proposition: Lemma sub_sumsmxP P m n (A : 'M_(m, n)) (B_ : I -> 'M_n) : reflect (exists u_, A = \sum_(i | P i) u_ i *m B_ i) (A <= \sum_(i | P i) B_ i)%MS.
proof: Proof. by rewrite -(eqmx_sums (fun _ _ => genmxE _)); apply/sub_sums_genmxP. 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)