feat(RingTheory/Localization/FractionRing): add IsFractionRing.fixingSubgroup_range_algebraMap

[xroblot]

Adds IsFractionRing.fixingSubgroup_range_algebraMap: if K and L are the fraction fields of A and B with A ⊆ B, then for G acting on B and on L, the fixing subgroup of (the image of) A in B equals the fixing subgroup of K in L.

This lemma was split out of #38864, and is used here to golf the proof of IsGaloisGroup.fixingSubgroup_range_algebraMap.

[github-actions]

PR summary 8749089eb3

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.RingTheory.Localization.FractionRing	941	947	+6 (+0.64%)

Import changes for all files

Files	Import difference
Mathlib.RingTheory.Polynomial.Morse	1
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Mathlib.RingTheory.IntegralClosure.IntegrallyClosed Mathlib.RingTheory.IntegralClosure.IsIntegral.AlmostIntegral Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic Mathlib.RingTheory.IntegralDomain Mathlib.RingTheory.IsAdjoinRoot Mathlib.RingTheory.Jacobson.Artinian Mathlib.RingTheory.Jacobson.Ring Mathlib.RingTheory.Kaehler.JacobiZariski Mathlib.RingTheory.Kaehler.TensorProduct Mathlib.RingTheory.KrullDimension.LocalRing Mathlib.RingTheory.KrullDimension.Module Mathlib.RingTheory.KrullDimension.NonZeroDivisors Mathlib.RingTheory.KrullDimension.PID Mathlib.RingTheory.KrullDimension.Polynomial Mathlib.RingTheory.KrullDimension.Regular Mathlib.RingTheory.KrullDimension.Zero Mathlib.RingTheory.LinearDisjoint Mathlib.RingTheory.LocalIso Mathlib.RingTheory.LocalProperties.Basic Mathlib.RingTheory.LocalProperties.InjectiveDimension Mathlib.RingTheory.LocalProperties.Injective Mathlib.RingTheory.LocalProperties.IntegrallyClosed Mathlib.RingTheory.LocalProperties.ProjectiveDimension Mathlib.RingTheory.LocalProperties.Reduced Mathlib.RingTheory.LocalProperties.Semilocal Mathlib.RingTheory.LocalRing.Length Mathlib.RingTheory.LocalRing.Module Mathlib.RingTheory.LocalRing.ResidueField.Fiber Mathlib.RingTheory.LocalRing.ResidueField.Ideal Mathlib.RingTheory.LocalRing.ResidueField.Instances Mathlib.RingTheory.Localization.AtPrime.Extension Mathlib.RingTheory.Localization.Away.AdjoinRoot Mathlib.RingTheory.Localization.Integral Mathlib.RingTheory.Localization.Pi Mathlib.RingTheory.MvPowerSeries.Equiv Mathlib.RingTheory.MvPowerSeries.Expand Mathlib.RingTheory.Nilpotent.GeometricallyReduced Mathlib.RingTheory.NoetherNormalization Mathlib.RingTheory.Norm.Basic Mathlib.RingTheory.Norm.Defs Mathlib.RingTheory.NormTrace Mathlib.RingTheory.Nullstellensatz Mathlib.RingTheory.OrderOfVanishing.Basic Mathlib.RingTheory.Perfection Mathlib.RingTheory.Perfectoid.BDeRham Mathlib.RingTheory.Perfectoid.FontaineTheta Mathlib.RingTheory.Perfectoid.Untilt Mathlib.RingTheory.PicardGroup Mathlib.RingTheory.Polynomial.DegreeLT Mathlib.RingTheory.Polynomial.Dickson Mathlib.RingTheory.Polynomial.GaussLemma Mathlib.RingTheory.Polynomial.IsIntegral Mathlib.RingTheory.Polynomial.RationalRoot