry.Manifold.MFDeriv.Defs",
        "import Mathlib.Geometry.Manifold.ContMDiff.Defs",
        "import Mathlib.Geometry.Manifold.LocalInvariantProperties\nimport Mathlib.Topology.Sheaves.LocalPredicate",
        "import Mathlib.Geometry.Manifold.ContMDiff.Atlas\nimport Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear\nimport Mathlib.Topology.VectorBundle.Constructions",
        "import Mathlib.Data.Seq.Seq\nimport Mathlib.Algebra.Field.Defs",
        "import Mathlib.Algebra.Order.Floor\nimport Mathlib.Algebra.ContinuedFractions.Basic",
        "import Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero",
        "import Mathlib.Algebra.Group.Basic\nimport Mathlib.Algebra.Group.Hom.Defs\nimport Mathlib.Algebra.GroupWithZero.NeZero\nimport Mathlib.Algebra.Opposites\nimport Mathlib.Algebra.Ring.Defs",
        "import Mathlib.Algebra.Divisibility.Basic\nimport Mathlib.Algebra.Group.Units.Hom\nimport Mathlib.Algebra.GroupWithZero.InjSurj\nimport Mathlib.Algebra.Ring.Hom.Defs\nimport Mathlib.Data.Set.Basic",
        "import Mathlib.Algebra.Divisibility.Basic\nimport Mathlib.Algebra.Group.Equiv.Basic\nimport Mathlib.Algebra.Ring.Defs",
        "import Mathlib.Algebra.Associated\nimport Mathlib.Algebra.Ring.Regular\nimport Mathlib.Tactic.Common",
        "import Mathlib.Algebra.BigOperators.Multiset.Lemmas\nimport Mathlib.Algebra.BigOperators.Multiset.Order\nimport Mathlib.Algebra.Function.Indicator\nimport Mathlib.Algebra.Ring.Opposite\nimport Mathlib.Data.Finset.Powerset\nimport Mathlib.Data.Finset.Preimage\nimport Mathlib.Data.Finset.Sigma\nimport Mathlib.Data.Finset.Sum\nimport Mathlib.Data.Fintype.Pi\nimport Mathlib.Data.Int.Cast.Lemmas\nimport Mathlib.Data.Set.Image",
        "import Mathlib.Algebra.BigOperators.List.Defs\nimport Mathlib.Data.List.Forall2\nimport Mathlib.Algebra.Divisibility.Basic\nimport Mathlib.Algebra.Ring.Commute\nimport Mathlib.Data.Nat.Order.Basic\nimport Mathlib.Data.Int.Basic",
        "import Mathlib.Algebra.Group.Hom.Basic\nimport Mathlib.Algebra.GroupPower.Hom\nimport Mathlib.Algebra.BigOperators.List.Basic\nimport Mathlib.Data.Multiset.Basic",
        "import Mathlib.Algebra.CharZero.Lemmas\nimport Mathlib.Algebra.Module.Submodule.Ker\nimport Mathlib.Algebra.Module.Submodule.RestrictScalars\nimport Mathlib.Algebra.Module.ULift\nimport Mathlib.RingTheory.Subring.Basic",
        "import Mathlib.Algebra.Algebra.Basic\nimport Mathlib.Data.Set.UnionLift\nimport Mathlib.LinearAlgebra.Finsupp\nimport Mathlib.RingTheory.Ideal.Operations",
        "import Mathlib.Algebra.Order.Monoid.Defs\nimport Mathlib.Algebra.Group.InjSurj\nimport Mathlib.Order.Hom.Basic",
        "import Mathlib.Logic.Basic\nimport Mathlib.Tactic.Positivity.Basic",
        "import Mathlib.Algebra.Order.AbsoluteValue\nimport Mathlib.Algebra.Order.Field.Basic\nimport Mathlib.Algebra.Order.Group.MinMax\nimport Mathlib.Algebra.Ring.Pi\nimport Mathlib.GroupTheory.GroupAction.Pi\nimport Mathlib.GroupTheory.GroupAction.Ring\nimport Mathlib.Init.Align\nimport Mathlib.Tactic.GCongr\nimport Mathlib.Tactic.Ring",
        "import Mathlib.Algebra.Group.Equiv.Basic\nimport Mathlib.Algebra.Ring.Basic\nimport Mathlib.Algebra.Order.Sub.Defs\nimport Mathlib.Order.Hom.Basic",
        "import Mathlib.Algebra.Field.Basic\nimport Mathlib.Algebra.GroupWithZero.Units.Equiv\nimport Mathlib.Algebra.Order.Field.Defs\nimport Mathlib.Algebra.Order.Ring.Abs\nimport Mathlib.Order.Bounds.OrderIso\nimport Mathlib.Tactic.Positivity.Core",
        "import Mathlib.Algebra.Order.Field.Canonical.Defs",
        "import Mathlib.Algebra.Field.Defs\nimport Mathlib.Algebra.GroupWithZero.Units.Lemmas\nimport Mathlib.Algebra.Ring.Commute\nimport Mathlib.Algebra.Ring.Hom.Defs",
        "import Mathlib.Algebra.Invertible.GroupWithZero\nimport Mathlib.Algebra.Group.Commute.Units\nimport Mathlib.Algebra.Group.Hom.Defs\nimport Mathlib.Algebra.Group.Units\nimport Mathlib.Algebra.GroupPower.Basic\nimport Mathlib.Algebra.GroupWithZero.Units.Basic\nimport Mathlib.Algebra.Ring.Defs",
        "import Mathlib.Data.Bracket\nimport Mathlib.LinearAlgebra.Basic",
        "import Mathlib.Algebra.Ring.Divisibility.Lemmas\nimport Mathlib.Algebra.Lie.Nilpotent\nimport Mathlib.Algebra.Lie.Engel\nimport Mathlib.LinearAlgebra.Eigenspace.Triangularizable\nimport Mathlib.RingTheory.Artinian\nimport Mathlib.LinearAlgebra.Trace\nimport Mathlib.LinearAlgebra.FreeModule.PID",
        "import Mathlib.Data.DFinsupp.Basic\nimport Mathlib.GroupTheory.Submonoid.Operations",
        "import Mathlib.Algebra.GroupWithZero.Units.Lemmas\nimport Mathlib.Algebra.Ring.Equiv\nimport Mathlib.GroupTheory.GroupAction.Group",
        "import Mathlib.RingTheory.UniqueFactorizationDomain",
        "import Mathlib.Algebra.GroupPower.Basic\nimport Mathlib.Algebra.Group.Hom.Defs",
        "import Mathlib.Algebra.BigOperators.List.Basic\nimport Mathlib.GroupTheory.GroupAction.Defs",
        "import Mathlib.Algebra.Module.Basic\nimport Mathlib.Algebra.Order.Archimedean\nimport Mathlib.Algebra.Order.Group.Instances",
        "import Mathlib.Data.Int.ModEq\nimport Mathlib.Data.Nat.Multiplicity\nimport Mathlib.Data.Nat.Choose.Sum\nimport Mathlib.Data.Nat.Cast.Prod\nimport Mathlib.Algebra.Group.ULift\nimport Mathlib.GroupTheory.OrderOfElement",
        "import Mathlib.Algebra.Lie.OfAssociative",
        "import Mathlib.Algebra.Category.MonCat.Basic\nimport Mathlib.CategoryTheory.Endomorphism",
        "import Mathlib.Algebra.Category.GroupCat.Preadditive\nimport Mathlib.CategoryTheory.Conj\nimport Mathlib.CategoryTheory.Linear.Basic\nimport Mathlib.CategoryTheory.Preadditive.AdditiveFunctor\nimport Mathlib.LinearAlgebra.Basic",
        "import Mathlib.Algebra.Category.ModuleCat.Basic\nimport Mathlib.LinearAlgebra.TensorProduct.Basic\nimport Mathlib.CategoryTheory.Monoidal.Linear",
        "import Mathlib.Algebra.Algebra.Subalgebra.Basic\nimport Mathlib.Algebra.FreeAlgebra\nimport Mathlib.Algebra.Category.Ring.Basic\nimport Mathlib.Algebra.Category.ModuleCat.Basic",
        "import Mathlib.CategoryTheory.ConcreteCategory.BundledHom\nimport Mathlib.Algebra.PUnitInstances\nimport Mathlib.CategoryTheory.Functor.ReflectsIso",
        "import Mathlib.Algebra.PEmptyInstances\nimport Mathlib.Algebra.Group.Equiv.Basic\nimport Mathlib.CategoryTheory.ConcreteCategory.BundledHom\nimport Mathlib.CategoryTheory.Functor.ReflectsIso",
        "import Mathlib.Algebra.Category.GroupCat.Basic\nimport Mathlib.CategoryTheory.ConcreteCategory.ReflectsIso\nimport Mathlib.Algebra.Ring.Equiv",
        "import Mathlib.CategoryTheory.Monoidal.Rigid.Basic\nimport Mathlib.CategoryTheory.Monoidal.Subcategory\nimport Mathlib.LinearAlgebra.Coevaluation\nimport Mathlib.LinearAlgebra.FreeModule.Finite.Matrix\nimport Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed",
        "import Mathlib.Algebra.Group.Commute.Basic\nimport Mathlib.Algebra.GroupWithZero.Defs\nimport Mathlib.Data.Int.Defs\nimport Mathlib.Tactic.Common",
        "import Mathlib.Algebra.GroupPower.CovariantClass\nimport Mathlib.Algebra.Order.Monoid.WithTop\nimport Mathlib.Algebra.SMulWithZero\nimport Mathlib.Order.Hom.Basic\nimport Mathlib.Data.Nat.Order.Basic",
        "import Mathlib.Algebra.EuclideanDomain.Defs\nimport Mathlib.Algebra.Ring.Divisibility.Basic\nimport Mathlib.Algebra.Ring.Regular\nimport Mathlib.Algebra.GroupWithZero.Divisibility\nimport Mathlib.Algebra.Ring.Basic",
        "import Mathlib.Algebra.Function.Indicator\nimport Mathlib.Algebra.SMulWithZero\nimport Mathlib.Data.Int.Basic\nimport Mathlib.Data.NNRat.Defs\nimport Mathlib.GroupTheory.GroupAction.Group\nimport Mathlib.GroupTheory.GroupAction.Pi\nimport Mathlib.Logic.Basic\nimport Mathlib.Tactic.Abel",
        "import Mathlib.GroupTheory.GroupAction.SubMulAction\nimport Mathlib.GroupTheory.Submonoid.Membership",
        "import Mathlib.Algebra.Module.Pi\nimport Mathlib.Algebra.Ring.CompTypeclasses\nimport Mathlib.Algebra.Star.Basic\nimport Mathlib.GroupTheory.GroupAction.DomAct.Basic\nimport Mathlib.GroupTheory.GroupAction.Hom",
        "import Mathlib.Algebra.Algebra.Equiv\nimport Mathlib.Algebra.Algebra.NonUnitalHom\nimport Mathlib.Algebra.BigOperators.Finsupp\nimport Mathlib.Algebra.Module.BigOperators\nimport Mathlib.LinearAlgebra.Finsupp",
        "import Mathlib.Algebra.Group.Commute.Defs\nimport Mathlib.Algebra.Group.Units\nimport Mathlib.Algebra.Order.Monoid.Lemmas\nimport Mathlib.Tactic.NthRewrite",
        "import Aesop\nimport Mathlib.Algebra.Group.Defs\nimport Mathlib.Logic.Function.Basic\nimport Mathlib.Tactic.Cases\nimport Mathlib.Tactic.SimpRw\nimport Mathlib.Tactic.SplitIfs",
        "import Mathlib.Algebra.Group.Semiconj.Defs\nimport Mathlib.Algebra.Group.Basic",
        "import Mathlib.Algebra.Group.Basic\nimport Mathlib.Algebra.Group.Hom.Defs",
        "import Mathlib.Algebra.Group.Defs\nimport Mathlib.Data.Prod.Basic\nimport Mathlib.Data.Sum.Basic\nimport Mathlib.Logic.Unique\nimport Mathlib.Tactic.Spread",
        "import Mathlib.Algebra.Group.Equiv.Basic\nimport Mathlib.Algebra.Group.WithOne.Defs\nimport Mathlib.Data.Option.Basic",
        "import Mathlib.Algebra.Group.Hom.Basic\nimport Mathlib.Data.FunLike.Equiv\nimport Mathlib.Logic.Equiv.Basic",
        "import Mathlib.Algebra.Group.Commute.Defs\nimport Mathlib.Algebra.Group.Semiconj.Basic",
        "import Mathlib.Algebra.Field.Opposite\nimport Mathlib.Algebra.Invertible.Defs\nimport Mathlib.Algebra.Ring.Aut\nimport Mathlib.Algebra.Ring.CompTypeclasses\nimport Mathlib.Algebra.Field.Opposite\nimport Mathlib.Algebra.Invertible.Defs\nimport Mathlib.Data.NNRat.Defs\nimport Mathlib.Data.Rat.Cast.Defs\nimport Mathlib.Data.SetLike.Basic\nimport Mathlib.GroupTheory.GroupAction.Opposite",
