refactor(Analysis): golf Mathlib/Analysis/Normed/Unbundled/SpectralNorm

[yuanyi-350]

• rewrites spectralValue_eq_zero_iff via eq_X_pow_iff_natDegree_le_natTrailingDegree and spectralValueTerms_of_lt_natDegree
• rewrites spectralNorm.eq_of_normalClosure' as two applications of spectralNorm.eq_of_tower
• tidies spectralNorm_unique by switching the local transported structures to set/letI/haveI with inferInstanceAs

Extracted from #37968

[github-actions]

PR summary 900c9b0390

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

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

---

Increase in tech debt: (relative, absolute) = (1.00, 0.07)

Current number	Change	Type
14	1	backward.inferInstanceAs.wrap.data

Current commit 7f61de83bf
Reference commit 900c9b0390

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):

• spectralValue_eq_zero_iff: 0.102787 -> 0.023925 (-76.72%)
• spectralNorm.eq_of_normalClosure': 1.672272 -> 0.474995 (-71.59%)
• spectralNorm_unique: 2.640024 -> 4.344001 (+64.54%)

Overall:

• spectralValue_eq_zero_iff and spectralNorm.eq_of_normalClosure' are substantially faster.
• spectralNorm_unique regresses noticeably and dominates the net slowdown.

[yuanyi-350]

!bench

[leanprover-radar]

Benchmark results for 7f61de8 against 900c9b0 are in. No significant results found. @yuanyi-350

• 🟥 build//instructions: +18.9G (+0.01%)

Small changes (1🟥)

• 🟥 build/module/Mathlib.Lean.MessageData.ForExprs//instructions: +248.7M (+6.13%)

[themathqueen]

I think you should revert all changes for this theorem