Mathlib.RingTheory.Polynomial.Resultant.Basic Mathlib.RingTheory.Polynomial.SeparableDegree Mathlib.RingTheory.Polynomial.UniversalFactorizationRing Mathlib.RingTheory.PowerBasis Mathlib.RingTheory.PowerSeries.Derivative Mathlib.RingTheory.PowerSeries.Exp Mathlib.RingTheory.PowerSeries.Expand Mathlib.RingTheory.PowerSeries.Ideal Mathlib.RingTheory.PowerSeries.Inverse Mathlib.RingTheory.PowerSeries.Log Mathlib.RingTheory.PowerSeries.WeierstrassPreparation Mathlib.RingTheory.QuasiFinite.Basic Mathlib.RingTheory.QuasiFinite.Weakly Mathlib.RingTheory.RamificationInertia.Inertia Mathlib.RingTheory.Regular.Depth Mathlib.RingTheory.Regular.Flat Mathlib.RingTheory.Regular.Free Mathlib.RingTheory.Regular.LinearMap Mathlib.RingTheory.Regular.ProjectiveDimension Mathlib.RingTheory.RegularLocalRing.Defs Mathlib.RingTheory.RingHom.Bijective Mathlib.RingTheory.RingHom.EssFiniteType Mathlib.RingTheory.RingHom.FaithfullyFlat Mathlib.RingTheory.RingHom.FinitePresentation Mathlib.RingTheory.RingHom.FiniteType Mathlib.RingTheory.RingHom.Finite Mathlib.RingTheory.RingHom.Flat Mathlib.RingTheory.RingHom.Injective Mathlib.RingTheory.RingHom.Integral Mathlib.RingTheory.RingHom.Locally Mathlib.RingTheory.RingHom.OpenImmersion Mathlib.RingTheory.RingHom.QuasiFinite Mathlib.RingTheory.RingHom.Smooth Mathlib.RingTheory.RingHom.Surjective Mathlib.RingTheory.RingHom.Unramified Mathlib.RingTheory.RingHomProperties Mathlib.RingTheory.RootsOfUnity.Basic Mathlib.RingTheory.RootsOfUnity.Complex Mathlib.RingTheory.RootsOfUnity.CyclotomicUnits Mathlib.RingTheory.RootsOfUnity.EnoughRootsOfUnity Mathlib.RingTheory.RootsOfUnity.Minpoly Mathlib.RingTheory.RootsOfUnity.PrimitiveRoots Mathlib.RingTheory.SimpleModule.IsAlgClosed Mathlib.RingTheory.Smooth.AdicCompletion Mathlib.RingTheory.Smooth.Basic Mathlib.RingTheory.Smooth.Flat Mathlib.RingTheory.Smooth.Kaehler Mathlib.RingTheory.Smooth.Local Mathlib.RingTheory.Smooth.Locus Mathlib.RingTheory.Smooth.NoetherianDescent Mathlib.RingTheory.Smooth.Pi Mathlib.RingTheory.Smooth.Quotient Mathlib.RingTheory.Smooth.StandardSmoothCotangent Mathlib.RingTheory.Smooth.StandardSmoothOfFree Mathlib.RingTheory.Smooth.StandardSmooth Mathlib.RingTheory.Spectrum.Maximal.Localization 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.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.RingHom Mathlib.RingTheory.Spectrum.Prime.TensorProduct Mathlib.RingTheory.Spectrum.Prime.Topology Mathlib.RingTheory.Support Mathlib.RingTheory.Teichmuller Mathlib.RingTheory.TensorProduct.IncludeLeftSubRight Mathlib.RingTheory.TensorProduct.IsBaseChangeHom Mathlib.RingTheory.Trace.Defs Mathlib.RingTheory.UniqueFactorizationDomain.ClassGroup Mathlib.RingTheory.Unramified.Basic Mathlib.RingTheory.Unramified.Finite Mathlib.RingTheory.Unramified.Locus Mathlib.RingTheory.Unramified.Pi Mathlib.RingTheory.Valuation.AlgebraInstances Mathlib.RingTheory.Valuation.Archimedean