proposition: Lemma summx_sub m1 m2 n (B : 'M_(m2, n)) I (r : seq I) (P : pred I) (A_ : I -> 'M_(m1, n)) : (forall i, P i -> A_ i <= B)%MS -> ((\sum_(i <- r | P i) A_ i)%R <= B)%MS.
proof: Proof. by move=> leAB; elim/big_ind: _ => // [|C D]; [apply/sub0mx | apply/addmx_sub]. 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)