proposition: 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.
proof: Proof. move=> sAC; move/(addsmxS sAC); apply: submx_trans. by rewrite addmx_sub ?addsmxSl ?addsmxSr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup perm order) mathcomp(div prime binomial ssralg finalg zmodp matrix)