        "import Mathlib.Algebra.Group.Basic\nimport Mathlib.Algebra.GroupWithZero.NeZero\nimport Mathlib.Algebra.Group.OrderSynonym",
        "import Mathlib.Algebra.GroupWithZero.Basic\nimport Mathlib.Algebra.Group.Units\nimport Mathlib.Tactic.Nontriviality\nimport Mathlib.Util.AssertExists\nimport Mathlib.Tactic.Contrapose",
        "import Mathlib.CategoryTheory.Category.Grpd\nimport Mathlib.CategoryTheory.Groupoid\nimport Mathlib.Topology.Category.TopCat.Basic\nimport Mathlib.Topology.Homotopy.Path\nimport Mathlib.Data.Set.Basic",
        "import Mathlib.RingTheory.IntegralClosure",
        "import Mathlib.FieldTheory.Normal\nimport Mathlib.FieldTheory.Perfect\nimport Mathlib.RingTheory.Localization.Integral",
        "import Mathlib.FieldTheory.Separable\nimport Mathlib.RingTheory.IntegralDomain\nimport Mathlib.Algebra.CharP.Reduced\nimport Mathlib.Tactic.ApplyFun",
        "import Lean\nimport Std\nimport Mathlib.Tactic.PPWithUniv\nimport Mathlib.Tactic.ExtendDoc\nimport Mathlib.Tactic.Lemma\nimport Mathlib.Tactic.TypeStar",
        "import Lean.Elab.Tactic.SolveByElim\nimport Mathlib.Tactic.Monotonicity.Attr",
        "import Lean.Elab.Tactic.Simp\nimport Lean.Elab.App\nimport Mathlib.Tactic.Simps.NotationClass\nimport Std.Data.String.Basic\nimport Std.Util.LibraryNote\nimport Mathlib.Lean.Expr.Basic",
        "import Mathlib.Tactic.NormNum.Inv\nimport Mathlib.Tactic.NormNum.Pow\nimport Mathlib.Util.AtomM\nimport Mathlib.Data.Rat.Order",
        "import Mathlib.Tactic.NormNum.Core\nimport Mathlib.Tactic.HaveI\nimport Mathlib.Data.Nat.Cast.Commute\nimport Mathlib.Data.Int.Basic\nimport Mathlib.Algebra.Invertible.Basic\nimport Mathlib.Tactic.Clear!\nimport Mathlib.Data.Nat.Cast.Basic",
        "import Mathlib.Algebra.GroupPower.Order\nimport Mathlib.Data.Int.CharZero\nimport Mathlib.Data.Int.Order.Basic\nimport Mathlib.Data.Nat.Factorial.Basic\nimport Mathlib.Data.Rat.Order\nimport Mathlib.Tactic.Positivity.Core\nimport Qq",
        "import Std.Data.Rat.Lemmas\nimport Mathlib.Mathport.Rename",
        "import Mathlib.Mathport.Rename",
        "import Std.Logic\nimport Mathlib.Mathport.Rename",
        "import Mathlib.Mathport.Rename\nimport Mathlib.Init.Data.Nat.Notation\nimport Std.Data.List.Basic",
        "import Mathlib.Init.ZeroOne\nimport Mathlib.Init.Data.Nat.Notation\nimport Mathlib.Util.CompileInductive",
        "import Mathlib.Init.Data.Nat.Notation",
        "import Mathlib.Mathport.Rename",
        "import Mathlib.Mathport.Rename\nimport Std.Data.Bool",
        "import Mathlib.AlgebraicGeometry.AffineScheme\nimport Mathlib.AlgebraicGeometry.Pullbacks\nimport Mathlib.CategoryTheory.MorphismProperty\nimport Mathlib.Data.List.TFAE",
        "import Mathlib.LinearAlgebra.Finsupp\nimport Mathlib.RingTheory.Ideal.Over\nimport Mathlib.RingTheory.Ideal.Prod\nimport Mathlib.RingTheory.Ideal.MinimalPrime\nimport Mathlib.RingTheory.Localization.Away.Basic\nimport Mathlib.RingTheory.Nilpotent\nimport Mathlib.Topology.Sets.Closeds\nimport Mathlib.Topology.Sober",
        "import Mathlib.Data.Set.Function\nimport Mathlib.Logic.Function.Iterate\nimport Mathlib.GroupTheory.Perm.Basic",
        "import Mathlib.Algebra.BigOperators.Basic\nimport Mathlib.Dynamics.FixedPoints.Basic",
        "import Mathlib.Algebra.Function.Support\nimport Mathlib.Order.Filter.Lift\nimport Mathlib.Topology.Defs.Filter",
        "import Mathlib.Order.SetNotation\nimport Mathlib.Tactic.Continuity\nimport Mathlib.Tactic.FunProp",
        "import Mathlib.Topology.Order.ProjIcc\nimport Mathlib.Topology.ContinuousFunction.Ordered\nimport Mathlib.Topology.CompactOpen\nimport Mathlib.Topology.UnitInterval",
        "import Mathlib.Analysis.NormedSpace.BoundedLinearMaps\nimport Mathlib.Topology.FiberBundle.Basic",
        "import Mathlib.Data.Set.Image\nimport Mathlib.Order.SuccPred.Relation\nimport Mathlib.Topology.Clopen\nimport Mathlib.Topology.Irreducible",
        "import Mathlib.CategoryTheory.ConcreteCategory.BundledHom\nimport Mathlib.CategoryTheory.Elementwise\nimport Mathlib.Topology.ContinuousFunction.Basic",
        "import Mathlib.Topology.Category.TopCat.Basic\nimport Mathlib.CategoryTheory.Limits.Types",
        "import Mathlib.Topology.Category.CompHaus.Basic\nimport Mathlib.Topology.LocallyConstant.Basic\nimport Mathlib.CategoryTheory.FintypeCat",
        "import Mathlib.Topology.Category.Profinite.Basic\nimport Mathlib.CategoryTheory.Limits.ConcreteCategory",
        "import Mathlib.Topology.ExtremallyDisconnected\nimport Mathlib.Topology.Category.CompHaus.Projective\nimport Mathlib.Topology.Category.Profinite.Basic",
        "import Mathlib.CategoryTheory.Adjunction.Reflective\nimport Mathlib.Topology.StoneCech\nimport Mathlib.CategoryTheory.Monad.Limits\nimport Mathlib.Topology.UrysohnsLemma\nimport Mathlib.Topology.Category.TopCat.Limits.Basic\nimport Mathlib.Data.Set.Basic",
        "import Mathlib.Order.Filter.SmallSets\nimport Mathlib.Tactic.Monotonicity\nimport Mathlib.Topology.Compactness.Compact\nimport Mathlib.Topology.NhdsSet\nimport Mathlib.Algebra.Group.Defs",
        "import Mathlib.Data.Set.Intervals.Pi\nimport Mathlib.Data.Set.Pointwise.Basic\nimport Mathlib.Order.Filter.Interval\nimport Mathlib.Tactic.TFAE\nimport Mathlib.Tactic.NormNum\nimport Mathlib.Topology.Order.LeftRight\nimport Mathlib.Topology.Order.OrderClosed",
        "import Mathlib.Order.Hom.Basic\nimport Mathlib.Topology.ContinuousFunction.Basic",
        "import Mathlib.Topology.Algebra.Ring.Basic\nimport Mathlib.Topology.Algebra.MulAction\nimport Mathlib.Topology.Algebra.UniformGroup\nimport Mathlib.Topology.ContinuousFunction.Basic\nimport Mathlib.Topology.UniformSpace.UniformEmbedding\nimport Mathlib.Algebra.Algebra.Basic\nimport Mathlib.LinearAlgebra.Projection\nimport Mathlib.LinearAlgebra.Pi\nimport Mathlib.LinearAlgebra.Finsupp",
        "import Mathlib.Topology.Algebra.Module.Basic\nimport Mathlib.LinearAlgebra.Multilinear.Basic",
        "import Mathlib.LinearAlgebra.Alternating.Basic\nimport Mathlib.LinearAlgebra.BilinearMap\nimport Mathlib.Topology.Algebra.Module.Multilinear.Basic",
        "import Mathlib.GroupTheory.Subgroup.Basic\nimport Mathlib.Topology.Algebra.OpenSubgroup\nimport Mathlib.Topology.Algebra.Ring.Basic",
        "import Mathlib.Algebra.Ring.Prod\nimport Mathlib.RingTheory.Subring.Basic\nimport Mathlib.Topology.Algebra.Group.Basic",
        "import Mathlib.Topology.Algebra.InfiniteSum.Defs\nimport Mathlib.Data.Fintype.BigOperators\nimport Mathlib.Topology.Algebra.Monoid",
        "import Mathlib.GroupTheory.GroupAction.ConjAct\nimport Mathlib.GroupTheory.GroupAction.Quotient\nimport Mathlib.GroupTheory.QuotientGroup\nimport Mathlib.Topology.Algebra.Monoid\nimport Mathlib.Topology.Algebra.Constructions",
        "import Mathlib.Data.Nat.Interval\nimport Mathlib.Data.ENNReal.Real\nimport Mathlib.Topology.UniformSpace.Pi\nimport Mathlib.Topology.UniformSpace.UniformConvergence\nimport Mathlib.Topology.UniformSpace.UniformEmbedding",
        "import Mathlib.Algebra.Function.Indicator\nimport Mathlib.Tactic.FinCases\nimport Mathlib.Topology.Sets.Closeds",
        "import Mathlib.Order.Filter.Cofinite",
        "import Mathlib.Topology.MetricSpace.ProperSpace",
        "import Mathlib.Topology.MetricSpace.Basic",
        "import Mathlib.Topology.FiberBundle.Trivialization",
        "import Mathlib.Data.Set.UnionLift\nimport Mathlib.Topology.Homeomorph",
        "import Mathlib.Algebra.GeomSum\nimport Mathlib.RingTheory.Ideal.Quotient",
        "import Mathlib.Algebra.Associated\nimport Mathlib.RingTheory.Int.Basic\nimport Mathlib.Tactic.Ring\nimport Mathlib.Algebra.Star.Unitary",
        "import Mathlib.Algebra.DirectSum.Algebra\nimport Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty\nimport Mathlib.Analysis.Complex.UpperHalfPlane.Manifold\nimport Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions\nimport Mathlib.NumberTheory.ModularForms.SlashInvariantForms",
        "import Mathlib.NumberTheory.ModularForms.SlashInvariantForms\nimport Mathlib.NumberTheory.ModularForms.CongruenceSubgroups",
        "import Mathlib.Data.Int.Parity\nimport Mathlib.RingTheory.DedekindDomain.IntegralClosure",
        "import Mathlib.Algebra.GCDMonoid.Finset\nimport Mathlib.Algebra.GroupPower.Ring\nimport Mathlib.Data.Nat.Parity\nimport Mathlib.Data.Rat.Defs\nimport Mathlib.Tactic.Positivity.Basic\nimport Mathlib.Tactic.TFAE",
        "import Mathlib.Analysis.PSeries\nimport Mathlib.NumberTheory.ArithmeticFunction\nimport Mathlib.Analysis.NormedSpace.FiniteDimension",
        "import Mathlib.Init.Core\nimport Mathlib.RingTheory.Polynomial.Cyclotomic.Roots\nimport Mathlib.NumberTheory.NumberField.Basic\nimport Mathlib.FieldTheory.Galois",
        "import Mathlib.Analysis.Calculus.MeanValue\nimport Mathlib.Analysis.Calculus.Deriv.Polynomial\nimport Mathlib.Data.Polynomial.DenomsClearable\nimport Mathlib.Data.Real.Irrational\nimport Mathlib.Topology.Algebra.Polynomial",
        "import Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic",
        "import Mathlib.Data.Fintype.Parity\nimport Mathlib.NumberTheory.LegendreSymbol.ZModChar\nimport Mathlib.FieldTheory.Finite.Basic",
        "import Mathlib.Algebra.Periodic\nimport Mathlib.Data.ZMod.Units\nimport Mathlib.NumberTheory.LegendreSymbol.MulCharacter",
