Canonical addsmx_comoid n := Monoid.ComLaw (@addsmxC n n n).

Lemma sub_addsmxP m1 m2 m3 n
(A : 'M_(m1, n)) (B : 'M_(m2, n)) (C : 'M_(m3, n)) :
reflect (exists u, A = u.1 *m B + u.2 *m C) (A <= B + C)%MS.