[Merged by Bors] - feat(Data/Nat/Factorization/Defs): more theorems about f.prod (· ^ ·)

[SnirBroshi]

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Follow-up to this comment from #34554

• depends on: [Merged by Bors] - feat(Data/Nat/Factorization/Divisors): calculate divisors using prime factorization #34554

[github-actions]

PR summary 034c50cbf6

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

+ dvd_iff_exists_le_factorization
+ dvd_prod_pow_of_factorization_le
+ factorization_prod_pow_eq_self_of_le_factorization
+ prod_pow_dvd_of_le_factorization

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.

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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).

[github-actions]

✅ PR Title Formatted Correctly

The title of this PR has been updated to match our commit style conventions.
Thank you!

[mathlib-dependent-issues]

This PR/issue depends on:

• [Merged by Bors] - feat(Data/Nat/Factorization/Divisors): calculate divisors using prime factorization #34554
  By Dependent Issues (🤖). Happy coding!

[Ruben-VandeVelde]

Looks good, modulo a naming issue.

maintainer delegate

[github-actions]

🚀 Pull request has been placed on the maintainer queue by Ruben-VandeVelde.

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pull_request_review, wf_run

[Vierkantor]

Thanks!

bors r+

[Vierkantor]

Oops, I mean:

bors r-

bors d+

[mathlib-bors]

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

[mathlib-bors]

Canceled.

[SnirBroshi]

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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