refactor(Analysis/Asymptotics): split long file Defs.lean

[loefflerd]

Split this > 1500 line file into:

• a bare-minimum Defs.lean (204 lines)
• Basic.lean: congruence & filter operations (the longest chunk, 534 lines)
• Arith.lean: interaction with +, -, constants (465)
• Ring.lean: interaction with *, / (261)
• Prod.lean: cartesian products (171)

Also move the definition of IsEquivalent from Defs.lean into AsymptoticEquivalent.lean, since it is much less used in the library than IsBigO and IsLittleO.

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AI disclosure: An AI agent did much of the grunt work; I (a human being) devised the split and instructed the agent which lemmas to put where, proof-read the output, spruced up the autogenerated file-level docstrings, and made careful verification checks.

[github-actions]

PR summary e7981895f8

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Computability.AkraBazzi.GrowsPolynomially	1815	1820	+5 (+0.28%)

Import changes for all files

Files	Import difference
Mathlib.Analysis.Normed.Operator.Asymptotics	1
67 files Mathlib.Analysis.Analytic.Basic Mathlib.Analysis.Analytic.CPolynomialDef Mathlib.Analysis.Analytic.CPolynomial Mathlib.Analysis.Analytic.ChangeOrigin Mathlib.Analysis.Analytic.Composition Mathlib.Analysis.Analytic.Constructions Mathlib.Analysis.Analytic.ConvergenceRadius Mathlib.Analysis.Analytic.Inverse Mathlib.Analysis.Analytic.Linear Mathlib.Analysis.Analytic.OfScalars Mathlib.Analysis.Analytic.Polynomial Mathlib.Analysis.Analytic.Uniqueness Mathlib.Analysis.Analytic.Within Mathlib.Analysis.Asymptotics.Lemmas Mathlib.Analysis.Asymptotics.SuperpolynomialDecay Mathlib.Analysis.CStarAlgebra.Exponential Mathlib.Analysis.Calculus.TangentCone.Seq Mathlib.Analysis.Complex.AbelLimit Mathlib.Analysis.Complex.UpperHalfPlane.FunctionsBoundedAtInfty Mathlib.Analysis.Convex.AmpleSet Mathlib.Analysis.Convex.Approximation Mathlib.Analysis.Convex.Cone.Dual Mathlib.Analysis.Convex.Cone.TensorProduct Mathlib.Analysis.Convex.KreinMilman Mathlib.Analysis.LocallyConvex.ContinuousOfBounded Mathlib.Analysis.LocallyConvex.HahnBanach Mathlib.Analysis.LocallyConvex.SeparatingDual Mathlib.Analysis.LocallyConvex.Separation Mathlib.Analysis.LocallyConvex.WeakOperatorTopology Mathlib.Analysis.LocallyConvex.WeakSpace Mathlib.Analysis.Normed.Algebra.Exponential Mathlib.Analysis.Normed.Group.ControlledClosure Mathlib.Analysis.Normed.Module.Connected Mathlib.Analysis.Normed.Module.ContinuousInverse Mathlib.Analysis.Normed.Module.HahnBanach Mathlib.Analysis.Normed.Operator.Compact.FiniteDimension Mathlib.Analysis.Normed.Operator.CompleteCodomain Mathlib.Analysis.Normed.Operator.Fredholm.Basic Mathlib.Analysis.Normed.Operator.Perturbation.StrictByFinite Mathlib.Analysis.Normed.Ring.Units Mathlib.Analysis.RCLike.ContinuousMap Mathlib.Analysis.Real.OfDigits Mathlib.Analysis.SpecialFunctions.OrdinaryHypergeometric Mathlib.Analysis.SpecificLimits.Fibonacci Mathlib.Analysis.SpecificLimits.Normed Mathlib.InformationTheory.Coding.KraftMcMillan Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap Mathlib.MeasureTheory.VectorMeasure.Variation.Semivariation Mathlib.NumberTheory.EulerProduct.Basic Mathlib.NumberTheory.ModularForms.BoundedAtCusp Mathlib.NumberTheory.Modular Mathlib.NumberTheory.Padics.AddChar Mathlib.NumberTheory.TsumDivisorsAntidiagonal Mathlib.Order.Filter.ZeroAndBoundedAtFilter Mathlib.Probability.Independence.Process.HasIndepIncrements.Basic Mathlib.Probability.Independence.Process.HasIndepIncrements Mathlib.Tactic.ComputeAsymptotics.Lemmas Mathlib.Topology.Algebra.Module.Cardinality Mathlib.Topology.Algebra.Module.EmbeddingOfLocal Mathlib.Topology.Algebra.Module.FiniteDimensionBilinear Mathlib.Topology.Algebra.Module.FiniteDimension Mathlib.Topology.Algebra.Module.PerfectSpace Mathlib.Topology.Algebra.Module.TopDualPairing Mathlib.Topology.ContinuousMap.Ideals Mathlib.Topology.ContinuousMap.Units Mathlib.Topology.Instances.CantorSet Mathlib.Topology.MetricSpace.HausdorffAlexandroff	3
