[Merged by Bors] - feat(FinitelyPresentedGroup): Additivize everything and add ℤ instance

[homeowmorphism]

We add to_additive annotations to the FinitelyPresentedGroup.lean API and show that it works with the AddGroup.IsFinitelyPresented ℤ as a test example.

Co-pilot and Gemini 3.1 Pro were used to assist in these changes.

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[mathlib-bors]

This pull request is now in draft mode. No active bors state needed cleanup.

While this PR remains draft, bors will ignore commands on this PR. Mark it ready for review before using commands like bors r+ or bors try.

[github-actions]

PR summary a535bdc11a

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ AddGroup.IsFinitelyPresented
+ instance : AddGroup.IsFinitelyPresented ℤ
+ instance [Finite α] : IsFinitelyPresented (FreeGroup α) := by
- instance [Finite α] : Group.IsFinitelyPresented (FreeGroup α) := by

You can run this locally as follows

## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

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).

[kbuzzard]

Excellent -- thanks! Probably this should have been done with the original PR. Thanks also for the docstrings on theorems -- these are far less common than they should be.

bors merge

[mathlib-bors]

Merge conflict.

Merge or rebase master into this PR and resolve the conflict, then someone with permission can run bors r+ or bors retry.

[homeowmorphism]

It looks like bors had difficulty merging both this and #36873 at the same time. I believe I have resolved the issue. @kbuzzard would you mind taking a look and merging again?

I probably don't have permission but just in case: bors r+.

[kbuzzard]

bors r+

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Lint style
• ci (staging) / Build
• ci (staging) / Post-Build Step
• ci (staging) / Post-CI job