Mathlib.RingTheory.Valuation.Discrete.Basic Mathlib.RingTheory.Valuation.Discrete.RankOne Mathlib.RingTheory.Valuation.Extension Mathlib.RingTheory.Valuation.FiniteField Mathlib.RingTheory.Valuation.Integral Mathlib.RingTheory.Valuation.LocalSubring Mathlib.RingTheory.Valuation.Minpoly Mathlib.RingTheory.Valuation.RamificationGroup Mathlib.RingTheory.Valuation.ValuationSubring 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.WittVector.WittPolynomial Mathlib.RingTheory.ZMod.Torsion Mathlib.RingTheory.ZMod.UnitsCyclic Mathlib.Tactic.NormNum.Irrational Mathlib.Topology.Algebra.Group.Matrix Mathlib.Topology.Algebra.Module.Determinant 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Mathlib.Topology.Sheaves.CommRingCat	2
113 files Mathlib.Algebra.Algebra.Epi Mathlib.Algebra.AlgebraicCard Mathlib.Algebra.Category.ModuleCat.Localization Mathlib.Algebra.Category.Ring.Epi Mathlib.Algebra.CharP.Algebra Mathlib.Algebra.CharP.IntermediateField Mathlib.Algebra.CharP.Subring Mathlib.Algebra.CubicDiscriminant Mathlib.Algebra.Lie.CartanSubalgebra Mathlib.Algebra.Lie.Character Mathlib.Algebra.Lie.InvariantForm Mathlib.Algebra.Lie.Loop Mathlib.Algebra.Lie.Nilpotent Mathlib.Algebra.Lie.Semisimple.Basic Mathlib.Algebra.Lie.Semisimple.Defs Mathlib.Algebra.Lie.Solvable Mathlib.Algebra.Module.FinitePresentation Mathlib.Algebra.Module.Lattice Mathlib.Algebra.Module.LocalizedModule.Submodule Mathlib.Algebra.Module.Presentation.Finite Mathlib.Algebra.MvPolynomial.Expand Mathlib.Algebra.MvPolynomial.Funext Mathlib.Algebra.MvPolynomial.Nilpotent Mathlib.Algebra.MvPolynomial.NoZeroDivisors Mathlib.Algebra.MvPolynomial.SchwartzZippel Mathlib.Algebra.Polynomial.Degree.CardPowDegree Mathlib.Algebra.Polynomial.FieldDivision Mathlib.Algebra.Polynomial.Homogenize Mathlib.Algebra.Polynomial.Roots Mathlib.Algebra.Polynomial.RuleOfSigns Mathlib.Algebra.Polynomial.SpecificDegree Mathlib.Algebra.Polynomial.Splits Mathlib.AlgebraicGeometry.EllipticCurve.Affine.AddSubMap Mathlib.AlgebraicGeometry.EllipticCurve.ModelsWithJ Mathlib.AlgebraicGeometry.EllipticCurve.NormalForms Mathlib.AlgebraicGeometry.EllipticCurve.VariableChange Mathlib.AlgebraicGeometry.EllipticCurve.Weierstrass Mathlib.Combinatorics.Additive.VerySmallDoubling Mathlib.Combinatorics.Nullstellensatz Mathlib.FieldTheory.MvRatFunc.Rank Mathlib.FieldTheory.RatFunc.Defs Mathlib.GroupTheory.DivisibleHull Mathlib.LinearAlgebra.Dimension.Localization Mathlib.LinearAlgebra.LinearIndependent.BaseChange Mathlib.ModelTheory.Arithmetic.Presburger.Definability Mathlib.ModelTheory.Arithmetic.Presburger.Semilinear.Basic Mathlib.NumberTheory.DiophantineApproximation.Basic Mathlib.NumberTheory.DiophantineApproximation.ContinuedFractions Mathlib.NumberTheory.FLT.MasonStothers Mathlib.NumberTheory.Rayleigh Mathlib.NumberTheory.Real.GoldenRatio Mathlib.NumberTheory.Real.Irrational Mathlib.RingTheory.Algebraic.Basic Mathlib.RingTheory.Algebraic.Cardinality Mathlib.RingTheory.Algebraic.MvPolynomial