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Mathlib.Probability.Kernel.Composition.RadonNikodym Mathlib.Probability.Kernel.CondDistrib Mathlib.Probability.Kernel.Condexp Mathlib.Probability.Kernel.Disintegration.CDFToKernel Mathlib.Probability.Kernel.Disintegration.CondCDF Mathlib.Probability.Kernel.Disintegration.Density Mathlib.Probability.Kernel.Disintegration.Integral Mathlib.Probability.Kernel.Disintegration.StandardBorel Mathlib.Probability.Kernel.Disintegration.Unique Mathlib.Probability.Kernel.Integral Mathlib.Probability.Kernel.IonescuTulcea.Traj Mathlib.Probability.Kernel.MeasurableIntegral Mathlib.Probability.Kernel.Posterior Mathlib.Probability.Kernel.RadonNikodym Mathlib.Probability.Kernel.Representation Mathlib.Probability.Kernel.SetIntegral Mathlib.Probability.Kernel.WithDensity Mathlib.Probability.Martingale.Basic Mathlib.Probability.Martingale.BorelCantelli Mathlib.Probability.Martingale.Centering Mathlib.Probability.Martingale.Convergence Mathlib.Probability.Martingale.OptionalSampling Mathlib.Probability.Martingale.OptionalStopping Mathlib.Probability.Martingale.Upcrossing Mathlib.Probability.Moments.Basic Mathlib.Probability.Moments.ComplexMGF Mathlib.Probability.Moments.CovarianceBilinDual Mathlib.Probability.Moments.CovarianceBilin Mathlib.Probability.Moments.Covariance Mathlib.Probability.Moments.IntegrableExpMul Mathlib.Probability.Moments.MGFAnalytic Mathlib.Probability.Moments.SubGaussian Mathlib.Probability.Moments.Tilted Mathlib.Probability.Moments.Variance Mathlib.Probability.Notation Mathlib.Probability.ProbabilityMassFunction.Binomial Mathlib.Probability.ProbabilityMassFunction.Constructions Mathlib.Probability.ProbabilityMassFunction.Integrals Mathlib.Probability.Process.Adapted Mathlib.Probability.Process.Filtration Mathlib.Probability.Process.FiniteDimensionalLaws Mathlib.Probability.Process.HittingTime Mathlib.Probability.Process.Kolmogorov Mathlib.Probability.Process.LocalProperty Mathlib.Probability.Process.PartitionFiltration Mathlib.Probability.Process.Predictable Mathlib.Probability.Process.Stopping Mathlib.Probability.ProductMeasure Mathlib.Probability.StrongLaw Mathlib.RingTheory.LittleWedderburn Mathlib.RingTheory.Perfection Mathlib.RingTheory.Perfectoid.BDeRham Mathlib.RingTheory.Perfectoid.FontaineTheta Mathlib.RingTheory.Perfectoid.Untilt Mathlib.RingTheory.Polynomial.Cyclotomic.Basic Mathlib.RingTheory.Polynomial.Cyclotomic.Eval Mathlib.RingTheory.Polynomial.Cyclotomic.Expand Mathlib.RingTheory.Polynomial.Cyclotomic.Factorization Mathlib.RingTheory.Polynomial.Cyclotomic.Roots Mathlib.RingTheory.Polynomial.Eisenstein.IsIntegral Mathlib.RingTheory.Polynomial.Hermite.Gaussian Mathlib.RingTheory.Polynomial.Selmer Mathlib.RingTheory.RootsOfUnity.AlgebraicallyClosed Mathlib.RingTheory.RootsOfUnity.Complex Mathlib.RingTheory.Teichmuller Mathlib.RingTheory.Valuation.Discrete.RankOne Mathlib.RingTheory.Valuation.DiscreteValuativeRel Mathlib.RingTheory.Valuation.RankOne Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basic Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basis Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs Mathlib.Tactic.ComputeAsymptotics.Multiseries.Majorized Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic Mathlib.Tactic.ComputeAsymptotics.Multiseries.Trimming Mathlib.Tactic.NormNum.Irrational Mathlib.Tactic.NormNum.LegendreSymbol Mathlib.Tactic Mathlib.Topology.Algebra.InfiniteSum.TsumUniformlyOn Mathlib.Topology.Algebra.PontryaginDual Mathlib.Topology.Algebra.Valued.LocallyCompact Mathlib.Topology.Algebra.Valued.NormedValued Mathlib.Topology.CWComplex.Abstract.Basic Mathlib.Topology.Category.TopCat.Sphere Mathlib.Topology.Compactification.OnePoint.Sphere Mathlib.Topology.EMetricSpace.PairReduction Mathlib.Topology.MetricSpace.GromovHausdorff Mathlib.Topology.MetricSpace.HausdorffDimension Mathlib.Topology.MetricSpace.HolderNorm Mathlib.Topology.MetricSpace.Holder Mathlib.Topology.MetricSpace.Kuratowski Mathlib.Topology.MetricSpace.Snowflaking Mathlib.Topology.VectorBundle.Basic Mathlib.Topology.VectorBundle.Constructions Mathlib.Topology.VectorBundle.ContinuousAlternatingMap Mathlib.Topology.VectorBundle.FiniteDimensional Mathlib.Topology.VectorBundle.Hom Mathlib.Topology.VectorBundle.Riemannian	4
Mathlib.Computability.AkraBazzi.GrowsPolynomially	5
Mathlib.Analysis.Asymptotics.Basic (new file)	1298
Mathlib.Analysis.Asymptotics.Arith (new file) Mathlib.Analysis.Asymptotics.Prod (new file)	1299
Mathlib.Analysis.Asymptotics.Ring (new file)	1300

---

Declarations diff (regex)

No declarations were harmed in the making of this PR! 🐙

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit e798189).

• +0 new declarations
• −0 removed declarations

No declaration differences.

---

No changes to strong technical debt.

Decrease in weak tech debt: (relative, absolute) = (1.00, 0.25)

Current number	Change	Type (weak)
4946	4	exposed public sections
4	-1	large files

Current commit e7981895f8
Reference commit 364b383469

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).