[Merged by Bors] - refactor(NumberTheory): golf Mathlib/NumberTheory/LegendreSymbol/GaussEisensteinLemmas

[yuanyi-350]

• golfs GaussEisensteinLemmas by replacing a manual prod_bij_ne_one argument with Finset.prod_ite
• closes the resulting product identity directly with simp

Extracted from #38144

[github-actions]

PR summary dd46575852

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).

[yuanyi-350]

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

Results (seconds):

• gauss_lemma_aux₁: 1.712065 -> 1.115671 (-34.8%)

Overall:

• gauss_lemma_aux₁ elaborates faster after replacing the manual prod_bij_ne_one argument with Finset.prod_ite and simp.

[yuanyi-350]

!bench

[leanprover-radar]

Benchmark results for 96eb16d against dd46575 are in. No significant results found. @yuanyi-350

• ✅ build//instructions: -9.8G (-0.01%)

Small changes (1✅)

• ✅ build/module/Mathlib.NumberTheory.LegendreSymbol.GaussEisensteinLemmas//instructions: -2.1G (-6.56%)

[MichaelStollBayreuth]

maintainer merge

[github-actions]

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

[riccardobrasca]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

• ci (staging) / Post-Build Step
• ci (staging) / Build
• ci (staging) / Lint style
• ci (staging) / Post-CI job