chore: use a type synonym instead of an abbrev for Interval

[sgouezel]

Otherwise, there are conflicting instances between Interval and its definition WithBot ..., creating diamonds.

---

[github-actions]

PR summary 865d150803

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ coe
+ coe_le_coe
+ inf_coe
+ instance : One (Interval α)
+ length_bot
- instance : Inhabited (Interval α) := WithBot.inhabited
- instance : LE (Interval α) := WithBot.instLE
- instance : OrderBot (Interval α) := WithBot.instOrderBot
-+-+ divisionCommMonoid

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).

[j-loreaux]

Otherwise this looks good to me.

bors d+

[j-loreaux]

Doesn't this already appear on Line 314? Note that this is in the root namespace which is why it didn't conflict with the pre-existing one.

[j-loreaux]

This assumes Lattice α, which seems too strong. I think you should move it up into the Preorder section.

[mathlib-bors]

✌️ sgouezel can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.