[Merged by Bors] - refactor(Analysis): golf Mathlib/Analysis/Complex/Spectrum

[yuanyi-350]

• golfs Complex/Spectrum by proving SpectrumRestricts.real_iff directly with simp
• removes the local backward.isDefEq.respectTransparency option from that proof

Extracted from #37968

[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.

---

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

Current number	Change	Type
6214	-1	backward.isDefEq.respectTransparency

Current commit 8457c66911
Reference commit dd46575852

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):

• SpectrumRestricts.real_iff: 0.055341 -> 0.028717 (-48.1%)

Overall:

• SpectrumRestricts.real_iff elaborates faster after replacing the manual proof with a direct simp proof.

[yuanyi-350]

!bench

[leanprover-radar]

Benchmark results for 8457c66 against dd46575 are in. No significant results found. @yuanyi-350

• ✅ build//instructions: -30.2G (-0.02%)

No significant changes detected.

[themathqueen]

Thanks! Btw, you don't need to !bench every time, the performance you provide is enough I think?

maintainer merge

[github-actions]

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

[j-loreaux]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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