[Merged by Bors] - chore: tidy results around Module.Finite

[eric-wieser]

In particular this replaces many chains of Module.finite_def and Submodule.fg_top with Module.Finite.iff_fg, or aliases for the forward and reverse implications.

This also golfs some FiniteDimensional results in terms of their Finite counterparts, and adds Submodule.fg_range as a shorthand for a common case of Submodule.fg_map.

---

[github-actions]

PR summary 25f07b41e7

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.LinearAlgebra.FiniteDimensional.Basic	1074	1075	+1 (+0.09%)
Mathlib.RingTheory.IntegralClosure.Algebra.Basic	1285	1286	+1 (+0.08%)
Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral	1293	1294	+1 (+0.08%)
Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic	1317	1318	+1 (+0.08%)
Mathlib.RingTheory.LinearDisjoint	1413	1414	+1 (+0.07%)
Mathlib.RingTheory.HopkinsLevitzki	1551	1552	+1 (+0.06%)
Mathlib.RingTheory.LocalRing.Module	1759	1760	+1 (+0.06%)
Mathlib.Analysis.Normed.Module.FiniteDimension	1866	1867	+1 (+0.05%)
Mathlib.RingTheory.Smooth.Local	1871	1872	+1 (+0.05%)
Mathlib.Algebra.Module.ZLattice.Basic	2150	2151	+1 (+0.05%)

