proposition: Lemma sumsmx_sup i0 P m n (A : 'M_(m, n)) (B_ : I -> 'M_n) : P i0 -> (A <= B_ i0)%MS -> (A <= \sum_(i | P i) B_ i)%MS.
proof: Proof. by move=> Pi0 sAB; apply: submx_trans sAB _; rewrite (bigD1 i0) // addsmxSl. 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)