        "import Mathlib.Analysis.Normed.Field.InfiniteSum\nimport Mathlib.Analysis.SpecificLimits.Normed\nimport Mathlib.NumberTheory.ArithmeticFunction\nimport Mathlib.NumberTheory.SmoothNumbers",
        "import Lean.Meta.Tactic.Rewrite\nimport Std.Lean.Expr\nimport Std.Lean.Name\nimport Std.Data.Rat.Basic\nimport Std.Data.List.Basic\nimport Std.Lean.Name\nimport Std.Logic",
        "import Mathlib.Lean.Meta",
        "import Lean.Meta.AppBuilder\nimport Lean.Meta.Basic",
        "import Mathlib.Data.Opposite\nimport Mathlib.Tactic.Cases",
        "import Mathlib.Combinatorics.SimpleGraph.Init\nimport Mathlib.Data.Rel\nimport Mathlib.Data.Set.Finite\nimport Mathlib.Data.Sym.Sym2",
        "import Mathlib.Algebra.GroupPower.Order\nimport Mathlib.Combinatorics.SimpleGraph.Clique\nimport Mathlib.Data.Finset.Sym\nimport Mathlib.Tactic.GCongr\nimport Mathlib.Tactic.Positivity",
        "import Mathlib.Dynamics.FixedPoints.Basic\nimport Mathlib.GroupTheory.Perm.Option\nimport Mathlib.Logic.Equiv.Defs\nimport Mathlib.Logic.Equiv.Option",
        "import Mathlib.Combinatorics.Hall.Finite\nimport Mathlib.CategoryTheory.CofilteredSystem\nimport Mathlib.Data.Rel"
    ],
    "working_file": "import Mathlib.MeasureTheory.Measure.GiryMonad\nimport Mathlib.Dynamics.Ergodic.MeasurePreserving\nimport Mathlib.MeasureTheory.Integral.Lebesgue\nimport Mathlib.MeasureTheory.Measure.OpenPos\nimport Mathlib.Analysis.Normed.Group.Basic\nimport Mathlib.MeasureTheory.Function.AEMeasurableSequence\nimport Mathlib.MeasureTheory.Group.Arithmetic\nimport Mathlib.MeasureTheory.Order.Lattice\nimport Mathlib.Topology.Instances.EReal\nimport Mathlib.Topology.MetricSpace.Thickening\nimport Mathlib.Topology.GDelta\nimport Mathlib.Topology.Order.Lattice\nimport Mathlib.Topology.Semicontinuous\nimport Mathlib.Analysis.SpecificLimits.Basic\nimport Mathlib.MeasureTheory.PiSystem\nimport Mathlib.Data.Countable.Basic\nimport Mathlib.Data.Fin.VecNotation\nimport Mathlib.MeasureTheory.Measure.Content\nimport Mathlib.MeasureTheory.Group.Prod\nimport Mathlib.Topology.Algebra.Group.Compact\nimport Mathlib.Dynamics.Ergodic.MeasurePreserving\nimport Mathlib.LinearAlgebra.Determinant\nimport Mathlib.LinearAlgebra.Matrix.Diagonal\nimport Mathlib.LinearAlgebra.Matrix.Transvection\nimport Mathlib.MeasureTheory.Constructions.Pi\nimport Mathlib.MeasureTheory.Measure.Stieltjes\nimport Mathlib.MeasureTheory.Measure.Haar.OfBasis\nimport Mathlib.Data.Finset.Update\nimport Mathlib.Data.Prod.TProd\nimport Mathlib.GroupTheory.Coset\nimport Mathlib.Logic.Equiv.Fin\nimport Mathlib.MeasureTheory.MeasurableSpace.Defs\nimport Mathlib.Order.Filter.SmallSets\nimport Mathlib.Order.LiminfLimsup\nimport Mathlib.Data.Set.UnionLift\nimport Mathlib.Analysis.NormedSpace.BoundedLinearMaps\nimport Mathlib.MeasureTheory.Measure.WithDensity\nimport Mathlib.MeasureTheory.Function.SimpleFuncDense\nimport Mathlib.Topology.Algebra.Module.FiniteDimension\nimport Mathlib.MeasureTheory.Function.AEEqFun.DomAct\nimport Mathlib.MeasureTheory.Function.LpSpace\nimport Mathlib.Analysis.SpecialFunctions.Pow.NNReal\nimport Mathlib.MeasureTheory.Constructions.BorelSpace.Complex\nimport Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1\nimport Mathlib.Analysis.NormedSpace.IndicatorFunction\nimport Mathlib.MeasureTheory.Function.EssSup\nimport Mathlib.MeasureTheory.Function.AEEqFun\nimport Mathlib.MeasureTheory.Function.SpecialFunctions.Basic\nimport Mathlib.Topology.Instances.ENNReal\nimport Mathlib.MeasureTheory.Measure.Dirac\nimport Mathlib.Probability.Notation\nimport Mathlib.Probability.Process.Stopping\nimport Mathlib.Probability.Independence.Kernel\nimport Mathlib.MeasureTheory.Integral.Bochner\nimport Mathlib.MeasureTheory.Measure.GiryMonad\nimport Mathlib.Algebra.Module.Hom\nimport Mathlib.Algebra.Module.Prod\nimport Mathlib.Algebra.Module.Submodule.Ker\nimport Mathlib.Data.Set.Finite\nimport Mathlib.Order.ConditionallyCompleteLattice.Basic\nimport Mathlib.LinearAlgebra.RootSystem.Defs\nimport Mathlib.LinearAlgebra.Matrix.Adjugate\nimport Mathlib.RingTheory.PolynomialAlgebra\nimport Mathlib.Algebra.AddTorsor\nimport Mathlib.GroupTheory.Perm.Sign\nimport Mathlib.Data.Fintype.Perm\nimport Mathlib.LinearAlgebra.Multilinear.Basis\nimport Mathlib.Data.Finsupp.Fintype\nimport Mathlib.LinearAlgebra.TensorProduct.Basis\nimport Mathlib.RingTheory.Finiteness\nimport Mathlib.LinearAlgebra.FreeModule.Basic\nimport Mathlib.Algebra.RingQuot\nimport Mathlib.LinearAlgebra.TensorAlgebra.Basic\nimport Mathlib.LinearAlgebra.QuadraticForm.Isometry\nimport Mathlib.LinearAlgebra.QuadraticForm.IsometryEquiv\nimport Mathlib.Algebra.Module.Submodule.Bilinear\nimport Mathlib.GroupTheory.Congruence\nimport Mathlib.LinearAlgebra.Basic\nimport Mathlib.Tactic.SuppressCompilation\nimport Mathlib.LinearAlgebra.Matrix.Determinant\nimport Mathlib.LinearAlgebra.Matrix.SesquilinearForm\nimport Mathlib.LinearAlgebra.Matrix.Symmetric\nimport Mathlib.Algebra.Algebra.Basic\nimport Mathlib.Algebra.BigOperators.Order\nimport Mathlib.Data.Fintype.BigOperators\nimport Mathlib.Data.Fintype.Sort\nimport Mathlib.Data.List.FinRange\nimport Mathlib.LinearAlgebra.Pi\nimport Mathlib.LinearAlgebra.CliffordAlgebra.Basic\nimport Mathlib.LinearAlgebra.Alternating.Basic\nimport Mathlib.Algebra.Algebra.Spectrum\nimport Mathlib.LinearAlgebra.GeneralLinearGroup\nimport Mathlib.LinearAlgebra.FiniteDimensional\nimport Mathlib.Algebra.FreeAlgebra\nimport Mathlib.Algebra.RingQuot\nimport Mathlib.Algebra.TrivSqZeroExt\nimport Mathlib.Algebra.Algebra.Operations\nimport Mathlib.LinearAlgebra.Multilinear.Basic\nimport Mathlib.Algebra.Algebra.Tower\nimport Mathlib.LinearAlgebra.FiniteDimensional\nimport Mathlib.LinearAlgebra.LinearIndependent\nimport Mathlib.LinearAlgebra.FreeModule.Finite.Basic\nimport Mathlib.LinearAlgebra.Matrix.Charpoly.Coeff\nimport Mathlib.FieldTheory.Minpoly.Field\nimport Mathlib.Init.Logic\nimport Mathlib.Init.Function\nimport Mathlib.Init.Algebra.Classes\nimport Std.Util.LibraryNote\nimport Std.Tactic.Lint.Basic\nimport Mathlib.Init.Order.Defs\nimport Mathlib.Logic.Nontrivial.Defs\nimport Mathlib.Tactic.Attr.Register\nimport Mathlib.Data.Prod.Basic\nimport Mathlib.Data.Subtype\nimport Mathlib.Logic.Function.Basic\nimport Mathlib.Logic.Unique\nimport Mathlib.Data.Bool.Basic\nimport Mathlib.Data.Option.Defs\nimport Mathlib.Data.Prod.Basic\nimport Mathlib.Data.Sigma.Basic\nimport Mathlib.Data.Subtype\nimport Mathlib.Data.Sum.Basic\nimport Mathlib.Init.Data.Sigma.Basic\nimport Mathlib.Logic.Equiv.Defs\nimport Mathlib.Logic.Function.Conjugate\nimport Mathlib.Tactic.Lift\nimport Mathlib.Tactic.Convert\nimport Mathlib.Tactic.Contrapose\nimport Mathlib.Tactic.GeneralizeProofs\nimport Mathlib.Tactic.SimpRw\nimport Mathlib.Logic.Equiv.Nat\nimport Mathlib.Data.PNat.Basic\nimport Mathlib.Order.Directed\nimport Mathlib.Data.Countable.Defs\nimport Mathlib.Order.RelIso.Basic\nimport Mathlib.Data.Fin.Basic\nimport Mathlib.Logic.Small.Defs\nimport Mathlib.Logic.Equiv.Set\nimport Mathlib.Logic.Nonempty\nimport Mathlib.Init.Set\nimport Mathlib.Logic.Basic\nimport Mathlib.Data.Option.Basic\nimport Mathlib.Data.Prod.PProd\nimport Mathlib.Logic.Equiv.Basic\nimport Mathlib.Analysis.Calculus.TangentCone\nimport Mathlib.Analysis.NormedSpace.OperatorNorm.Asymptotics\nimport Mathlib.Analysis.Calculus.Deriv.Add\nimport Mathlib.Analysis.InnerProductSpace.Dual\nimport Mathlib.Analysis.Calculus.FDeriv.Basic\nimport Mathlib.Analysis.Calculus.Deriv.Basic\nimport Mathlib.Analysis.Calculus.ContDiff.Basic\nimport Mathlib.Analysis.NormedSpace.FiniteDimension\nimport Mathlib.Analysis.Calculus.Deriv.Comp\nimport Mathlib.Analysis.Calculus.Deriv.Add\nimport Mathlib.Analysis.Calculus.Deriv.Mul\nimport Mathlib.Analysis.Calculus.Deriv.Slope\nimport Mathlib.Analysis.Calculus.FDeriv.Basic\nimport Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace\nimport Mathlib.Analysis.Calculus.ContDiff.Defs\nimport Mathlib.Analysis.Calculus.FDeriv.Add\nimport Mathlib.Analysis.Calculus.FDeriv.Mul\nimport Mathlib.Analysis.Calculus.Deriv.Inverse\nimport Mathlib.Algebra.DirectSum.Module\nimport Mathlib.Analysis.Complex.Basic\nimport Mathlib.Analysis.Convex.Uniform\nimport Mathlib.Analysis.NormedSpace.Completion\nimport Mathlib.Analysis.NormedSpace.BoundedLinearMaps\nimport Mathlib.Algebra.Algebra.NonUnitalSubalgebra\nimport Mathlib.Algebra.Algebra.Subalgebra.Basic\nimport Mathlib.Analysis.Normed.Group.Basic\nimport Mathlib.GroupTheory.OrderOfElement\nimport Mathlib.Topology.Instances.NNReal\nimport Mathlib.Topology.MetricSpace.DilationEquiv\nimport Mathlib.Algebra.Order.Group.TypeTags\nimport Mathlib.Analysis.Normed.Field.Basic\nimport Mathlib.Analysis.Normed.Group.Seminorm\nimport Mathlib.Order.LiminfLimsup\nimport Mathlib.Topology.Instances.Rat\nimport Mathlib.Topology.MetricSpace.Algebra\nimport Mathlib.Topology.MetricSpace.IsometricSMul\nimport Mathlib.Topology.Sequences\nimport Mathlib.Analysis.SpecialFunctions.Exp\nimport Mathlib.Data.Nat.Factorization.Basic\nimport Mathlib.Analysis.NormedSpace.Real\nimport Mathlib.Analysis.SpecialFunctions.Exp\nimport Mathlib.Tactic.Positivity.Core\nimport Mathlib.MeasureTheory.Integral.ExpDecay\nimport Mathlib.Analysis.SpecialFunctions.ImproperIntegrals\nimport Mathlib.Analysis.MellinTransform\nimport Mathlib.Analysis.Convex.Basic\nimport Mathlib.Analysis.Convex.Hull\nimport Mathlib.Analysis.NormedSpace.Basic\nimport Mathlib.Topology.Bornology.Absorbs\nimport Mathlib.Analysis.NormedSpace.Dual\nimport Mathlib.Analysis.NormedSpace.Star.Basic\nimport Mathlib.Analysis.Complex.Basic\nimport Mathlib.Analysis.InnerProductSpace.Adjoint\nimport