Mathlib.RingTheory.AlgebraicIndependent.Transcendental Mathlib.RingTheory.Artinian.Instances Mathlib.RingTheory.Bialgebra.GroupLike Mathlib.RingTheory.Coalgebra.GroupLike Mathlib.RingTheory.Finiteness.FiniteTypeLocal Mathlib.RingTheory.Flat.Domain Mathlib.RingTheory.Flat.FaithfullyFlat.Basic Mathlib.RingTheory.Flat.Localization Mathlib.RingTheory.Flat.Stability Mathlib.RingTheory.FractionalIdeal.Basic Mathlib.RingTheory.FractionalIdeal.Inverse Mathlib.RingTheory.FractionalIdeal.Operations Mathlib.RingTheory.HopfAlgebra.GroupLike Mathlib.RingTheory.Ideal.AssociatedPrime.Finiteness Mathlib.RingTheory.Lasker Mathlib.RingTheory.LocalProperties.Exactness Mathlib.RingTheory.LocalProperties.FinitePresentation Mathlib.RingTheory.LocalProperties.Projective Mathlib.RingTheory.LocalProperties.Submodule Mathlib.RingTheory.Localization.Algebra Mathlib.RingTheory.Localization.AsSubring Mathlib.RingTheory.Localization.Away.Lemmas Mathlib.RingTheory.Localization.BaseChange Mathlib.RingTheory.Localization.Cardinality Mathlib.RingTheory.Localization.Finiteness Mathlib.RingTheory.Localization.FractionRing Mathlib.RingTheory.Localization.Free Mathlib.RingTheory.Localization.LocalizationLocalization Mathlib.RingTheory.Localization.Module Mathlib.RingTheory.Localization.NumDen Mathlib.RingTheory.Localization.Rat Mathlib.RingTheory.Localization.Submodule Mathlib.RingTheory.MvPolynomial.EulerIdentity Mathlib.RingTheory.MvPolynomial.Expand Mathlib.RingTheory.MvPolynomial.Groebner Mathlib.RingTheory.MvPolynomial.Homogeneous Mathlib.RingTheory.MvPolynomial.Ideal Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic Mathlib.RingTheory.MvPolynomial.Localization Mathlib.RingTheory.MvPolynomial.MonomialOrder.DegLex Mathlib.RingTheory.MvPolynomial.MonomialOrder Mathlib.RingTheory.Polynomial.ContentIdeal Mathlib.RingTheory.Polynomial.Content Mathlib.RingTheory.Polynomial.Eisenstein.Basic Mathlib.RingTheory.Polynomial.Eisenstein.Criterion Mathlib.RingTheory.Polynomial.Eisenstein.Distinguished Mathlib.RingTheory.Polynomial.HilbertPoly Mathlib.RingTheory.Polynomial.IntegralNormalization Mathlib.RingTheory.Polynomial.Radical Mathlib.RingTheory.Polynomial.ScaleRoots Mathlib.RingTheory.Polynomial.SmallDegreeVieta Mathlib.RingTheory.Polynomial.UniqueFactorization Mathlib.RingTheory.Polynomial.Vieta Mathlib.RingTheory.TensorProduct.IsBaseChangeFree Mathlib.RingTheory.TensorProduct.IsBaseChangePi Mathlib.RingTheory.TensorProduct.Nontrivial Mathlib.RingTheory.Valuation.IsTrivialOn Mathlib.RingTheory.Valuation.ValuationRing	6

---

Declarations diff (regex)

+ fixingSubgroup_range_algebraMap

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 8749089).

• +1 new declarations
• −0 removed declarations

+IsFractionRing.fixingSubgroup_range_algebraMap

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 8749089eb3
Reference commit e5836dbb05

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).