[Merged by Bors] - feat(data/matrix/rank): rank of multiplication #18784
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src/data/matrix/rank.lean
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| lemma rank_mul_le_right [strong_rank_condition R] (A : matrix l m R) (B : matrix m n R) : | ||
| (A ⬝ B).rank ≤ B.rank := | ||
| begin | ||
| classical, |
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Why do we need classical here and not in the proof of rank_mul_le_left?
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Because to_lin'_mul is asymmetric in which arguments it needs decidable equality in (the truth is that it doesn't need it at all, but that's a refactor for another time).
I've changed this to a letI to make the reason clearer.
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The "another time" is now: #18800
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This adds a universe-polymorphic version of `rank_comp_le_right`, and then uses it to show `(A ⬝ B).rank ≤ B.rank`; previously we only had `(A ⬝ B).rank ≤ A.rank`. For convenience, this adds the spellings `(A ⬝ B).rank ≤ min A.rank B.rank` and `rank (f.comp g) ≤ min (rank f) (rank g)`, as these map well to the way that rank would be described in words.
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This adds a universe-polymorphic version of
rank_comp_le_right, and then uses it to show(A ⬝ B).rank ≤ B.rank; previously we only had(A ⬝ B).rank ≤ A.rank.For convenience, this adds the spellings
(A ⬝ B).rank ≤ min A.rank B.rankandrank (f.comp g) ≤ min (rank f) (rank g), as these map well to the way that rank would be described in words.