proposition: Lemma col_mx_sub m3 (C : 'M_(m3, n)) : (col_mx A B <= C)%MS = (A <= C)%MS && (B <= C)%MS.
proof: Proof. rewrite !submxE mul_col_mx -col_mx0. by apply/eqP/andP; [case/eq_col_mx=> -> -> | case; do 2!move/eqP->]. 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)