chore(Analysis): golf Order, Asymptotic, and Between

[yuanyi-350]

This PR extracts from #37968 the changes to the following files:

• Mathlib/Analysis/CStarAlgebra/ContinuousFunctionalCalculus/Order.lean
• Mathlib/Analysis/Complex/ValueDistribution/LogCounting/Asymptotic.lean
• Mathlib/Analysis/Convex/Between.lean

This is intended to split those refactors into a standalone PR.

[github-actions]

PR summary c27c098f0d

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.

You can run this locally as

./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, using [Elab.definition.value] on the actual merge-base c290b55c6e (before) and the PR head ab0cb64496 (after).

Results (seconds):

• CStarAlgebra.isUnit_of_le: 0.553297 -> 0.207085 (-62.6%)
• CStarAlgebra.norm_le_norm_of_nonneg_of_le: 5.278791 -> 3.585134 (-32.1%)
• Function.locallyFinsuppWithin.one_isLittleO_logCounting_single: 0.218979 -> 0.028834 (-86.8%)
• ValueDistribution.logCounting_isBigO_one_iff_analyticOnNhd: 0.441337 -> 0.050721 (-88.5%)
• Wbtw.sameRay_vsub: 0.519748 -> 0.068429 (-86.8%)
• Wbtw.collinear: 0.092810 -> 0.023367 (-74.8%)
• wbtw_iff_sameRay_vsub: 0.634995 -> 0.035643 (-94.4%)

Overall:

• All seven modified declarations got faster in this run.
• The largest speedups were in wbtw_iff_sameRay_vsub, ValueDistribution.logCounting_isBigO_one_iff_analyticOnNhd, Wbtw.sameRay_vsub, and Function.locallyFinsuppWithin.one_isLittleO_logCounting_single.
• No regression showed up.

Caveat:

• This was a single-run trace.profiler comparison on the declaration bodies only, using [Elab.definition.value], so absolute times may vary slightly across runs.

[grunweg]

For reference, let me cross-link the comments here and here. (Can you update the PR description accordingly? Thanks!)