[Merged by Bors] - feat(Analysis/Asymptotics): if u is eventually positive and u ~ v then v is eventually positive

[vasnesterov]

Prove that Asymptotics.IsEquivalent respects (non)positivity and (non)negativity of functions.

---

[github-actions]

PR summary 1ba90ab6bb

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ IsEquivalent.eventually_neg
+ IsEquivalent.eventually_nonneg
+ IsEquivalent.eventually_nonpos
+ IsEquivalent.eventually_pos
+ IsEquivalent.exists_pos_eq_mul

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).

[vihdzp]

Can we also have the versions for ≤, and for eventually negative?

[vasnesterov]

Can we also have the versions for ≤, and for eventually negative?

Sure, done.

[j-loreaux]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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