Mathlib.Algebra.Star.Subalgebra\nimport Mathlib.Analysis.BoxIntegral.Partition.Filter\nimport Mathlib.Analysis.BoxIntegral.Partition.Measure\nimport Mathlib.Topology.UniformSpace.Compact\nimport Mathlib.Init.Data.Bool.Lemmas\nimport Mathlib.Algebra.BigOperators.Option\nimport Mathlib.Analysis.BoxIntegral.Box.Basic\nimport Mathlib.Data.Set.Pairwise.Lattice\nimport Mathlib.Data.Set.Intervals.Monotone\nimport Mathlib.Topology.MetricSpace.Basic\nimport Mathlib.Topology.MetricSpace.Bounded\nimport Mathlib.Topology.Order.MonotoneConvergence\nimport Mathlib.Data.Complex.Module\nimport Mathlib.Data.Complex.Order\nimport Mathlib.Data.Complex.Exponential\nimport Mathlib.Data.RCLike.Basic\nimport Mathlib.Topology.Algebra.InfiniteSum.Module\nimport Mathlib.Topology.Instances.RealVectorSpace\nimport Mathlib.Analysis.Complex.Circle\nimport Mathlib.Analysis.NormedSpace.BallAction\nimport Mathlib.Data.Fintype.Parity\nimport Mathlib.LinearAlgebra.Matrix.SpecialLinearGroup\nimport Mathlib.Analysis.Complex.Basic\nimport Mathlib.GroupTheory.GroupAction.Defs\nimport Mathlib.LinearAlgebra.Matrix.GeneralLinearGroup\nimport Mathlib.Tactic.LinearCombination\nimport Mathlib.Algebra.GeomSum\nimport Mathlib.Order.Filter.Archimedean\nimport Mathlib.Order.Iterate\nimport Mathlib.Topology.Instances.ENNReal\nimport Mathlib.Topology.Algebra.Algebra\nimport Mathlib.Algebra.Order.Module.OrderedSMul\nimport Mathlib.Analysis.Convex.Star\nimport Mathlib.LinearAlgebra.AffineSpace.AffineSubspace\nimport Mathlib.Analysis.Convex.Hull\nimport Mathlib.LinearAlgebra.AffineSpace.Independent\nimport Mathlib.Analysis.Convex.Hull\nimport Mathlib.Analysis.Convex.Slope\nimport Mathlib.Analysis.SpecialFunctions.Pow.Real\nimport Mathlib.Tactic.LinearCombination\nimport Mathlib.Algebra.Algebra.Pi\nimport Mathlib.Algebra.Algebra.RestrictScalars\nimport Mathlib.Analysis.Normed.Field.Basic\nimport Mathlib.Analysis.Normed.MulAction\nimport Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace\nimport Mathlib.Topology.Algebra.Module.Multilinear.Basic\nimport Mathlib.Algebra.Algebra.Tower\nimport Mathlib.Analysis.LocallyConvex.WithSeminorms\nimport Mathlib.Topology.Algebra.Module.StrongTopology\nimport Mathlib.Analysis.NormedSpace.LinearIsometry\nimport Mathlib.Analysis.NormedSpace.ContinuousLinearMap\nimport Mathlib.Tactic.SuppressCompilation\nimport Mathlib.Analysis.Normed.Group.Hom\nimport Mathlib.Analysis.NormedSpace.Basic\nimport Mathlib.Analysis.NormedSpace.LinearIsometry\nimport Mathlib.Algebra.Star.SelfAdjoint\nimport Mathlib.Algebra.Star.Subalgebra\nimport Mathlib.Algebra.Star.Unitary\nimport Mathlib.Topology.Algebra.Module.Star\nimport Mathlib.Analysis.Calculus.FormalMultilinearSeries\nimport Mathlib.Analysis.SpecificLimits.Normed\nimport Mathlib.Logic.Equiv.Fin\nimport Mathlib.Topology.Algebra.InfiniteSum.Module\nimport Mathlib.CategoryTheory.Sites.Sheaf\nimport Mathlib.Topology.Category.CompHaus.EffectiveEpi\nimport Mathlib.Data.Fin.VecNotation\nimport Mathlib.SetTheory.Cardinal.Basic\nimport Mathlib.ModelTheory.Syntax\nimport Mathlib.ModelTheory.Semantics\nimport Mathlib.ModelTheory.Algebra.Ring.Basic\nimport Mathlib.Algebra.Field.MinimalAxioms\nimport Mathlib.ModelTheory.Syntax\nimport Mathlib.ModelTheory.Semantics\nimport Mathlib.Algebra.Ring.Equiv\nimport Mathlib.Init.Control.Combinators\nimport Mathlib.Init.Function\nimport Mathlib.Tactic.CasesM\nimport Mathlib.Tactic.Attr.Core\nimport Mathlib.Logic.Equiv.Defs\nimport Mathlib.Data.Option.Defs\nimport Mathlib.Control.Functor\nimport Mathlib.Control.Bifunctor\nimport Mathlib.Control.Traversable.Basic\nimport Mathlib.Init.Order.LinearOrder\nimport Mathlib.Data.Prod.Basic\nimport Mathlib.Data.Subtype\nimport Mathlib.Tactic.Spread\nimport Mathlib.Tactic.Convert\nimport Mathlib.Tactic.SimpRw\nimport Mathlib.Tactic.Cases\nimport Mathlib.Order.Notation\nimport Mathlib.Logic.Equiv.Option\nimport Mathlib.Order.RelIso.Basic\nimport Mathlib.Order.Disjoint\nimport Mathlib.Order.WithBot\nimport Mathlib.Tactic.Monotonicity.Attr\nimport Mathlib.Util.AssertExists\nimport Mathlib.Data.SetLike.Basic\nimport Mathlib.Data.Set.Intervals.OrdConnected\nimport Mathlib.Data.Set.Intervals.OrderIso\nimport Mathlib.Data.Set.Lattice\nimport Mathlib.Order.PropInstances\nimport Mathlib.Data.Set.Finite\nimport Mathlib.Logic.Function.Iterate\nimport Mathlib.Init.Data.Int.Order\nimport Mathlib.Order.Compare\nimport Mathlib.Order.Max\nimport Mathlib.Order.RelClasses\nimport Mathlib.Tactic.Choose\nimport Mathlib.Order.CompleteLattice\nimport Mathlib.Order.Cover\nimport Mathlib.Order.Iterate\nimport Mathlib.Init.Algebra.Classes\nimport Mathlib.Data.FunLike.Basic\nimport Mathlib.Logic.Embedding.Basic\nimport Mathlib.Order.RelClasses\nimport Mathlib.Order.Atoms\nimport Mathlib.Order.OrderIsoNat\nimport Mathlib.Order.RelIso.Set\nimport Mathlib.Order.SupClosed\nimport Mathlib.Order.SupIndep\nimport Mathlib.Order.Zorn\nimport Mathlib.Data.Finset.Order\nimport Mathlib.Data.Set.Intervals.OrderIso\nimport Mathlib.Data.Finite.Set\nimport Mathlib.Tactic.TFAE\nimport Mathlib.Order.Bounds.Basic\nimport Mathlib.Order.WellFounded\nimport Mathlib.Data.Set.Image\nimport Mathlib.Data.Set.Intervals.Basic\nimport Mathlib.Data.Set.Lattice\nimport Mathlib.Data.Set.Intervals.Basic\nimport Mathlib.Data.Set.NAry\nimport Mathlib.Order.Directed\nimport Mathlib.Data.Sum.Order\nimport Mathlib.Order.InitialSeg\nimport Mathlib.SetTheory.Cardinal.Basic\nimport Mathlib.Tactic.PPWithUniv\nimport Mathlib.Data.Set.Lattice\nimport Mathlib.Logic.Small.Basic\nimport Mathlib.Logic.Function.OfArity\nimport Mathlib.Order.WellFounded\nimport Mathlib.Data.Int.Basic\nimport Mathlib.SetTheory.Game.PGame\nimport Mathlib.Tactic.Abel\nimport Mathlib.Algebra.Order.Hom.Monoid\nimport Mathlib.SetTheory.Game.Ordinal\nimport Mathlib.Algebra.Module.Basic\nimport Mathlib.Data.Fintype.BigOperators\nimport Mathlib.Data.Finsupp.Defs\nimport Mathlib.Data.Set.Countable\nimport Mathlib.Logic.Small.Set\nimport Mathlib.Order.ConditionallyCompleteLattice.Basic\nimport Mathlib.Order.SuccPred.CompleteLinearOrder\nimport Mathlib.SetTheory.Cardinal.SchroederBernstein\nimport Mathlib.Tactic.PPWithUniv\nimport Mathlib.Algebra.Group.Equiv.TypeTags\nimport Mathlib.Algebra.Module.Basic\nimport Mathlib.Algebra.Module.LinearMap.Basic\nimport Mathlib.Algebra.MonoidAlgebra.Basic\nimport Mathlib.LinearAlgebra.Dual\nimport Mathlib.LinearAlgebra.Contraction\nimport Mathlib.RingTheory.TensorProduct.Basic\nimport Mathlib.Algebra.Category.GroupCat.Basic\nimport Mathlib.CategoryTheory.SingleObj\nimport Mathlib.CategoryTheory.Limits.FunctorCategory\nimport Mathlib.CategoryTheory.Limits.Preserves.Basic\nimport Mathlib.CategoryTheory.Adjunction.Limits\nimport Mathlib.CategoryTheory.Conj\nimport Mathlib.Algebra.Homology.Opposite\nimport Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex\nimport Mathlib.RepresentationTheory.GroupCohomology.Resolution\nimport Mathlib.CategoryTheory.Limits.HasLimits\nimport Mathlib.CategoryTheory.Limits.Connected\nimport Mathlib.CategoryTheory.Limits.Constructions.Over.Products\nimport Mathlib.CategoryTheory.Limits.Constructions.Over.Connected\nimport Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers\nimport Mathlib.CategoryTheory.Limits.Constructions.Equalizers\nimport Mathlib.CategoryTheory.Limits.Shapes.RegularMono\nimport Mathlib.CategoryTheory.Limits.Shapes.Kernels\nimport Mathlib.CategoryTheory.Limits.Preserves.Basic\nimport Mathlib.CategoryTheory.NatIso\nimport Mathlib.CategoryTheory.Limits.Constructions.Pullbacks\nimport Mathlib.CategoryTheory.Preadditive.Biproducts\nimport Mathlib.CategoryTheory.Limits.Shapes.Images\nimport Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers\nimport Mathlib.CategoryTheory.Abelian.NonPreadditive\nimport Mathlib.CategoryTheory.Subobject.MonoOver\nimport Mathlib.CategoryTheory.Skeletal\nimport Mathlib.CategoryTheory.ConcreteCategory.Basic\nimport Mathlib.Tactic.ApplyFun\nimport Mathlib.Tactic.CategoryTheory.Elementwise\nimport Mathlib.CategoryTheory.EqToHom\nimport Mathlib.CategoryTheory.Functor.Const\nimport Mathlib.CategoryTheory.Opposites\nimport Mathlib.Data.Prod.Basic\nimport Mathlib.CategoryTheory.CommSq\nimport Mathlib.Algebra.BigOperators.Basic\nimport Mathlib.Algebra.Group.Hom.Defs\nimport Mathlib.Algebra.Module.Basic\nimport Mathlib.CategoryTheory.Endomorphism\nimport Mathlib.CategoryTheory.Limits.Shapes.Kernels\nimport Mathlib.CategoryTheory.Preadditive.Opposite\nimport Mathlib.Algebra.Category.ModuleCat.Basic\nimport Mathlib.Algebra.Category.GroupCat.Preadditive\nimport Mathlib.CategoryTheory.Functor.Category\nimport Mathlib.CategoryTheory.Functor.FullyFaithful\nimport Mathlib.CategoryTheory.Functor.ReflectsIso\nimport Mathlib.CategoryTheory.EqToHom\nimport Mathlib.CategoryTheory.NatIso\nimport Mathlib.CategoryTheory.Products.Basic\nimport Mathlib.Algebra.Group.Basic\nimport Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero\nimport Mathlib.CategoryTheory.Monoidal.End\nimport Mathlib.CategoryTheory.Monoidal.Discrete\nimport Mathlib.CategoryTheory.Equivalence\nimport Mathlib.CategoryTheory.FinCategory.Basic\nimport Mathlib.CategoryTheory.Limits.Cones\nimport Mathlib.CategoryTheory.Limits.Shapes.FiniteLimits\nimport Mathlib.CategoryTheory.Adjunction.Basic\nimport Mathlib.CategoryTheory.Category.Preorder\nimport Mathlib.CategoryTheory.Category.ULift\nimport Mathlib.CategoryTheory.PEmpty\nimport Mathlib.CategoryTheory.Monoidal.Types.Symmetric\nimport Mathlib.CategoryTheory.Monoidal.Types.Coyoneda\nimport Mathlib.CategoryTheory.Monoidal.Center\nimport