feat: A disjoint union is finite iff all sets are finite, and all but finitely many are empty

[sgouezel]

From the Carleson project

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[github-actions]

PR summary 67885573b4

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ PairwiseDisjoint.finite_biUnion_iff
+ PairwiseDisjoint.finite_iUnion_iff
+ finite_iUnion_iff
+ finite_iUnion_of_subsingleton

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/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).

[sgouezel]

Thanks for the review!

[eric-wieser]

I'd liked to have seen this be of the more general form

Suggested change

	Set.Finite (⋃ i ∈ s, f i)
	Set.Finite (⋃ (i) (h : i ∈ s, f i h)

but I guess the definition of PairwiseDisjoint doesn't permit this; so no action needed.

[eric-wieser]

bors d+

Consider waiting a day or two to let @YaelDillies have a look for any other API like elim_set that can make this more concise

[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.

[YaelDillies]

I guess this now duplicates finite_iUnion_iff