[Merged by Bors] - feat(data/finset/noncomm_prod): add noncomm_prod_mul_distrib #12524
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adding `list.prod_commute`, `multiset.noncomm_prod_commute` and `finset.noncomm_prod_commute`.
The non-commutative version of `finset.sum_union`
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This was referenced Mar 8, 2022
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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src/data/finset/noncomm_prod.lean
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| noncomm_prod s (f * g) | ||
| begin | ||
| intros x hx y hy, | ||
| by_cases h : x = y, { subst h }, | ||
| apply commute.mul_left; apply commute.mul_right, | ||
| { exact comm_ff x hx y hy }, | ||
| { exact (comm_gf y hy x hx (ne.symm h)).symm }, | ||
| { exact comm_gf x hx y hy h }, | ||
| { exact comm_gg x hx y hy }, | ||
| end | ||
| = noncomm_prod s f comm_ff * noncomm_prod s g comm_gg := |
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I think the statement would become more readable if you extracted the subproof into a separate aux-lemma.
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The non-commutative version of `finset.sum_union`.
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The non-commutative version of `finset.sum_union`.
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The non-commutative version of
finset.sum_union.