feat(Fin/Parity): add `Fin.even_iff`

[urkud]

Motivated by this Zulip question.

---

• [ ] depends on: #8974

[leanprover-community-mathlib4-bot]

This PR/issue depends on:

• ~~leanprover-community/mathlib4#8974~~ By Dependent Issues (🤖). Happy coding!

[github-actions[bot]]

PR summary 2c581bd163

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Data.Fin.Parity	471

---

Declarations diff

+ add_one_lt_of_even + even_iff + even_iff_imp + even_iff_of_even + even_of_odd + even_of_val + odd_iff + odd_iff_imp + odd_iff_of_even + odd_of_odd + odd_of_val + one_lt_of_ne_zero_of_even + val_add_eq_of_add_lt

You can run this locally as follows

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

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

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

[IvanRenison]

@urkud are you going to continue with this pull request? If not, can I continue with it?

[urkud]

Feel free to take over this PR. Thanks!

[github-actions[bot]]

🚀 Pull request has been placed on the maintainer queue by Ruben-VandeVelde.

[kim-em]

bors merge

[IvanRenison]

For some reason the commit has the "Co-authored-by" two times

[mathlib-bors[bot]]

Build failed:

• Build

[bryangingechen]

bors d=IvanRenison

[mathlib-bors[bot]]

:v: IvanRenison can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[bryangingechen]

Please merge master, fix the breakage and then merge with bors d+ when done, thanks!

[Command-Master]

Apologies for the late review, I forgot to send it earlier

[IvanRenison]

Thanks for the review @Command-Master, I was very surprised that the first two reviewers didn't find anything. I was very lucky that the build failed

[IvanRenison]

bors r+

[mathlib-bors[bot]]

Pull request successfully merged into master.

Build succeeded:

• Lint style
• Build