Mathlib.Tactic.ApplyFun\nimport Mathlib.CategoryTheory.Abelian.Basic\nimport Mathlib.CategoryTheory.EqToHom\nimport Mathlib.CategoryTheory.Iso\nimport Mathlib.CategoryTheory.Functor.Category\nimport Mathlib.CategoryTheory.EqToHom\nimport Mathlib.CategoryTheory.Whiskering\nimport Mathlib.CategoryTheory.Functor.FullyFaithful\nimport Mathlib.CategoryTheory.NatIso\nimport Mathlib.CategoryTheory.Extensive\nimport Mathlib.CategoryTheory.Sites.Coverage\nimport Mathlib.CategoryTheory.EffectiveEpi.Basic\nimport Mathlib.CategoryTheory.Adjunction.Limits\nimport Mathlib.CategoryTheory.Limits.Preserves.Shapes.Products\nimport Mathlib.CategoryTheory.Limits.Shapes.Biproducts\nimport Mathlib.CategoryTheory.Shift.Basic\nimport Mathlib.CategoryTheory.Types\nimport Mathlib.CategoryTheory.Functor.EpiMono\nimport Mathlib.CategoryTheory.Limits.Constructions.EpiMono\nimport Mathlib.CategoryTheory.Monoidal.Free.Coherence\nimport Mathlib.CategoryTheory.Monoidal.Discrete\nimport Mathlib.CategoryTheory.Monoidal.NaturalTransformation\nimport Mathlib.CategoryTheory.Monoidal.Opposite\nimport Mathlib.Tactic.CategoryTheory.Coherence\nimport Mathlib.CategoryTheory.CommSq\nimport Mathlib.CategoryTheory.Monoidal.Functor\nimport Mathlib.CategoryTheory.ChosenFiniteProducts\nimport Mathlib.CategoryTheory.Limits.Shapes.Types\nimport Mathlib.Logic.Equiv.Fin\nimport Mathlib.CategoryTheory.Monoidal.Functor\nimport Mathlib.CategoryTheory.Monoidal.Free.Coherence\nimport Mathlib.Tactic.CategoryTheory.Coherence\nimport Mathlib.CategoryTheory.Closed.Monoidal\nimport Mathlib.Tactic.ApplyFun\nimport Mathlib.CategoryTheory.Monoidal.Category\nimport Mathlib.CategoryTheory.Limits.Shapes.BinaryProducts\nimport Mathlib.CategoryTheory.PEmpty\nimport Mathlib.CategoryTheory.Preadditive.Basic\nimport Mathlib.Algebra.Module.LinearMap.Basic\nimport Mathlib.Algebra.Algebra.Basic\nimport Mathlib.CategoryTheory.Category.Init\nimport Mathlib.Combinatorics.Quiver.Basic\nimport Mathlib.Tactic.PPWithUniv\nimport Mathlib.Tactic.Common\nimport Mathlib.CategoryTheory.Limits.Shapes.Products\nimport Mathlib.Data.Fintype.Basic\nimport Mathlib.CategoryTheory.DiscreteCategory\nimport Mathlib.CategoryTheory.Opposites\nimport Mathlib.CategoryTheory.Category.ULift\nimport Mathlib.CategoryTheory.Category.Basic\nimport Mathlib.CategoryTheory.Comma.StructuredArrow\nimport Mathlib.CategoryTheory.Limits.Shapes.Equivalence\nimport Mathlib.CategoryTheory.FintypeCat\nimport Mathlib.CategoryTheory.Limits.Constructions.LimitsOfProductsAndEqualizers\nimport Mathlib.CategoryTheory.Limits.FintypeCat\nimport Mathlib.CategoryTheory.Limits.MonoCoprod\nimport Mathlib.CategoryTheory.Limits.Preserves.Shapes.Terminal\nimport Mathlib.CategoryTheory.Limits.Shapes.Types\nimport Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory\nimport Mathlib.CategoryTheory.Limits.Shapes.Diagonal\nimport Mathlib.CategoryTheory.SingleObj\nimport Mathlib.Data.Finite.Card\nimport Mathlib.CategoryTheory.Groupoid\nimport Mathlib.Combinatorics.Quiver.Basic\nimport Mathlib.LinearAlgebra.StdBasis\nimport Mathlib.Tactic.Linarith\nimport Mathlib.Data.Finset.PiAntidiagonal\nimport Mathlib.Data.MvPolynomial.Basic\nimport Mathlib.Tactic.FinCases\nimport Mathlib.Data.Nat.Choose.Sum\nimport Mathlib.LinearAlgebra.Finsupp\nimport Mathlib.Algebra.GroupPower.Order\nimport Mathlib.RingTheory.Ideal.Operations\nimport Mathlib.Tactic.TFAE\nimport Mathlib.RingTheory.Adjoin.Basic\nimport Mathlib.Algebra.Ring.Equiv\nimport Mathlib.Algebra.Ring.Prod\nimport Mathlib.Data.Set.Finite\nimport Mathlib.GroupTheory.Submonoid.Membership\nimport Mathlib.GroupTheory.Subsemigroup.Membership\nimport Mathlib.GroupTheory.Subsemigroup.Centralizer\nimport Mathlib.Algebra.EuclideanDomain.Basic\nimport Mathlib.Data.Nat.Factors\nimport Mathlib.RingTheory.Coprime.Basic\nimport Mathlib.RingTheory.PrincipalIdealDomain\nimport Mathlib.Algebra.CharP.ExpChar\nimport Mathlib.Algebra.GeomSum\nimport Mathlib.Data.MvPolynomial.CommRing\nimport Mathlib.Data.MvPolynomial.Equiv\nimport Mathlib.RingTheory.Polynomial.Content\nimport Mathlib.RingTheory.UniqueFactorizationDomain\nimport Mathlib.Algebra.NeZero\nimport Mathlib.Algebra.Polynomial.BigOperators\nimport Mathlib.RingTheory.RootsOfUnity.Complex\nimport Mathlib.Data.Polynomial.Lifts\nimport Mathlib.Data.Polynomial.Splits\nimport Mathlib.FieldTheory.RatFunc\nimport Mathlib.NumberTheory.ArithmeticFunction\nimport Mathlib.RingTheory.RootsOfUnity.Basic\nimport Mathlib.Data.Polynomial.Derivative\nimport Mathlib.Data.Nat.Parity\nimport Mathlib.Data.Nat.Factorial.DoubleFactorial\nimport Mathlib.RingTheory.EisensteinCriterion\nimport Mathlib.RingTheory.Polynomial.ScaleRoots\nimport Mathlib.Algebra.GroupPower.Ring\nimport Mathlib.Algebra.Ring.Divisibility.Basic\nimport Mathlib.Algebra.Ring.Hom.Defs\nimport Mathlib.GroupTheory.GroupAction.Units\nimport Mathlib.Logic.Basic\nimport Mathlib.Tactic.Ring\nimport Mathlib.RingTheory.Noetherian\nimport Mathlib.Algebra.DirectSum.Module\nimport Mathlib.Algebra.DirectSum.Finsupp\nimport Mathlib.Algebra.Module.Projective\nimport Mathlib.Algebra.Module.Injective\nimport Mathlib.Algebra.Module.CharacterModule\nimport Mathlib.LinearAlgebra.DirectSum.TensorProduct\nimport Mathlib.LinearAlgebra.FreeModule.Basic\nimport Mathlib.Algebra.Module.Projective\nimport Mathlib.GroupTheory.Subgroup.Basic\nimport Mathlib.RingTheory.Subsemiring.Basic\nimport Mathlib.Algebra.Algebra.Operations\nimport Mathlib.Algebra.Algebra.Subalgebra.Tower\nimport Mathlib.LinearAlgebra.Prod\nimport Mathlib.LinearAlgebra.Finsupp\nimport Mathlib.Algebra.Module.Basic\nimport Mathlib.Algebra.Ring.Equiv\nimport Mathlib.Algebra.Ring.Prod\nimport Mathlib.Algebra.GroupRingAction.Subobjects\nimport Mathlib.Data.Set.Finite\nimport Mathlib.GroupTheory.Submonoid.Centralizer\nimport Mathlib.GroupTheory.Submonoid.Membership\nimport Mathlib.RingTheory.NonUnitalSubsemiring.Basic\nimport Mathlib.GroupTheory.MonoidLocalization\nimport Mathlib.Algebra.GroupWithZero.NonZeroDivisors\nimport Mathlib.RingTheory.OreLocalization.OreSet\nimport Mathlib.Tactic.NoncommRing\nimport Mathlib.Algebra.Function.Support\nimport Mathlib.Order.WellFoundedSet\nimport Mathlib.RingTheory.Ideal.Over\nimport Mathlib.RingTheory.Polynomial.RationalRoot\nimport Mathlib.Algebra.CharP.Basic\nimport Mathlib.Data.Polynomial.AlgebraMap\nimport Mathlib.Data.MvPolynomial.Degrees\nimport Mathlib.LinearAlgebra.FinsuppVectorSpace\nimport Mathlib.LinearAlgebra.FreeModule.Finite.Basic\nimport Mathlib.Algebra.DirectSum.Algebra\nimport Mathlib.Algebra.DirectSum.Decomposition\nimport Mathlib.Algebra.DirectSum.Internal\nimport Mathlib.Algebra.DirectSum.Ring\nimport Mathlib.Algebra.Algebra.Tower\nimport Mathlib.Algebra.GroupWithZero.NonZeroDivisors\nimport Mathlib.GroupTheory.MonoidLocalization\nimport Mathlib.RingTheory.Ideal.Basic\nimport Mathlib.GroupTheory.GroupAction.Ring\nimport Mathlib.Init.Data.Int.CompLemmas\nimport Mathlib.RingTheory.UniqueFactorizationDomain\nimport Mathlib.RingTheory.Localization.Basic\nimport Mathlib.Algebra.CharP.Two\nimport Mathlib.Algebra.CharP.Reduced\nimport Mathlib.Algebra.NeZero\nimport Mathlib.Data.Polynomial.RingDivision\nimport Mathlib.GroupTheory.SpecificGroups.Cyclic\nimport Mathlib.NumberTheory.Divisors\nimport Mathlib.RingTheory.IntegralDomain\nimport Mathlib.Tactic.Zify\nimport Mathlib.LinearAlgebra.FiniteDimensional\nimport Mathlib.LinearAlgebra.TensorProduct.Tower\nimport Mathlib.RingTheory.Adjoin.Basic\nimport Mathlib.LinearAlgebra.DirectSum.Finsupp\nimport Mathlib.Data.MvPolynomial.Counit\nimport Mathlib.Data.MvPolynomial.Invertible\nimport Mathlib.RingTheory.WittVector.Defs\nimport Mathlib.RingTheory.MvPowerSeries.Basic\nimport Mathlib.Data.Polynomial.Basic\nimport Mathlib.Data.Polynomial.AlgebraMap\nimport Mathlib.RingTheory.PrincipalIdealDomain\nimport Mathlib.RingTheory.Ideal.LocalRing\nimport Mathlib.RingTheory.Valuation.PrimeMultiplicity\nimport Mathlib.LinearAlgebra.AdicCompletion\nimport Mathlib.GroupTheory.Subgroup.Basic\nimport Mathlib.RingTheory.NonUnitalSubsemiring.Basic\nimport Mathlib.RingTheory.Localization.Integer\nimport Mathlib.RingTheory.Localization.Submodule\nimport Mathlib.Algebra.Group.Conj\nimport Mathlib.Algebra.Group.Pi.Lemmas\nimport Mathlib.Data.Set.Image\nimport Mathlib.GroupTheory.Submonoid.Centralizer\nimport Mathlib.Order.Atoms\nimport Mathlib.Tactic.ApplyFun\nimport Mathlib.Algebra.Group.Prod\nimport Mathlib.Algebra.Group.Units.Equiv\nimport Mathlib.Algebra.GroupPower.IterateHom\nimport Mathlib.Logic.Equiv.Set\nimport Mathlib.Algebra.Module.BigOperators\nimport Mathlib.Data.Fintype.Perm\nimport Mathlib.GroupTheory.Perm.Finite\nimport Mathlib.GroupTheory.Perm.List\nimport Mathlib.Algebra.Group.Hom.Defs\nimport Mathlib.Algebra.Group.Units\nimport Mathlib.GroupTheory.Subsemigroup.Basic\nimport Mathlib.Algebra.PUnitInstances\nimport Mathlib.GroupTheory.Subgroup.Basic\nimport Mathlib.GroupTheory.Congruence\nimport Mathlib.GroupTheory.Submonoid.Membership\nimport Mathlib.Data.Fintype.Card\nimport Mathlib.GroupTheory.GroupAction.Defs\nimport Mathlib.GroupTheory.GroupAction.Group\nimport Mathlib.Data.Setoid.Basic\nimport Mathlib.Data.Set.Pointwise.SMul\nimport Mathlib.GroupTheory.Subgroup.Basic\nimport Mathlib.Algebra.Group.Opposite\nimport Mathlib.Algebra.Group.Pi.Lemmas\nimport Mathlib.GroupTheory.GroupAction.Defs\nimport Mathlib.Algebra.Group.Hom.Defs\nimport Mathlib.Data.Set.Lattice\nimport Mathlib.Data.SetLike.Basic\nimport Mathlib.Data.Fintype.Basic\nimport Mathlib.Data.List.Sublists\nimport Mathlib.Data.List.InsertNth\nimport