chore(Algebra/Order): bound on |n / m|ₘ and |n - m|

[mathlib-splicebot]

This PR was automatically created from PR #34722 by @GrigorenkoPV via a review comment by @Vierkantor.

[github-actions]

PR summary 0f8bcdff02

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ abs_div_lt_of_lt_lt

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).

[Vierkantor]

I was confused for a moment until I saw that this was mabs, not abs. Let's clarify the name:

Suggested change

	@[to_additive] lemma abs_div_lt_of_lt_lt {N M n m : α} (hn : 1 ≤ n) (hm : 1 ≤ m) (hnN : n < N)
	@[to_additive] lemma mabs_div_lt_of_lt_lt {N M n m : α} (hn : 1 ≤ n) (hm : 1 ≤ m) (hnN : n < N)

[bryangingechen]

Unfortunately I don't think @GrigorenkoPV will have permission to accept the suggestion, since the PR was created by a bot.

[Vierkantor]

Thanks!

bors d+

[mathlib-bors]

✌️ mathlib-splicebot[bot] can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[bryangingechen]

@Vierkantor I'm guessing you didn't mean to delegate to the bot?

[Vierkantor]

I'm guessing you didn't mean to delegate to the bot?

Ah oops! Yes, I did not take into account how GitHub's interface factors into this... @GrigorenkoPV I suppose if you agree with the change then I'll apply it and merge this PR myself using maintainer powers.