chore(GroupTheory): make smul_eq_self_of_mem_zpowers to_additive

[attilavjda]

This PR makes smul_eq_self_of_mem_zpowers amenable to @[to_additive] by reproving it via the action stabilizer and Subgroup.zpowers_le.

This allows the additive counterpart to be generated automatically, removing the hand-written additive proof and the to_additive existing workaround.

Used Aristotle AI to find this refactor and help write the proof.

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[github-actions]

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[github-actions]

PR summary 4a7c367bdb

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff (regex)

- vadd_eq_self_of_mem_zmultiples

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 4a7c367).

• +0 new declarations
• −0 removed declarations

No declaration differences.

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Decrease in strong tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type (strong)
418	-1	porting notes

No changes to weak technical debt.

Current commit 4a7c367bdb
Reference commit 4d476f6d44

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).

[tb65536]

I'm not sure if OrderOfElement is necessarily the right file for this anymore?

[attilavjda]

moving it to a stabilizer or zpowers file would pull in an import, what do you think, maybe leave it?

Mathlib/GroupTheory/GroupAction/Basic.lean the stabilizer file needs only one extra import

[SnirBroshi]

Could you use backticks to make the title a bit easier to parse? e.g.

tag `smul_eq_self_of_mem_zpowers` with `to_additive`