Mathlib.GroupTheory.Subgroup.Basic\nimport Mathlib.Algebra.Group.TypeTags\nimport Mathlib.Algebra.Ring.Defs\nimport Mathlib.Data.Int.Cast.Basic\nimport Mathlib.Order.Monotone.Basic\nimport Mathlib.Data.Nat.Order.Basic\nimport Mathlib.Data.Int.Basic\nimport Mathlib.Algebra.Order.Group.Abs\nimport Mathlib.Algebra.Order.Ring.CharZero\nimport Mathlib.Algebra.Divisibility.Basic\nimport Mathlib.Init.Data.Nat.Lemmas\nimport Mathlib.Data.Int.Cast.Defs\nimport Mathlib.Algebra.Group.Basic\nimport Mathlib.Data.Int.Order.Basic\nimport Mathlib.Data.Nat.Cast.Order\nimport Mathlib.Algebra.Ring.Divisibility.Basic\nimport Mathlib.Data.DList.Defs\nimport Mathlib.Tactic.TypeStar\nimport Mathlib.Mathport.Rename\nimport Mathlib.Data.Nat.SuccPred\nimport Mathlib.Algebra.CharZero.Lemmas\nimport Mathlib.Algebra.Order.Sub.WithTop\nimport Mathlib.Algebra.Order.Ring.WithTop\nimport Mathlib.Data.Real.Sqrt\nimport Mathlib.Analysis.NormedSpace.Star.Basic\nimport Mathlib.Analysis.NormedSpace.ContinuousLinearMap\nimport Mathlib.Analysis.NormedSpace.Basic\nimport Mathlib.Init.ZeroOne\nimport Mathlib.Data.Set.Defs\nimport Mathlib.Order.Basic\nimport Mathlib.Order.SymmDiff\nimport Mathlib.Tactic.Tauto\nimport Mathlib.Tactic.ByContra\nimport Mathlib.Util.Delaborators\nimport Mathlib.Data.Set.Function\nimport Mathlib.Logic.Relation\nimport Mathlib.Logic.Pairwise\nimport Mathlib.Algebra.Group.Equiv.Basic\nimport Mathlib.Algebra.Group.Units.Hom\nimport Mathlib.Algebra.GroupPower.Basic\nimport Mathlib.Algebra.GroupWithZero.Basic\nimport Mathlib.Algebra.Opposites\nimport Mathlib.Data.Nat.Order.Basic\nimport Mathlib.Data.Set.Lattice\nimport Mathlib.Tactic.Common\nimport Mathlib.Order.MinMax\nimport Mathlib.Data.Set.Basic\nimport Mathlib.Tactic.Says\nimport Mathlib.Data.List.Lex\nimport Mathlib.Data.Char\nimport Mathlib.Logic.Function.Basic\nimport Mathlib.Tactic.MkIffOfInductiveProp\nimport Mathlib.Data.PNat.Defs\nimport Mathlib.Data.Nat.Bits\nimport Mathlib.Data.Nat.Order.Basic\nimport Mathlib.Data.Set.Basic\nimport Mathlib.Algebra.GroupWithZero.Divisibility\nimport Mathlib.Algebra.Order.Positive.Ring\nimport Mathlib.Order.Hom.Basic\nimport Mathlib.Data.W.Basic\nimport Mathlib.Control.Functor.Multivariate\nimport Mathlib.Data.PFunctor.Univariate.Basic\nimport Mathlib.Init.Function\nimport Mathlib.Logic.Function.Basic\nimport Mathlib.Tactic.Inhabit\nimport Mathlib.Algebra.Module.LinearMap.Basic\nimport Mathlib.Algebra.BigOperators.Basic\nimport Mathlib.Data.Set.Finite\nimport Mathlib.GroupTheory.Submonoid.Membership\nimport Mathlib.GroupTheory.GroupAction.BigOperators\nimport Mathlib.Data.Finset.Preimage\nimport Lean.Linter.Deprecated\nimport Mathlib.Mathport.Rename\nimport Mathlib.Init.Data.Nat.Bitwise\nimport Mathlib.Init.Data.Int.Basic\nimport Mathlib.Init.ZeroOne\nimport Mathlib.Logic.Equiv.List\nimport Mathlib.Init.Function\nimport Mathlib.Logic.Function.Basic\nimport Mathlib.Algebra.Algebra.Tower\nimport Mathlib.Algebra.GroupPower.Ring\nimport Mathlib.Algebra.Regular.Pow\nimport Mathlib.Algebra.MonoidAlgebra.Support\nimport Mathlib.Data.Finsupp.Antidiagonal\nimport Mathlib.Order.SymmDiff\nimport Mathlib.RingTheory.Adjoin.Basic\nimport Mathlib.Control.Traversable.Equiv\nimport Mathlib.Control.Traversable.Instances\nimport Std.Data.LazyList\nimport Mathlib.Lean.Thunk\nimport Mathlib.Logic.Relation\nimport Mathlib.Order.GaloisConnection\nimport Mathlib.Data.Vector\nimport Mathlib.Data.List.Nodup\nimport Mathlib.Data.List.OfFn\nimport Mathlib.Data.List.InsertNth\nimport Mathlib.Control.Applicative\nimport Mathlib.Control.Traversable.Basic\nimport Mathlib.Algebra.GroupPower.Ring\nimport Mathlib.Algebra.MonoidAlgebra.Basic\nimport Mathlib.Data.Finset.Sort\nimport Mathlib.RingTheory.Finiteness\nimport Mathlib.Data.Polynomial.AlgebraMap\nimport Std.Tactic.Alias\nimport Mathlib.Algebra.BigOperators.Finsupp\nimport Mathlib.Algebra.Regular.SMul\nimport Mathlib.Data.Finset.Preimage\nimport Mathlib.Data.Rat.BigOperators\nimport Mathlib.GroupTheory.GroupAction.Hom\nimport Mathlib.Data.Set.Basic\nimport Mathlib.Data.Finset.Attr\nimport Mathlib.Data.Multiset.Bind\nimport Mathlib.Data.Multiset.FinsetOps\nimport Mathlib.Data.Set.Lattice\nimport Mathlib.Order.Cover\nimport Mathlib.Order.LocallyFinite\nimport Mathlib.Data.Set.Intervals.Monoid\nimport Mathlib.Algebra.Group.TypeTags\nimport Mathlib.Algebra.Ring.Defs\nimport Mathlib.Algebra.GroupWithZero.Defs\nimport Mathlib.Algebra.Order.Monoid.WithZero\nimport Mathlib.Algebra.Order.Ring.Canonical\nimport Mathlib.Data.Nat.Basic\nimport Mathlib.Data.Nat.Defs\nimport Mathlib.Tactic.GCongr.Core\nimport Mathlib.Tactic.Common\nimport Mathlib.Tactic.Monotonicity.Attr\nimport Mathlib.Algebra.GroupPower.Basic\nimport Mathlib.Algebra.GroupWithZero.Divisibility\nimport Mathlib.Data.Nat.Order.Lemmas\nimport Mathlib.Tactic.NthRewrite\nimport Mathlib.Algebra.Divisibility.Basic\nimport Mathlib.Algebra.Group.Equiv.Basic\nimport Mathlib.Algebra.Group.TypeTags\nimport Mathlib.Algebra.Ring.Hom.Defs\nimport Mathlib.Data.Nat.Basic\nimport Mathlib.Init.Data.Nat.Lemmas\nimport Mathlib.Init.Data.Nat.Bitwise\nimport Mathlib.Data.Nat.GCD.Basic\nimport Mathlib.Logic.Function.Iterate\nimport Mathlib.Data.Finset.NatAntidiagonal\nimport Mathlib.Algebra.BigOperators.Basic\nimport Mathlib.Tactic.Ring\nimport Mathlib.Tactic.Zify\nimport Mathlib.Data.Nat.Factorial.Basic\nimport Mathlib.Order.Monotone.Basic\nimport Mathlib.Algebra.BigOperators.Finsupp\nimport Mathlib.Data.Finsupp.Multiset\nimport Mathlib.Data.Nat.PrimeFin\nimport Mathlib.NumberTheory.Padics.PadicVal\nimport Mathlib.Data.Nat.GCD.BigOperators\nimport Mathlib.Data.Nat.Interval\nimport Mathlib.Tactic.IntervalCases\nimport Mathlib.Algebra.GroupPower.Order\nimport Mathlib.Data.Set.Basic\nimport Mathlib.Tactic.Monotonicity.Attr\nimport Mathlib.Tactic.SetLike\nimport Mathlib.Algebra.NeZero\nimport Mathlib.Order.RelIso.Basic\nimport Mathlib.Data.Nat.Order.Basic\nimport Mathlib.Order.Hom.Set\nimport Std.Data.Fin.Lemmas\nimport Mathlib.Data.Fin.OrderHom\nimport Mathlib.Data.Pi.Lex\nimport Mathlib.Data.Set.Intervals.Basic\nimport Mathlib.Algebra.Star.Basic\nimport Mathlib.Algebra.Order.CauSeq.Completion\nimport Mathlib.Algebra.CharP.Basic\nimport Mathlib.RingTheory.Ideal.Operations\nimport Mathlib.Data.Fintype.Units\nimport Mathlib.Data.Nat.Parity\nimport Mathlib.Tactic.FinCases\nimport Mathlib.Logic.Function.Basic\nimport Mathlib.Util.CompileInductive\nimport Mathlib.Algebra.Algebra.Opposite\nimport Mathlib.Algebra.Algebra.Pi\nimport Mathlib.Algebra.BigOperators.Pi\nimport Mathlib.Algebra.BigOperators.Ring\nimport Mathlib.Algebra.BigOperators.RingEquiv\nimport Mathlib.Algebra.Module.LinearMap.Basic\nimport Mathlib.Algebra.Module.Pi\nimport Mathlib.Algebra.Star.BigOperators\nimport Mathlib.Algebra.Star.Module\nimport Mathlib.Algebra.Star.Pi\nimport Mathlib.Data.Fintype.BigOperators\nimport Mathlib.GroupTheory.GroupAction.BigOperators\nimport Mathlib.Init.Data.Nat.Lemmas\nimport Mathlib.Init.Function\nimport Mathlib.Data.Semiquot\nimport Mathlib.Data.Nat.Size\nimport Mathlib.Tactic.Ring.RingNF\nimport Mathlib.Data.Set.Card\nimport Mathlib.Order.Minimal\nimport Mathlib.Data.Matroid.Init\nimport Mathlib.Data.Set.List\nimport Mathlib.Data.List.Perm\nimport Mathlib.Init.Quot -- Porting note: added import\nimport Mathlib.Order.Hom.Basic\nimport Mathlib.Mathport.Rename\nimport Mathlib.Data.PFunctor.Univariate.M\nimport Mathlib.Data.PFunctor.Multivariate.Basic\nimport Mathlib.Init.Control.Combinators\nimport Mathlib.Data.Option.Defs\nimport Mathlib.Logic.IsEmpty\nimport Mathlib.Logic.Relator\nimport Mathlib.Util.CompileInductive\nimport Aesop\nimport Mathlib.Algebra.Order.Ring.WithTop\nimport Mathlib.Algebra.Order.Sub.WithTop\nimport Mathlib.Data.Real.NNReal\nimport Mathlib.Data.Set.Intervals.WithBotTop\nimport Mathlib.Data.Bool.Basic\nimport Mathlib.Data.Nat.Defs\nimport Mathlib.Data.Option.Basic\nimport Mathlib.Data.List.Defs\nimport Mathlib.Init.Data.List.Basic\nimport Mathlib.Init.Data.List.Instances\nimport Mathlib.Init.Data.List.Lemmas\nimport Mathlib.Logic.Unique\nimport Mathlib.Order.Basic\nimport Std.Data.List.Lemmas\nimport Mathlib.Tactic.Common\nimport Mathlib.Logic.Equiv.Nat\nimport Mathlib.Logic.Equiv.Fin\nimport Mathlib.Data.Countable.Defs\nimport Mathlib.Data.Multiset.Basic\nimport Mathlib.Data.Vector.Basic\nimport Mathlib.Data.Setoid.Basic\nimport Mathlib.Tactic.ApplyFun\nimport Mathlib.Init.Align\nimport Mathlib.Data.Fintype.Powerset\nimport Mathlib.Data.Fintype.Prod\nimport Mathlib.Data.Fintype.Sigma\nimport Mathlib.Data.Fintype.Sum\nimport Mathlib.Data.Fintype.Vector\nimport Mathlib.Algebra.CharZero.Lemmas\nimport Mathlib.Algebra.GroupPower.Ring\nimport Mathlib.Algebra.GroupWithZero.Bitwise\nimport Mathlib.Data.Real.Basic\nimport Mathlib.Data.Set.Image\nimport Mathlib.Algebra.Ring.Hom.Defs -- FIXME: This import is bogus\nimport Mathlib.Data.Finset.Image\nimport Mathlib.Data.Fin.OrderHom\nimport Mathlib.Algebra.Category.Ring.FilteredColimits\nimport Mathlib.Geometry.RingedSpace.SheafedSpace\nimport Mathlib.Topology.Sheaves.Stalks\nimport Mathlib.Algebra.Category.Ring.Colimits\nimport Mathlib.Algebra.Category.Ring.Limits\nimport Mathlib.Analysis.InnerProductSpace.Projection\nimport Mathlib.Geometry.Euclidean.PerpBisector\nimport Mathlib.Algebra.QuadraticDiscriminant\nimport Mathlib.Analysis.Convex.StrictConvexBetween\nimport Mathlib.Geometry.Euclidean.Basic\nimport Mathlib.Analysis.InnerProductSpace.Basic\nimport Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse\nimport