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[Merged by Bors] - feat(data/nat/unique_factorization): a unique_factorization_monoid instance on N #4194

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[Merged by Bors] - feat(data/nat/unique_factorization): a unique_factorization_monoid instance on N #4194

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Provides a unique_factorization_monoid instance on nat
Shows its equivalence to nat.factors, which is list-valued

@awainverse awainverse added awaiting-review The author would like community review of the PR blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. labels Sep 21, 2020
@github-actions github-actions bot added the merge-conflict Please `git merge origin/master` then a bot will remove this label. label Sep 21, 2020
@awainverse awainverse removed the blocked-by-other-PR This PR depends on another PR which is still in the queue. A bot manages this label via PR comment. label Sep 22, 2020
@awainverse awainverse changed the title feat(number_theory/unique_factorization): a unique_factorization_monoid instance on N (deps: #4156) feat(number_theory/unique_factorization): a unique_factorization_monoid instance on N Sep 22, 2020
@github-actions github-actions bot removed the merge-conflict Please `git merge origin/master` then a bot will remove this label. label Sep 22, 2020
Vierkantor
Vierkantor requested changes Sep 25, 2020
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Some minor suggestions, it looks good otherwise!

src/algebra/associated.lean
section unique_units
variables [monoid α] [unique (units α)]

theorem associated_iff_eq {x y : α} : x ~ᵤ y ↔ x = y :=
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Remark that you shouldn't feel the need to follow up on: we also have the implication associated = eq → unique (units α) from associated_one_iff_is_unit.

src/number_theory/unique_factorization.lean Outdated
import data.nat.prime
import ring_theory.unique_factorization_domain

theorem nat.prime_iff {p : ℕ} : p.prime ↔ prime p :=
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I never realized nat.prime had its own incompatible definition! Can you move this theorem to data/nat/prime.lean or will that cause cyclical imports?

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I made a new file, so as not to import algebra.associated into data.nat.prime for one lemma.

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Hmm, I'm a fan of small files but in this case I'm not sure. That nat.prime is the same as _root_.prime is a very fundamental result, so I would not expect it to be "hidden" in another file, as it were. And adding algebra.associated to the imports of data.nat.prime will only add two files to the import graph: algebra.associated itself and data.multiset.basic.

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Unfortunately, the proof of perm_of_prod_eq_prod seems to be screwed up by importing data.multiset.basic through algebra.associated.

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Ah, I figured it out.

src/number_theory/unique_factorization.lean Outdated
{ right, rw [hn, nat.is_unit_iff.1 un, mul_one], } }
end

namespace nat
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I guess the above two lemmas aren't in the nat namespace because it would interpret prime p as nat.prime, right? It looks a bit funny though.

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Exactly. I should look into seeing how bad it'd be to replace nat.prime altogether.

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It sounds like a good way to get rid of some spare time :)

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

Vierkantor
Vierkantor approved these changes Sep 26, 2020
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Thank you 🎉

I'm happy with the changes as they are, except that I'm in favour of incorporating data.nat.associated into data.nat.prime. It won't cause me to reject the PR though, so I'll let you decide what happens to it.

bors d+

@Vierkantor Vierkantor removed the awaiting-review The author would like community review of the PR label Sep 26, 2020
@Vierkantor Vierkantor added the delegated The PR author may merge after reviewing final suggestions. label Sep 26, 2020
@awainverse awainverse changed the title feat(number_theory/unique_factorization): a unique_factorization_monoid instance on N feat(data/nat/unique_factorization): a unique_factorization_monoid instance on N Sep 26, 2020
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bors r+

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bors bot commented Sep 26, 2020

Canceled.

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bors r+

bors bot pushed a commit that referenced this pull request Sep 26, 2020
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feat(data/nat/unique_factorization): a unique_factorization_monoid …
376ab30 
…instance on N (#4194)

Provides a `unique_factorization_monoid` instance on `nat`
Shows its equivalence to `nat.factors`, which is list-valued



Co-authored-by: Aaron Anderson <65780815+awainverse@users.noreply.github.com>
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Pull request successfully merged into master.

Build succeeded:

@bors bors bot changed the title feat(data/nat/unique_factorization): a unique_factorization_monoid instance on N [Merged by Bors] - feat(data/nat/unique_factorization): a unique_factorization_monoid instance on N Sep 26, 2020
@bors bors bot closed this Sep 26, 2020
@bors bors bot deleted the nat_ufmonoid branch September 26, 2020 19:15
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