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

Lemma addmx_sub_adds m m1 m2 n (A : 'M_(m, n)) (B : 'M_(m, n))
(C : 'M_(m1, n)) (D : 'M_(m2, n)) :
(A <= C -> B <= D -> (A + B)%R <= C + D)%MS.