Mathlib.Analysis.InnerProductSpace.TwoDim\nimport Mathlib.Geometry.Euclidean.Angle.Unoriented.Basic\nimport Mathlib.Analysis.Normed.Group.AddTorsor\nimport Mathlib.Analysis.InnerProductSpace.Basic\nimport Mathlib.Geometry.Manifold.MFDeriv.Defs\nimport Mathlib.Geometry.Manifold.ContMDiff.Defs\nimport Mathlib.Geometry.Manifold.LocalInvariantProperties\nimport Mathlib.Topology.Sheaves.LocalPredicate\nimport Mathlib.Geometry.Manifold.ContMDiff.Atlas\nimport Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear\nimport Mathlib.Topology.VectorBundle.Constructions\nimport Mathlib.Data.Seq.Seq\nimport Mathlib.Algebra.Field.Defs\nimport Mathlib.Algebra.Order.Floor\nimport Mathlib.Algebra.ContinuedFractions.Basic\nimport Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero\nimport Mathlib.Algebra.Group.Basic\nimport Mathlib.Algebra.Group.Hom.Defs\nimport Mathlib.Algebra.GroupWithZero.NeZero\nimport Mathlib.Algebra.Opposites\nimport Mathlib.Algebra.Ring.Defs\nimport Mathlib.Algebra.Divisibility.Basic\nimport Mathlib.Algebra.Group.Units.Hom\nimport Mathlib.Algebra.GroupWithZero.InjSurj\nimport Mathlib.Algebra.Ring.Hom.Defs\nimport Mathlib.Data.Set.Basic\nimport Mathlib.Algebra.Divisibility.Basic\nimport Mathlib.Algebra.Group.Equiv.Basic\nimport Mathlib.Algebra.Ring.Defs\nimport Mathlib.Algebra.Associated\nimport Mathlib.Algebra.Ring.Regular\nimport Mathlib.Tactic.Common\nimport Mathlib.Algebra.BigOperators.Multiset.Lemmas\nimport Mathlib.Algebra.BigOperators.Multiset.Order\nimport Mathlib.Algebra.Function.Indicator\nimport Mathlib.Algebra.Ring.Opposite\nimport Mathlib.Data.Finset.Powerset\nimport Mathlib.Data.Finset.Preimage\nimport Mathlib.Data.Finset.Sigma\nimport Mathlib.Data.Finset.Sum\nimport Mathlib.Data.Fintype.Pi\nimport Mathlib.Data.Int.Cast.Lemmas\nimport Mathlib.Data.Set.Image\nimport Mathlib.Algebra.BigOperators.List.Defs\nimport Mathlib.Data.List.Forall2\nimport Mathlib.Algebra.Divisibility.Basic\nimport Mathlib.Algebra.Ring.Commute\nimport Mathlib.Data.Nat.Order.Basic\nimport Mathlib.Data.Int.Basic\nimport Mathlib.Algebra.Group.Hom.Basic\nimport Mathlib.Algebra.GroupPower.Hom\nimport Mathlib.Algebra.BigOperators.List.Basic\nimport Mathlib.Data.Multiset.Basic\nimport Mathlib.Algebra.CharZero.Lemmas\nimport Mathlib.Algebra.Module.Submodule.Ker\nimport Mathlib.Algebra.Module.Submodule.RestrictScalars\nimport Mathlib.Algebra.Module.ULift\nimport Mathlib.RingTheory.Subring.Basic\nimport Mathlib.Algebra.Algebra.Basic\nimport Mathlib.Data.Set.UnionLift\nimport Mathlib.LinearAlgebra.Finsupp\nimport Mathlib.RingTheory.Ideal.Operations\nimport Mathlib.Algebra.Order.Monoid.Defs\nimport Mathlib.Algebra.Group.InjSurj\nimport Mathlib.Order.Hom.Basic\nimport Mathlib.Logic.Basic\nimport Mathlib.Tactic.Positivity.Basic\nimport Mathlib.Algebra.Order.AbsoluteValue\nimport Mathlib.Algebra.Order.Field.Basic\nimport Mathlib.Algebra.Order.Group.MinMax\nimport Mathlib.Algebra.Ring.Pi\nimport Mathlib.GroupTheory.GroupAction.Pi\nimport Mathlib.GroupTheory.GroupAction.Ring\nimport Mathlib.Init.Align\nimport Mathlib.Tactic.GCongr\nimport Mathlib.Tactic.Ring\nimport Mathlib.Algebra.Group.Equiv.Basic\nimport Mathlib.Algebra.Ring.Basic\nimport Mathlib.Algebra.Order.Sub.Defs\nimport Mathlib.Order.Hom.Basic\nimport Mathlib.Algebra.Field.Basic\nimport Mathlib.Algebra.GroupWithZero.Units.Equiv\nimport Mathlib.Algebra.Order.Field.Defs\nimport Mathlib.Algebra.Order.Ring.Abs\nimport Mathlib.Order.Bounds.OrderIso\nimport Mathlib.Tactic.Positivity.Core\nimport Mathlib.Algebra.Order.Field.Canonical.Defs\nimport Mathlib.Algebra.Field.Defs\nimport Mathlib.Algebra.GroupWithZero.Units.Lemmas\nimport Mathlib.Algebra.Ring.Commute\nimport Mathlib.Algebra.Ring.Hom.Defs\nimport Mathlib.Algebra.Invertible.GroupWithZero\nimport Mathlib.Algebra.Group.Commute.Units\nimport Mathlib.Algebra.Group.Hom.Defs\nimport Mathlib.Algebra.Group.Units\nimport Mathlib.Algebra.GroupPower.Basic\nimport Mathlib.Algebra.GroupWithZero.Units.Basic\nimport Mathlib.Algebra.Ring.Defs\nimport Mathlib.Data.Bracket\nimport Mathlib.LinearAlgebra.Basic\nimport Mathlib.Algebra.Ring.Divisibility.Lemmas\nimport Mathlib.Algebra.Lie.Nilpotent\nimport Mathlib.Algebra.Lie.Engel\nimport Mathlib.LinearAlgebra.Eigenspace.Triangularizable\nimport Mathlib.RingTheory.Artinian\nimport Mathlib.LinearAlgebra.Trace\nimport Mathlib.LinearAlgebra.FreeModule.PID\nimport Mathlib.Data.DFinsupp.Basic\nimport Mathlib.GroupTheory.Submonoid.Operations\nimport Mathlib.Algebra.GroupWithZero.Units.Lemmas\nimport Mathlib.Algebra.Ring.Equiv\nimport Mathlib.GroupTheory.GroupAction.Group\nimport Mathlib.RingTheory.UniqueFactorizationDomain\nimport Mathlib.Algebra.GroupPower.Basic\nimport Mathlib.Algebra.Group.Hom.Defs\nimport Mathlib.Algebra.BigOperators.List.Basic\nimport Mathlib.GroupTheory.GroupAction.Defs\nimport Mathlib.Algebra.Module.Basic\nimport Mathlib.Algebra.Order.Archimedean\nimport Mathlib.Algebra.Order.Group.Instances\nimport Mathlib.Data.Int.ModEq\nimport Mathlib.Data.Nat.Multiplicity\nimport Mathlib.Data.Nat.Choose.Sum\nimport Mathlib.Data.Nat.Cast.Prod\nimport Mathlib.Algebra.Group.ULift\nimport Mathlib.GroupTheory.OrderOfElement\nimport Mathlib.Algebra.Lie.OfAssociative\nimport Mathlib.Algebra.Category.MonCat.Basic\nimport Mathlib.CategoryTheory.Endomorphism\nimport Mathlib.Algebra.Category.GroupCat.Preadditive\nimport Mathlib.CategoryTheory.Conj\nimport Mathlib.CategoryTheory.Linear.Basic\nimport Mathlib.CategoryTheory.Preadditive.AdditiveFunctor\nimport Mathlib.LinearAlgebra.Basic\nimport Mathlib.Algebra.Category.ModuleCat.Basic\nimport Mathlib.LinearAlgebra.TensorProduct.Basic\nimport Mathlib.CategoryTheory.Monoidal.Linear\nimport Mathlib.Algebra.Algebra.Subalgebra.Basic\nimport Mathlib.Algebra.FreeAlgebra\nimport Mathlib.Algebra.Category.Ring.Basic\nimport Mathlib.Algebra.Category.ModuleCat.Basic\nimport Mathlib.CategoryTheory.ConcreteCategory.BundledHom\nimport Mathlib.Algebra.PUnitInstances\nimport Mathlib.CategoryTheory.Functor.ReflectsIso\nimport Mathlib.Algebra.PEmptyInstances\nimport Mathlib.Algebra.Group.Equiv.Basic\nimport Mathlib.CategoryTheory.ConcreteCategory.BundledHom\nimport Mathlib.CategoryTheory.Functor.ReflectsIso\nimport Mathlib.Algebra.Category.GroupCat.Basic\nimport Mathlib.CategoryTheory.ConcreteCategory.ReflectsIso\nimport Mathlib.Algebra.Ring.Equiv\nimport Mathlib.CategoryTheory.Monoidal.Rigid.Basic\nimport Mathlib.CategoryTheory.Monoidal.Subcategory\nimport Mathlib.LinearAlgebra.Coevaluation\nimport Mathlib.LinearAlgebra.FreeModule.Finite.Matrix\nimport Mathlib.Algebra.Category.ModuleCat.Monoidal.Closed\nimport Mathlib.Algebra.Group.Commute.Basic\nimport Mathlib.Algebra.GroupWithZero.Defs\nimport Mathlib.Data.Int.Defs\nimport Mathlib.Tactic.Common\nimport Mathlib.Algebra.GroupPower.CovariantClass\nimport Mathlib.Algebra.Order.Monoid.WithTop\nimport Mathlib.Algebra.SMulWithZero\nimport Mathlib.Order.Hom.Basic\nimport Mathlib.Data.Nat.Order.Basic\nimport Mathlib.Algebra.EuclideanDomain.Defs\nimport Mathlib.Algebra.Ring.Divisibility.Basic\nimport Mathlib.Algebra.Ring.Regular\nimport Mathlib.Algebra.GroupWithZero.Divisibility\nimport Mathlib.Algebra.Ring.Basic\nimport Mathlib.Algebra.Function.Indicator\nimport Mathlib.Algebra.SMulWithZero\nimport Mathlib.Data.Int.Basic\nimport Mathlib.Data.NNRat.Defs\nimport Mathlib.GroupTheory.GroupAction.Group\nimport Mathlib.GroupTheory.GroupAction.Pi\nimport Mathlib.Logic.Basic\nimport Mathlib.Tactic.Abel\nimport Mathlib.GroupTheory.GroupAction.SubMulAction\nimport Mathlib.GroupTheory.Submonoid.Membership\nimport Mathlib.Algebra.Module.Pi\nimport Mathlib.Algebra.Ring.CompTypeclasses\nimport Mathlib.Algebra.Star.Basic\nimport Mathlib.GroupTheory.GroupAction.DomAct.Basic\nimport Mathlib.GroupTheory.GroupAction.Hom\nimport Mathlib.Algebra.Algebra.Equiv\nimport Mathlib.Algebra.Algebra.NonUnitalHom\nimport Mathlib.Algebra.BigOperators.Finsupp\nimport Mathlib.Algebra.Module.BigOperators\nimport Mathlib.LinearAlgebra.Finsupp\nimport Mathlib.Algebra.Group.Commute.Defs\nimport Mathlib.Algebra.Group.Units\nimport Mathlib.Algebra.Order.Monoid.Lemmas\nimport Mathlib.Tactic.NthRewrite\nimport Aesop\nimport Mathlib.Algebra.Group.Defs\nimport Mathlib.Logic.Function.Basic\nimport Mathlib.Tactic.Cases\nimport Mathlib.Tactic.SimpRw\nimport Mathlib.Tactic.SplitIfs\nimport Mathlib.Algebra.Group.Semiconj.Defs\nimport Mathlib.Algebra.Group.Basic\nimport Mathlib.Algebra.Group.Basic\nimport Mathlib.Algebra.Group.Hom.Defs\nimport Mathlib.Algebra.Group.Defs\nimport Mathlib.Data.Prod.Basic\nimport Mathlib.Data.Sum.Basic\nimport Mathlib.Logic.Unique\nimport Mathlib.Tactic.Spread\nimport Mathlib.Algebra.Group.Equiv.Basic\nimport Mathlib.Algebra.Group.WithOne.Defs\nimport Mathlib.Data.Option.Basic\nimport Mathlib.Algebra.Group.Hom.Basic\nimport Mathlib.Data.FunLike.Equiv\nimport Mathlib.Logic.Equiv.Basic\nimport Mathlib.Algebra.Group.Commute.Defs\nimport Mathlib.Algebra.Group.Semiconj.Basic\nimport Mathlib.Algebra.Field.Opposite\nimport Mathlib.Algebra.Invertible.Defs\nimport Mathlib.Algebra.Ring.Aut\nimport Mathlib.Algebra.Ring.CompTypeclasses\nimport Mathlib.Algebra.Field.Opposite\nimport Mathlib.Algebra.Invertible.Defs\nimport Mathlib.Data.NNRat.Defs\nimport Mathlib.Data.Rat.Cast.Defs\nimport Mathlib.Data.SetLike.Basic\nimport Mathlib.GroupTheory.GroupAction.Opposite\nimport Mathlib.Algebra.Group.Basic\nimport Mathlib.Algebra.GroupWithZero.NeZero\nimport Mathlib.Algebra.Group.OrderSynonym\nimport Mathlib.Algebra.GroupWithZero.Basic\nimport Mathlib.Algebra.Group.Units\nimport Mathlib.Tactic.Nontriviality\nimport Mathlib.Util.AssertExists\nimport Mathlib.Tactic.Contrapose\nimport Mathlib.CategoryTheory.Category.Grpd\nimport Mathlib.CategoryTheory.Groupoid\nimport Mathlib.Topology.Category.TopCat.Basic\nimport Mathlib.Topology.Homotopy.Path\nimport Mathlib.Data.Set.Basic\nimport Mathlib.RingTheory.IntegralClosure\nimport Mathlib.FieldTheory.Normal\nimport Mathlib.FieldTheory.Perfect\nimport Mathlib.RingTheory.Localization.Integral\nimport Mathlib.FieldTheory.Separable\nimport Mathlib.RingTheory.IntegralDomain\nimport Mathlib.Algebra.CharP.Reduced\nimport Mathlib.Tactic.ApplyFun\nimport Lean\nimport Std\nimport Mathlib.Tactic.PPWithUniv\nimport Mathlib.Tactic.ExtendDoc\nimport Mathlib.Tactic.Lemma\nimport Mathlib.Tactic.TypeStar\nimport Lean.Elab.Tactic.SolveByElim\nimport Mathlib.Tactic.Monotonicity.Attr\nimport Lean.Elab.Tactic.Simp\nimport Lean.Elab.App\nimport Mathlib.Tactic.Simps.NotationClass\nimport Std.Data.String.Basic\nimport Std.Util.LibraryNote\nimport Mathlib.Lean.Expr.Basic\nimport Mathlib.Tactic.NormNum.Inv\nimport Mathlib.Tactic.NormNum.Pow\nimport Mathlib.Util.AtomM\nimport Mathlib.Data.Rat.Order\nimport Mathlib.Tactic.NormNum.Core\nimport Mathlib.Tactic.HaveI\nimport Mathlib.Data.Nat.Cast.Commute\nimport Mathlib.Data.Int.Basic\nimport Mathlib.Algebra.Invertible.Basic\nimport Mathlib.Tactic.Clear!