feat (RingTheory/Binomial) : Standard lemmas for Ring.choose

[ScottCarnahan]

This PR has basic identities satisfied by general binomial coefficients, together with corresponding lemmas about evaluating Pochhammer polynomials.

---

• [ ] depends on: #13428
• [ ] depends on: #13430

[github-actions[bot]]

PR summary c7da75cf94

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ choose_add_smul_choose + choose_eq_nat_choose + choose_one_right + choose_one_right' + choose_smul_choose + choose_succ_succ + choose_zero_ite + choose_zero_pos + choose_zero_right + choose_zero_right' + choose_zero_succ + descPochhammer_succ_succ_smeval

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>

[leanprover-community-mathlib4-bot]

This PR/issue depends on:

• ~~leanprover-community/mathlib4#13428~~
• ~~leanprover-community/mathlib4#13430~~ By Dependent Issues (🤖). Happy coding!

[kim-em]

bors d+

[mathlib-bors[bot]]

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

[ScottCarnahan]

Thank you for the review!

bors r+

[mathlib-bors[bot]]

This PR was included in a batch that was canceled, it will be automatically retried

[mathlib-bors[bot]]

Pull request successfully merged into master.

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