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[Merged by Bors] - feat(Nat/Factorization): add exists_eq_two_pow_mul_odd#14166

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[Merged by Bors] - feat(Nat/Factorization): add exists_eq_two_pow_mul_odd#14166
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@rwst rwst commented Jun 26, 2024

Any nonzero natural number is the product of an odd part m and a power of two 2 ^ k.

This is a trivial consequence of the existing exists_eq_pow_mul_and_not_dvd, but performs a convenient restatement in terms of Odd.

Needed by #14049.

Co-authored-by: Thomas Browning tb65536@uw.edu


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@rwst rwst added awaiting-review easy < 20s of review time. See the lifecycle page for guidelines. awaiting-CI This PR does not pass CI yet. This label is automatically removed once it does. t-number-theory Number theory (also use t-algebra or t-analysis to specialize) labels Jun 26, 2024
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github-actions bot commented Jun 26, 2024

PR summary 3fab56ec89

Import changes

No significant changes to the import graph


Declarations diff

+ exists_eq_two_pow_mul_odd

You can run this locally as follows
## summary with just the declaration names:
./scripts/no_lost_declarations.sh short <optional_commit>

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

@github-actions github-actions bot removed the awaiting-CI This PR does not pass CI yet. This label is automatically removed once it does. label Jun 26, 2024
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LGTM, but someone else should take a look since I helped write it.

@eric-wieser eric-wieser changed the title feat(Nat/Factorization): lemma feat(Nat/Factorization): add exists_eq_two_pow_mul_odd Jun 26, 2024
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bors merge

Thanks! I updated the PR description to explain why I think this lemma is just over the line of "too trivial a consequence of an existing result"

@github-actions github-actions bot added ready-to-merge This PR has been sent to bors. and removed awaiting-review labels Jun 26, 2024
mathlib-bors bot pushed a commit that referenced this pull request Jun 27, 2024
Any nonzero natural number is the product of an odd part `m` and a power of two `2 ^ k`.

This is a trivial consequence of the existing `exists_eq_pow_mul_and_not_dvd`, but performs a convenient restatement in terms of `Odd`.

Needed by #14049.

Co-authored-by: Thomas Browning <tb65536@uw.edu>
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mathlib-bors bot commented Jun 27, 2024

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(Nat/Factorization): add exists_eq_two_pow_mul_odd [Merged by Bors] - feat(Nat/Factorization): add exists_eq_two_pow_mul_odd Jun 27, 2024
@mathlib-bors mathlib-bors bot closed this Jun 27, 2024
@mathlib-bors mathlib-bors bot deleted the rwst/factorization02 branch June 27, 2024 00:36
dagurtomas pushed a commit that referenced this pull request Jul 2, 2024
Any nonzero natural number is the product of an odd part `m` and a power of two `2 ^ k`.

This is a trivial consequence of the existing `exists_eq_pow_mul_and_not_dvd`, but performs a convenient restatement in terms of `Odd`.

Needed by #14049.

Co-authored-by: Thomas Browning <tb65536@uw.edu>
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