[Merged by Bors] - feat(ring_theory): factorize a non-unit into irreducible factors without multiplying a unit #13682
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multiset.prod_erase
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If @eric-wieser has no further comments can I get a bors d+? |
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Thanks! bors d+ |
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…out multiplying a unit (#13682) Used in https://proofassistants.stackexchange.com/a/1312/93. Also adds simp lemma `multiset.prod_erase` used in the main proof and the auto-generated additive version, which is immediately analogous to [list.prod_erase](https://leanprover-community.github.io/mathlib_docs/data/list/big_operators.html#list.prod_erase). Also removes some extraneous namespace prefix.
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+ Shorten the proof of `exists_irreducible_factor` using `well_founded.has_min` instead of `well_founded.fix`. + Remove use of `simp` in `induction_on_irreducible`; now a pure term-mode proof except for the classical instance. + Change the proof of `not_unit_iff_exists_factors_eq` (just added in [#13682](#13682)) to use induction. The new proof doesn't require the `multiset.prod_erase` introduced in [#13682](#13682), but is about as complex as the old one, so I might change it back if reviewers prefer.
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Used in https://proofassistants.stackexchange.com/a/1312/93. Also adds simp lemma
multiset.prod_eraseused in the main proof and the auto-generated additive version, which is immediately analogous to list.prod_erase. Also removes some extraneous namespace prefix.