Import changes for all files

Files

Import difference

1289 files Mathlib.Algebra.Algebra.Subalgebra.IsSimpleOrder Mathlib.Algebra.Category.FGModuleCat.Abelian Mathlib.Algebra.Category.FGModuleCat.Basic Mathlib.Algebra.Category.FGModuleCat.Colimits Mathlib.Algebra.Category.FGModuleCat.EssentiallySmall Mathlib.Algebra.Category.FGModuleCat.Limits Mathlib.Algebra.Category.ModuleCat.ExteriorPower Mathlib.Algebra.Category.ModuleCat.Simple Mathlib.Algebra.Category.Ring.Under.Limits Mathlib.Algebra.DirectSum.LinearMap Mathlib.Algebra.GCDMonoid.IntegrallyClosed Mathlib.Algebra.Lie.CartanExists Mathlib.Algebra.Lie.CartanSubalgebra Mathlib.Algebra.Lie.Classical Mathlib.Algebra.Lie.Derivation.Killing Mathlib.Algebra.Lie.EngelSubalgebra Mathlib.Algebra.Lie.Engel Mathlib.Algebra.Lie.InvariantForm Mathlib.Algebra.Lie.Killing Mathlib.Algebra.Lie.LieTheorem Mathlib.Algebra.Lie.Matrix Mathlib.Algebra.Lie.Nilpotent Mathlib.Algebra.Lie.Rank Mathlib.Algebra.Lie.Semisimple.Lemmas Mathlib.Algebra.Lie.SkewAdjoint Mathlib.Algebra.Lie.Sl2 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Mathlib.RepresentationTheory.Homological.GroupCohomology.FiniteCyclic Mathlib.RepresentationTheory.Homological.GroupCohomology.Functoriality Mathlib.RepresentationTheory.Homological.GroupCohomology.Hilbert90 Mathlib.RepresentationTheory.Homological.GroupCohomology.LongExactSequence Mathlib.RepresentationTheory.Homological.GroupCohomology.LowDegree Mathlib.RepresentationTheory.Homological.GroupCohomology.Shapiro Mathlib.RepresentationTheory.Homological.GroupHomology.Basic Mathlib.RepresentationTheory.Homological.GroupHomology.FiniteCyclic Mathlib.RepresentationTheory.Homological.GroupHomology.Functoriality Mathlib.RepresentationTheory.Homological.GroupHomology.LongExactSequence Mathlib.RepresentationTheory.Homological.GroupHomology.LowDegree Mathlib.RepresentationTheory.Homological.GroupHomology.Shapiro Mathlib.RepresentationTheory.Homological.Resolution Mathlib.RepresentationTheory.Induced Mathlib.RepresentationTheory.Invariants Mathlib.RepresentationTheory.Rep 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Mathlib.RingTheory.DedekindDomain.Ideal.Lemmas Mathlib.RingTheory.DedekindDomain.Instances Mathlib.RingTheory.DedekindDomain.IntegralClosure Mathlib.RingTheory.DedekindDomain.LinearDisjoint Mathlib.RingTheory.DedekindDomain.PID Mathlib.RingTheory.DedekindDomain.SInteger Mathlib.RingTheory.DedekindDomain.SelmerGroup Mathlib.RingTheory.Derivation.MapCoeffs Mathlib.RingTheory.DiscreteValuationRing.TFAE Mathlib.RingTheory.Discriminant Mathlib.RingTheory.Etale.Basic Mathlib.RingTheory.Etale.Field Mathlib.RingTheory.Etale.Kaehler Mathlib.RingTheory.Etale.Locus Mathlib.RingTheory.Etale.Pi Mathlib.RingTheory.Etale.StandardEtale Mathlib.RingTheory.Extension.Cotangent.Basis Mathlib.RingTheory.Extension.Cotangent.Free Mathlib.RingTheory.Extension.Cotangent.LocalizationAway Mathlib.RingTheory.Extension.Presentation.Submersive Mathlib.RingTheory.Finiteness.ModuleFinitePresentation Mathlib.RingTheory.Flat.FaithfullyFlat.Descent Mathlib.RingTheory.Flat.TorsionFree Mathlib.RingTheory.FractionalIdeal.Extended Mathlib.RingTheory.FractionalIdeal.Norm Mathlib.RingTheory.Frobenius Mathlib.RingTheory.Grassmannian Mathlib.RingTheory.HopkinsLevitzki Mathlib.RingTheory.Ideal.GoingDown Mathlib.RingTheory.Ideal.GoingUp Mathlib.RingTheory.Ideal.Height Mathlib.RingTheory.Ideal.Int Mathlib.RingTheory.Ideal.KrullsHeightTheorem Mathlib.RingTheory.Ideal.Norm.AbsNorm Mathlib.RingTheory.Ideal.Norm.RelNorm Mathlib.RingTheory.IntegralClosure.Algebra.Basic Mathlib.RingTheory.IntegralClosure.Algebra.Ideal Mathlib.RingTheory.IntegralClosure.GoingDown Mathlib.RingTheory.IntegralClosure.IntegralRestrict Mathlib.RingTheory.IntegralClosure.IntegrallyClosed Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic Mathlib.RingTheory.Invariant.Basic Mathlib.RingTheory.Invariant.Profinite Mathlib.RingTheory.IsAdjoinRoot Mathlib.RingTheory.Jacobson.Artinian Mathlib.RingTheory.Jacobson.Ring Mathlib.RingTheory.KrullDimension.LocalRing Mathlib.RingTheory.KrullDimension.Module Mathlib.RingTheory.KrullDimension.PID Mathlib.RingTheory.KrullDimension.Polynomial Mathlib.RingTheory.KrullDimension.Regular Mathlib.RingTheory.KrullDimension.Zero Mathlib.RingTheory.LaurentSeries Mathlib.RingTheory.LinearDisjoint Mathlib.RingTheory.LittleWedderburn Mathlib.RingTheory.LocalProperties.IntegrallyClosed Mathlib.RingTheory.LocalProperties.Semilocal Mathlib.RingTheory.LocalRing.Module Mathlib.RingTheory.LocalRing.ResidueField.Fiber Mathlib.RingTheory.LocalRing.ResidueField.Instances Mathlib.RingTheory.LocalRing.ResidueField.Polynomial Mathlib.RingTheory.Localization.AtPrime.Extension Mathlib.RingTheory.Localization.Away.AdjoinRoot Mathlib.RingTheory.Localization.Integral Mathlib.RingTheory.Localization.NormTrace Mathlib.RingTheory.Localization.Pi