feat: Add AffineEquiv.image_intrinsicInterior

[TTony2019]

Summary

This PR generalizes the existing lemma AffineIsometry.image_intrinsicInterior to the setting of affine equivalences, yielding the corresponding result AffineEquiv.image_intrinsicInterior.

Since affine equivalences are more general than affine isometries, the proof requires an additional finite-dimensionality assumption. The key extra input is that in finite-dimensional spaces, an affine equivalence induces a homeomorphism via AffineEquiv.toHomeomorphOfFiniteDimensional, so the assumptions are adjusted accordingly.

Apart from these extra assumptions, the argument is essentially the same as for AffineIsometry.image_intrinsicInterior.

Collaboration

This PR was developed together with @imathwy.

[github-actions]

Welcome new contributor!

Thank you for contributing to Mathlib! If you haven't done so already, please review our contribution guidelines, as well as the style guide and naming conventions. In particular, we kindly remind contributors that we have guidelines regarding the use of AI when making pull requests.

We use a review queue to manage reviews. If your PR does not appear there, it is probably because it is not successfully building (i.e., it doesn't have a green checkmark), has the awaiting-author tag, or another reason described in the Lifecycle of a PR. The review dashboard has a dedicated webpage which shows whether your PR is on the review queue, and (if not), why.

If you haven't already done so, please come to https://leanprover.zulipchat.com/, introduce yourself, and mention your new PR.

Thank you again for joining our community.

[github-actions]

PR summary b80f227194

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ intrinsicInterior_image

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.

---

No changes to technical debt.

You can run this locally as

./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).

[github-actions]

✅ PR Title Formatted Correctly

The title of this PR has been updated to match our commit style conventions.
Thank you!