feat(IsGaloisGroup): add restrictHom

[xroblot]

This PR adds the restriction map for the Galois group for domains.

Given a tower of domains A ≤ B ≤ C, G a Galois group for C/A and G' a Galois group for B/A, we define:

• restrictHom: the restriction of the G-action on C to the G'-action on B.
• quotientMulEquiv: the isomorphism between the quotient of G by the fixing subgroup of B and the Galois group of B/A.

Supporting lemmas include:

• normal_of_isGalois: if G is a finite Galois group for L/K, H is a Galois group for L/E, and E/K is Galois, then H is a normal subgroup of G.
• restrictHom_surjective: the restriction map is surjective.

---

• depends on: [Merged by Bors] - feat(FieldTheory/Galois/IsGaloisGroup): add IsGaloisGroup.of_algEquiv and of_ringEquiv #38902
• depends on: [Merged by Bors] - feat(FieldTheory/Galois/IsGaloisGroup): generalize mulEquivCongr #38464
• depends on: [Merged by Bors] - refactor(RingTheory/Localization/FractionRing): remove bottom ring and field from IsFractionRing.mulSemiringAction #40804

[github-actions]

PR summary 55f521fae9

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ algebraMap_quotientMulEquiv_smul
+ algebraMap_restrictHom_smul
+ mulEquivCongr_mapSubgroup_fixingSubgroup
+ normal_of_isGalois
+ of_isScalarTower
+ quotientMulEquiv
+ restrictHom
+ restrictHom_surjective

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 55f521f).

• +10 new declarations
• −0 removed declarations

+IsGaloisGroup.algebraMap_quotientMulEquiv_smul
+IsGaloisGroup.algebraMap_restrictHom_smul
+IsGaloisGroup.mulEquivCongr.congr_simp
+IsGaloisGroup.mulEquivCongr_mapSubgroup_fixingSubgroup
+IsGaloisGroup.normal_of_isGalois
+IsGaloisGroup.of_isScalarTower
+IsGaloisGroup.quotientMulEquiv
+IsGaloisGroup.quotientMulEquiv.congr_simp
+IsGaloisGroup.restrictHom
+IsGaloisGroup.restrictHom_surjective

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 55f521fae9
Reference commit 0bee4471e4

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).

[mathlib-merge-conflicts]

This pull request has conflicts, please merge master and resolve them.

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - feat(FieldTheory/Galois/IsGaloisGroup): add IsGaloisGroup.of_algEquiv and of_ringEquiv #38902
• [Merged by Bors] - feat(FieldTheory/Galois/IsGaloisGroup): generalize mulEquivCongr #38464
• [Merged by Bors] - refactor(RingTheory/Localization/FractionRing): remove bottom ring and field from IsFractionRing.mulSemiringAction #40804
  By Dependent Issues (🤖). Happy coding!

[xroblot]

Thanks for the thorough review, @tb65536! I think I've incorporated everything. Should be ready for another look.