Mathlib.RingTheory.Nilpotent.GeometricallyReduced Mathlib.RingTheory.NoetherNormalization Mathlib.RingTheory.Norm.Basic 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Mathlib.RingTheory.Polynomial.UniversalFactorizationRing Mathlib.RingTheory.PowerBasis Mathlib.RingTheory.Regular.Depth Mathlib.RingTheory.RingHom.Etale Mathlib.RingTheory.RingHom.FaithfullyFlat Mathlib.RingTheory.RingHom.FinitePresentation Mathlib.RingTheory.RingHom.Flat Mathlib.RingTheory.RingHom.Integral Mathlib.RingTheory.RingHom.Smooth Mathlib.RingTheory.RingHom.StandardSmooth Mathlib.RingTheory.RingHom.Unramified Mathlib.RingTheory.RootsOfUnity.AlgebraicallyClosed Mathlib.RingTheory.RootsOfUnity.Lemmas Mathlib.RingTheory.RootsOfUnity.Minpoly Mathlib.RingTheory.SimpleModule.IsAlgClosed Mathlib.RingTheory.SimpleModule.Rank Mathlib.RingTheory.Smooth.AdicCompletion Mathlib.RingTheory.Smooth.Basic Mathlib.RingTheory.Smooth.Flat Mathlib.RingTheory.Smooth.Local Mathlib.RingTheory.Smooth.Locus Mathlib.RingTheory.Smooth.NoetherianDescent Mathlib.RingTheory.Smooth.Pi Mathlib.RingTheory.Smooth.StandardSmoothCotangent Mathlib.RingTheory.Smooth.StandardSmoothOfFree Mathlib.RingTheory.Smooth.StandardSmooth Mathlib.RingTheory.Spectrum.Maximal.Topology Mathlib.RingTheory.Spectrum.Prime.ChevalleyComplexity Mathlib.RingTheory.Spectrum.Prime.Chevalley Mathlib.RingTheory.Spectrum.Prime.ConstructibleSet Mathlib.RingTheory.Spectrum.Prime.FreeLocus Mathlib.RingTheory.Spectrum.Prime.Homeomorph Mathlib.RingTheory.Spectrum.Prime.IsOpenComapC Mathlib.RingTheory.Spectrum.Prime.Jacobson Mathlib.RingTheory.Spectrum.Prime.LTSeries Mathlib.RingTheory.Spectrum.Prime.Module Mathlib.RingTheory.Spectrum.Prime.Noetherian Mathlib.RingTheory.Spectrum.Prime.Polynomial Mathlib.RingTheory.Spectrum.Prime.TensorProduct Mathlib.RingTheory.Spectrum.Prime.Topology Mathlib.RingTheory.TensorProduct.IsBaseChangeHom Mathlib.RingTheory.Trace.Basic Mathlib.RingTheory.Trace.Defs Mathlib.RingTheory.Trace.Quotient Mathlib.RingTheory.Unramified.Basic Mathlib.RingTheory.Unramified.Field Mathlib.RingTheory.Unramified.Finite Mathlib.RingTheory.Unramified.LocalRing Mathlib.RingTheory.Unramified.Locus Mathlib.RingTheory.Unramified.Pi Mathlib.RingTheory.Valuation.AlgebraInstances Mathlib.RingTheory.Valuation.Discrete.Basic Mathlib.RingTheory.Valuation.Integral Mathlib.RingTheory.Valuation.IntegrallyClosed Mathlib.RingTheory.Valuation.LocalSubring Mathlib.RingTheory.Valuation.Minpoly Mathlib.RingTheory.WittVector.Basic Mathlib.RingTheory.WittVector.Compare Mathlib.RingTheory.WittVector.Complete Mathlib.RingTheory.WittVector.Defs Mathlib.RingTheory.WittVector.DiscreteValuationRing Mathlib.RingTheory.WittVector.Domain Mathlib.RingTheory.WittVector.FrobeniusFractionField Mathlib.RingTheory.WittVector.Frobenius Mathlib.RingTheory.WittVector.Identities Mathlib.RingTheory.WittVector.InitTail Mathlib.RingTheory.WittVector.IsPoly Mathlib.RingTheory.WittVector.Isocrystal Mathlib.RingTheory.WittVector.MulCoeff Mathlib.RingTheory.WittVector.MulP Mathlib.RingTheory.WittVector.StructurePolynomial Mathlib.RingTheory.WittVector.TeichmullerSeries Mathlib.RingTheory.WittVector.Teichmuller Mathlib.RingTheory.WittVector.Truncated Mathlib.RingTheory.WittVector.Verschiebung Mathlib.RingTheory.ZMod.Torsion Mathlib.RingTheory.ZMod.UnitsCyclic Mathlib.Topology.Algebra.AsymptoticCone Mathlib.Topology.Algebra.Module.Determinant Mathlib.Topology.Algebra.Module.FiniteDimension Mathlib.Topology.Algebra.Ring.Compact Mathlib.Topology.Algebra.Valued.WithVal Mathlib.Topology.CWComplex.Abstract.Basic Mathlib.Topology.Category.TopCat.Sphere Mathlib.Topology.Compactification.OnePoint.ProjectiveLine Mathlib.Topology.Compactification.OnePoint.Sphere Mathlib.Topology.Instances.Complex Mathlib.Topology.Instances.Matrix Mathlib.Topology.MetricSpace.HausdorffDimension

1

---

Declarations diff

+ _root_.Submodule.FG.of_finite
+ fg_map_iff
+ fg_range
+ of_fg

You can run this locally as follows

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

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/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).

[Ruben-VandeVelde]

lgtm, thanks

maintainer delegate

[Ruben-VandeVelde]

Suggested change

	have : FiniteDimensional R (adjoin R {x}) := Module.Finite.iff_fg.2 int.fg_adjoin_singleton
	have : FiniteDimensional R (adjoin R {x}) := Module.Finite.iff_fg.mpr int.fg_adjoin_singleton

[github-actions]

🚀 Pull request has been placed on the maintainer queue by Ruben-VandeVelde.

[jcommelin]

Thanks 🎉

bors d+

[mathlib-bors]

✌️ eric-wieser can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[leanprover-community-mathlib4-bot]

As this PR is labelled auto-merge-after-CI, we are now sending it to bors:

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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• Build
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