feat: IsMulApplyEqComp instances for RelHom/RelEmbedding/RelIso and MulAction (α →o α) α

[kim-em]

This PR adds IsMulApplyEqComp/IsOneApplyEqSelf instances for RelHom, RelEmbedding and RelIso (fulfilling a TODO recorded in Mathlib/Algebra/Order/Group/End.lean, so these types get the generic pow_apply_eq_iterate/coe_pow_eq_iterate lemmas), and add the tautological MulAction (α →o α) α instance together with smul_def and FaithfulSMul in Mathlib/Algebra/Order/Group/Action/End.lean (requested in review; it cannot live in End.lean because of assert_not_exists MulAction), matching the existing RelHom/RelEmbedding/RelIso instances in that file.

Follow-up to #40515 (feat: Monoid and Group instances for OrderHom and OrderIso).

🤖 Prepared with Claude Code

[github-actions]

PR summary 47abf247ed

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

+ applyMulAction
+ apply_faithfulSMul
+ instance : IsMulApplyEqComp (r →r r) α where mul_apply_eq_comp _ _ _ := rfl
+ instance : IsMulApplyEqComp (r ↪r r) α where mul_apply_eq_comp _ _ _ := rfl
+ instance : IsMulApplyEqComp (r ≃r r) α where mul_apply_eq_comp _ _ _ := rfl
+ instance : IsOneApplyEqSelf (r →r r) α where one_apply_eq_self _ := rfl
+ instance : IsOneApplyEqSelf (r ↪r r) α where one_apply_eq_self _ := rfl
+ instance : IsOneApplyEqSelf (r ≃r r) α where one_apply_eq_self _ := rfl
+ smul_def

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 47abf24).

• +9 new declarations
• −0 removed declarations

+OrderHom.applyMulAction
+OrderHom.apply_faithfulSMul
+OrderHom.smul_def
+RelEmbedding.instIsMulApplyEqComp
+RelEmbedding.instIsOneApplyEqSelf
+RelHom.instIsMulApplyEqComp
+RelHom.instIsOneApplyEqSelf
+RelIso.instIsMulApplyEqComp
+RelIso.instIsOneApplyEqSelf

---

No changes to strong technical debt.

No changes to weak technical debt.

Current commit 47abf247ed
Reference commit a33a5ccd63

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).