refactor(NumberTheory): golf Mathlib/NumberTheory/PellMatiyasevic

[yuanyi-350]

• simplifies pellZd_succ_succ in Mathlib/NumberTheory/PellMatiyasevic by replacing a hand-written intermediate equality with a direct ext/simp/ring_nf proof

Extracted from #38144

[github-actions]

PR summary 9268b22206

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.

---

Decrease in tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type
6205	-1	backward.isDefEq.respectTransparency

Current commit 1c154ec9da
Reference commit 9268b22206

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).

[yuanyi-350]

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

Results (seconds):

• Pell.pellZd_succ_succ: 0.592 -> 0.433 (-26.9%)

Overall:

• Pell.pellZd_succ_succ is faster after replacing the hand-written intermediate equality with a direct ext/simp/ring_nf proof.

[yuanyi-350]

!bench

[leanprover-radar]

Benchmark results for 83d958a against 9268b22 are in. No significant results found. @yuanyi-350

• 🟥 build//instructions: +3.6G (+0.00%)

Small changes (1✅, 1🟥)

• 🟥 build/module/Mathlib.MeasureTheory.MeasurableSpace.Card//instructions: +432.9M (+3.60%)
• ✅ build/module/Mathlib.Tactic.SimpRw//instructions: -547.6M (-12.11%)