\nimport Mathlib.Data.Nat.Cast.Basic\nimport Mathlib.Algebra.GroupPower.Order\nimport Mathlib.Data.Int.CharZero\nimport Mathlib.Data.Int.Order.Basic\nimport Mathlib.Data.Nat.Factorial.Basic\nimport Mathlib.Data.Rat.Order\nimport Mathlib.Tactic.Positivity.Core\nimport Qq\nimport Std.Data.Rat.Lemmas\nimport Mathlib.Mathport.Rename\nimport Mathlib.Mathport.Rename\nimport Std.Logic\nimport Mathlib.Mathport.Rename\nimport Mathlib.Mathport.Rename\nimport Mathlib.Init.Data.Nat.Notation\nimport Std.Data.List.Basic\nimport Mathlib.Init.ZeroOne\nimport Mathlib.Init.Data.Nat.Notation\nimport Mathlib.Util.CompileInductive\nimport Mathlib.Init.Data.Nat.Notation\nimport Mathlib.Mathport.Rename\nimport Mathlib.Mathport.Rename\nimport Std.Data.Bool\nimport Mathlib.AlgebraicGeometry.AffineScheme\nimport Mathlib.AlgebraicGeometry.Pullbacks\nimport Mathlib.CategoryTheory.MorphismProperty\nimport Mathlib.Data.List.TFAE\nimport Mathlib.LinearAlgebra.Finsupp\nimport Mathlib.RingTheory.Ideal.Over\nimport Mathlib.RingTheory.Ideal.Prod\nimport Mathlib.RingTheory.Ideal.MinimalPrime\nimport Mathlib.RingTheory.Localization.Away.Basic\nimport Mathlib.RingTheory.Nilpotent\nimport Mathlib.Topology.Sets.Closeds\nimport Mathlib.Topology.Sober\nimport Mathlib.Data.Set.Function\nimport Mathlib.Logic.Function.Iterate\nimport Mathlib.GroupTheory.Perm.Basic\nimport Mathlib.Algebra.BigOperators.Basic\nimport Mathlib.Dynamics.FixedPoints.Basic\nimport Mathlib.Algebra.Function.Support\nimport Mathlib.Order.Filter.Lift\nimport Mathlib.Topology.Defs.Filter\nimport Mathlib.Order.SetNotation\nimport Mathlib.Tactic.Continuity\nimport Mathlib.Tactic.FunProp\nimport Mathlib.Topology.Order.ProjIcc\nimport Mathlib.Topology.ContinuousFunction.Ordered\nimport Mathlib.Topology.CompactOpen\nimport Mathlib.Topology.UnitInterval\nimport Mathlib.Analysis.NormedSpace.BoundedLinearMaps\nimport Mathlib.Topology.FiberBundle.Basic\nimport Mathlib.Data.Set.Image\nimport Mathlib.Order.SuccPred.Relation\nimport Mathlib.Topology.Clopen\nimport Mathlib.Topology.Irreducible\nimport Mathlib.CategoryTheory.ConcreteCategory.BundledHom\nimport Mathlib.CategoryTheory.Elementwise\nimport Mathlib.Topology.ContinuousFunction.Basic\nimport Mathlib.Topology.Category.TopCat.Basic\nimport Mathlib.CategoryTheory.Limits.Types\nimport Mathlib.Topology.Category.CompHaus.Basic\nimport Mathlib.Topology.LocallyConstant.Basic\nimport Mathlib.CategoryTheory.FintypeCat\nimport Mathlib.Topology.Category.Profinite.Basic\nimport Mathlib.CategoryTheory.Limits.ConcreteCategory\nimport Mathlib.Topology.ExtremallyDisconnected\nimport Mathlib.Topology.Category.CompHaus.Projective\nimport Mathlib.Topology.Category.Profinite.Basic\nimport Mathlib.CategoryTheory.Adjunction.Reflective\nimport Mathlib.Topology.StoneCech\nimport Mathlib.CategoryTheory.Monad.Limits\nimport Mathlib.Topology.UrysohnsLemma\nimport Mathlib.Topology.Category.TopCat.Limits.Basic\nimport Mathlib.Data.Set.Basic\nimport Mathlib.Order.Filter.SmallSets\nimport Mathlib.Tactic.Monotonicity\nimport Mathlib.Topology.Compactness.Compact\nimport Mathlib.Topology.NhdsSet\nimport Mathlib.Algebra.Group.Defs\nimport Mathlib.Data.Set.Intervals.Pi\nimport Mathlib.Data.Set.Pointwise.Basic\nimport Mathlib.Order.Filter.Interval\nimport Mathlib.Tactic.TFAE\nimport Mathlib.Tactic.NormNum\nimport Mathlib.Topology.Order.LeftRight\nimport Mathlib.Topology.Order.OrderClosed\nimport Mathlib.Order.Hom.Basic\nimport Mathlib.Topology.ContinuousFunction.Basic\nimport Mathlib.Topology.Algebra.Ring.Basic\nimport Mathlib.Topology.Algebra.MulAction\nimport Mathlib.Topology.Algebra.UniformGroup\nimport Mathlib.Topology.ContinuousFunction.Basic\nimport Mathlib.Topology.UniformSpace.UniformEmbedding\nimport Mathlib.Algebra.Algebra.Basic\nimport Mathlib.LinearAlgebra.Projection\nimport Mathlib.LinearAlgebra.Pi\nimport Mathlib.LinearAlgebra.Finsupp\nimport Mathlib.Topology.Algebra.Module.Basic\nimport Mathlib.LinearAlgebra.Multilinear.Basic\nimport Mathlib.LinearAlgebra.Alternating.Basic\nimport Mathlib.LinearAlgebra.BilinearMap\nimport Mathlib.Topology.Algebra.Module.Multilinear.Basic\nimport Mathlib.GroupTheory.Subgroup.Basic\nimport Mathlib.Topology.Algebra.OpenSubgroup\nimport Mathlib.Topology.Algebra.Ring.Basic\nimport Mathlib.Algebra.Ring.Prod\nimport Mathlib.RingTheory.Subring.Basic\nimport Mathlib.Topology.Algebra.Group.Basic\nimport Mathlib.Topology.Algebra.InfiniteSum.Defs\nimport Mathlib.Data.Fintype.BigOperators\nimport Mathlib.Topology.Algebra.Monoid\nimport Mathlib.GroupTheory.GroupAction.ConjAct\nimport Mathlib.GroupTheory.GroupAction.Quotient\nimport Mathlib.GroupTheory.QuotientGroup\nimport Mathlib.Topology.Algebra.Monoid\nimport Mathlib.Topology.Algebra.Constructions\nimport Mathlib.Data.Nat.Interval\nimport Mathlib.Data.ENNReal.Real\nimport Mathlib.Topology.UniformSpace.Pi\nimport Mathlib.Topology.UniformSpace.UniformConvergence\nimport Mathlib.Topology.UniformSpace.UniformEmbedding\nimport Mathlib.Algebra.Function.Indicator\nimport Mathlib.Tactic.FinCases\nimport Mathlib.Topology.Sets.Closeds\nimport Mathlib.Order.Filter.Cofinite\nimport Mathlib.Topology.MetricSpace.ProperSpace\nimport Mathlib.Topology.MetricSpace.Basic\nimport Mathlib.Topology.FiberBundle.Trivialization\nimport Mathlib.Data.Set.UnionLift\nimport Mathlib.Topology.Homeomorph\nimport Mathlib.Algebra.GeomSum\nimport Mathlib.RingTheory.Ideal.Quotient\nimport Mathlib.Algebra.Associated\nimport Mathlib.RingTheory.Int.Basic\nimport Mathlib.Tactic.Ring\nimport Mathlib.Algebra.Star.Unitary\nimport Mathlib.Algebra.DirectSum.Algebra\nimport Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty\nimport Mathlib.Analysis.Complex.UpperHalfPlane.Manifold\nimport Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions\nimport Mathlib.NumberTheory.ModularForms.SlashInvariantForms\nimport Mathlib.NumberTheory.ModularForms.SlashInvariantForms\nimport Mathlib.NumberTheory.ModularForms.CongruenceSubgroups\nimport Mathlib.Data.Int.Parity\nimport Mathlib.RingTheory.DedekindDomain.IntegralClosure\nimport Mathlib.Algebra.GCDMonoid.Finset\nimport Mathlib.Algebra.GroupPower.Ring\nimport Mathlib.Data.Nat.Parity\nimport Mathlib.Data.Rat.Defs\nimport Mathlib.Tactic.Positivity.Basic\nimport Mathlib.Tactic.TFAE\nimport Mathlib.Analysis.PSeries\nimport Mathlib.NumberTheory.ArithmeticFunction\nimport Mathlib.Analysis.NormedSpace.FiniteDimension\nimport Mathlib.Init.Core\nimport Mathlib.RingTheory.Polynomial.Cyclotomic.Roots\nimport Mathlib.NumberTheory.NumberField.Basic\nimport Mathlib.FieldTheory.Galois\nimport Mathlib.Analysis.Calculus.MeanValue\nimport Mathlib.Analysis.Calculus.Deriv.Polynomial\nimport Mathlib.Data.Polynomial.DenomsClearable\nimport Mathlib.Data.Real.Irrational\nimport Mathlib.Topology.Algebra.Polynomial\nimport Mathlib.NumberTheory.LegendreSymbol.QuadraticChar.Basic\nimport Mathlib.Data.Fintype.Parity\nimport Mathlib.NumberTheory.LegendreSymbol.ZModChar\nimport Mathlib.FieldTheory.Finite.Basic\nimport Mathlib.Algebra.Periodic\nimport Mathlib.Data.ZMod.Units\nimport Mathlib.NumberTheory.LegendreSymbol.MulCharacter\nimport Mathlib.Analysis.Normed.Field.InfiniteSum\nimport Mathlib.Analysis.SpecificLimits.Normed\nimport Mathlib.NumberTheory.ArithmeticFunction\nimport Mathlib.NumberTheory.SmoothNumbers\nimport Lean.Meta.Tactic.Rewrite\nimport Std.Lean.Expr\nimport Std.Lean.Name\nimport Std.Data.Rat.Basic\nimport Std.Data.List.Basic\nimport Std.Lean.Name\nimport Std.Logic\nimport Mathlib.Lean.Meta\nimport Lean.Meta.AppBuilder\nimport Lean.Meta.Basic\nimport Mathlib.Data.Opposite\nimport Mathlib.Tactic.Cases\nimport Mathlib.Combinatorics.SimpleGraph.Init\nimport Mathlib.Data.Rel\nimport Mathlib.Data.Set.Finite\nimport Mathlib.Data.Sym.Sym2\nimport Mathlib.Algebra.GroupPower.Order\nimport Mathlib.Combinatorics.SimpleGraph.Clique\nimport Mathlib.Data.Finset.Sym\nimport Mathlib.Tactic.GCongr\nimport Mathlib.Tactic.Positivity\nimport Mathlib.Dynamics.FixedPoints.Basic\nimport Mathlib.GroupTheory.Perm.Option\nimport Mathlib.Logic.Equiv.Defs\nimport Mathlib.Logic.Equiv.Option\nimport Mathlib.Combinatorics.Hall.Finite\nimport Mathlib.CategoryTheory.CofilteredSystem\nimport Mathlib.Data.Rel"
}