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[Merged by Bors] - feat(ring_theory/localization/away) : Add num_denom section #18830

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Added a section num_denom: the main result is the lemma exists_reduced_fraction that shows that every non-zero element b in a localization.away x of a UFM can be written in a unique way as b=x^n * a with n : ℤ and a not divisible by x.


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@faenuccio faenuccio added awaiting-review The author would like community review of the PR t-algebra Algebra (groups, rings, fields etc) labels Apr 18, 2023
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variables [is_domain R] [normalization_monoid R] [unique_factorization_monoid R]
include hx

lemma max_power_factor {a₀ : R} (h : a₀ ≠ 0) [nontrivial R] :
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Can you move this to unique_factorization_domain.lean? (Or perhaps add a remark to do so after the port?)

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@faenuccio faenuccio Apr 19, 2023

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Do you mean just this lemma max_power_factor or all the additions?

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Just this lemma, since it doesn't assume anything about localizations, right?

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I'll try later.

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@faenuccio faenuccio Apr 20, 2023

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I have moved max_power_factor to unique _factorization_domain and I have opened the corresponding PR in mathlib4 3558.

@Vierkantor Vierkantor added awaiting-author A reviewer has asked the author a question or requested changes and removed awaiting-review The author would like community review of the PR labels Apr 19, 2023
@Vierkantor Vierkantor self-assigned this Apr 19, 2023
faenuccio and others added 4 commits April 19, 2023 15:31
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
@faenuccio faenuccio added awaiting-review The author would like community review of the PR and removed awaiting-author A reviewer has asked the author a question or requested changes labels Apr 19, 2023
@YaelDillies YaelDillies changed the title feat(src\ring_theory\localization\away.lean) : add section num_denom feat(ring_theory/localization/away) : Add num_denom section Apr 20, 2023
@github-actions github-actions bot added the modifies-synchronized-file This PR touches a files that has already been ported to mathlib4, and may need a synchronization PR. label Apr 20, 2023
@faenuccio faenuccio added WIP Work in progress review-in-progress A reviewer is thinking about this PR offline. labels Apr 25, 2023
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I have closed all goals, and commented all the stuff relative to the old version using self_as_unit. I have also moved the assumption hx : irreducible x to the final theorem, since it was not needed for any of the preparatory lemmas. @Vierkantor if you are ok, I can get rid of all the previous stuff and then it should be ready to go.

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Thank you for your work and your patience in the past days! I think we're nearly there, just a few steps:

  • address my suggestion
  • fix the linting errors
  • delete commented-out (or otherwise unused code)

If the above steps went straightforwardly, then please feel free to bors merge this yourself.

bors d+

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bors bot commented Apr 28, 2023

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

@leanprover-community-bot-assistant leanprover-community-bot-assistant added delegated The PR author may merge after reviewing final suggestions. and removed awaiting-review The author would like community review of the PR labels Apr 28, 2023
Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>
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bors merge

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bors bot commented May 4, 2023

👎 Rejected by label

@faenuccio faenuccio removed WIP Work in progress review-in-progress A reviewer is thinking about this PR offline. labels May 4, 2023
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bors r+

bors bot pushed a commit that referenced this pull request May 4, 2023
Added a section `num_denom`: the main result is the lemma `exists_reduced_fraction` that shows that every non-zero element `b` in a `localization.away x` of a UFM can be written in a unique way as `b=x^n * a` with `n : ℤ` and `a` not divisible by `x`.



Co-authored-by: Vierkantor <vierkantor@vierkantor.com>
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@bors bors bot changed the title feat(ring_theory/localization/away) : Add num_denom section [Merged by Bors] - feat(ring_theory/localization/away) : Add num_denom section May 4, 2023
@bors bors bot closed this May 4, 2023
@bors bors bot deleted the PR_away branch May 4, 2023 15:44
bors bot pushed a commit to leanprover-community/mathlib4 that referenced this pull request May 10, 2023
…tor` as in #18830 (#3558)

Add lemma `max_powerFactor` needed in leanprover-community/mathlib#18830 and modified there.
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