proposition: Lemma sub_rVP n (u v : 'rV[F]_n) : reflect (exists a, u = a *: v) (u <= v)%MS.
proof: Proof. apply: (iffP submxP) => [[w ->] | [a ->]]. by exists (w 0 0); rewrite -mul_scalar_mx -mx11_scalar. by exists a%:M; rewrite mul_scalar_mx. 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)