refactor(NumberTheory): golf Mathlib/NumberTheory/Dioph

[yuanyi-350]

• golfs Mathlib/NumberTheory/Dioph by replacing the arithmetic proof in sub_dioph with grind
• simplifies div_dioph by splitting on y = 0 ∨ 0 < y, then closing the positive case with Nat.div_eq_iff and grind

Extracted from #38144

[yuanyi-350]

!bench

[github-actions]

PR summary 7705510fbc

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

No declarations were harmed in the making of this PR! 🐙

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.

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).

[leanprover-radar]

Benchmark results for 14367bd against 7705510 are in. No significant results found. @yuanyi-350

• 🟥 build//instructions: +6.6G (+0.00%)

No significant changes detected.

[grunweg]

Feel free to remove the label once you have commented on the performance!

[yuanyi-350]

I ran a profiler comparison for the changed declarations in this PR.

Results (seconds):

• Dioph.sub_dioph: 0.048198 -> 0.056772 (+17.79%)
• Dioph.div_dioph: 0.053122 -> 0.094187 (+77.30%)

Overall:

• both changed declarations got slower in this measurement, with a small regression in Dioph.sub_dioph and a larger regression in Dioph.div_dioph

[grunweg]

I think the proofs are an improvement --- and would justify the minor performance loss.

[grunweg]

Why do you need eq_comm here?

[yuanyi-350]

simp can simplify this expression to z = 0 ↔ 0 = z, and then eq_comm is needed.

[grunweg]

Thanks!
maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by grunweg.