refactor(Analysis): golf Mathlib/Analysis/Normed/Operator/Mul

[yuanyi-350]

• refactors Normed/Operator/Mul by defining ring_lmap_equiv_selfₗ as the symmetry of ContinuousLinearMap.toSpanSingletonLE
• shortens the norm proof for ring_lmap_equiv_self to ContinuousLinearMap.norm_toSpanSingleton

Extracted from #37968

[github-actions]

PR summary c3e588b468

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ toContinuousLinearEquiv_toSpanSingletonₗᵢ
+ toLinearEquiv_toSpanSingletonₗᵢ
+ toSpanSingletonₗᵢ
+ toSpanSingletonₗᵢ_apply
+ toSpanSingletonₗᵢ_symm_apply

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):

• ContinuousLinearMap.ring_lmap_equiv_selfₗ: 0.210 -> 0.089 (-57.9%)
• ContinuousLinearMap.ring_lmap_equiv_self: 0.254 -> 0.155 (-39.0%)

Overall:

• Both changed declarations elaborated faster.

[yuanyi-350]

@grunweg , I think the current PR now meets your guidelines.

[themathqueen]

There's also 0 api for these two definitions. I know this wasn't the initial plan for this PR, but can you add some basic supporting lemmas for the second one please (like _apply, _symm_apply, toLinearEquiv_, etc)?

[themathqueen]

I know I suggested the name, but it currently doesn't indicate that it's an equivalence, so that needs to probably change, I don't know to what 🤔

[themathqueen]

Can you ask on Zulip what a good name for the linear isometric version would be?

I think toSpanSingletonLIE might be okay-ish? We have toSpanSingletonLE and toSpanSingletonCLE, so it makes sense in that way.

[themathqueen]

@yuanyi-350, can you please tag me in the Zulip post? Or post the link here? (I can't find it)

[yuanyi-350]

@themathqueen , https://leanprover.zulipchat.com/#narrow/channel/144837-PR-reviews/topic/.2338272.20refactors.20.60ring_lmap_equiv_self.60/with/590692293