proposition: Lemma capmxS m1 m2 m3 m4 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) (C : 'M_(m3, n)) (D : 'M_(m4, n)) : (A <= C -> B <= D -> A :&: B <= C :&: D)%MS.
proof: Proof. by move=> sAC sBD; rewrite sub_capmx {1}capmxC !(submx_trans (capmxSr _ _)). 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)