feat(NumberTheory/Divisors): Add infinite_setOf_divisors_iff

[adrianmartir]

This proves that the set of divisors { m | m | n } of a natural number n is infinite if and only if n is zero. The first proof draft was by @Aristotle-Harmonic.

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✅ PR Title Formatted Correctly

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PR summary 0fbcb39f55

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

+ infinite_setOf_divisors_iff

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 scripts/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).

[alexjbest]

The pr description is a bit confusing! It should have the other part of the iff in.

And this should probably be a @[simp] lemma

[adrianmartir]

Indeed, I had written the PR description incorrectly. I fixed it now, renamed the lemma and added it as a simp lemma.

I also wasn't sure if this was the best place to put the lemma, since the file is mainly about Nat.divisors, which is not the same. However, it felt like it was the best place to put it, since I didn't find a suitable file in Data/Nat.

I also do have an integer version for the lemma, which I did not include here.