refactor(FieldTheory/Galois/IsGaloisGroup): generalize mulEquivAlgEquiv to domains

[tb65536]

This PR generalizes mulEquivAlgEquiv to domains. This allows us to remove mulEquivCongr' (a field version of mulEquivCongr).

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• depends on: [Merged by Bors] - refactor(RingTheory/Localization/FractionRing): remove bottom ring and field from IsFractionRing.mulSemiringAction #40804

[github-actions]

PR summary 3f827664e3

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff (regex)

+ Bijective.of_comp_left

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 3f82766).

• +1 new declarations
• −0 removed declarations

+Function.Bijective.of_comp_left

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 3f827664e3
Reference commit 843d7890de

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-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - refactor(RingTheory/Localization/FractionRing): remove bottom ring and field from IsFractionRing.mulSemiringAction #40804
  By Dependent Issues (🤖). Happy coding!

[xroblot]

LGTM. The generalization of mulEquivAlgEquiv to domains lets mulEquivCongr be defined directly. Thanks!

[riccardobrasca]

Thanks!

bors d+

[mathlib-bors]

✌️ tb65536 can now approve this pull request until 2026-07-04 14:30 UTC (in 2 weeks). To approve and merge, reply with bors r+. More detailed instructions are available here.

⚠️ This delegation only covers changes within Archive/**, Counterexamples/**, docs/**, DownstreamTest/**, Mathlib/**, MathlibTest/**, widget/**, Archive.lean, Counterexamples.lean, docs.lean, Mathlib.lean; an author commit touching anything else will revoke it. Bors also revokes it if a later push changes too many files for it to check the full list — even if it stays within scope.

[tb65536]

bors r+