proposition: Lemma sumsmxMr P n (A_ : I -> 'M[F]_n) (B : 'M_n) : ((\sum_(i | P i) A_ i)%MS *m B :=: \sum_(i | P i) (A_ i *m B))%MS.
proof: Proof. by apply: eqmx_trans (sumsmxMr_gen _ _ _) (eqmx_sums _) => i _; apply: genmxE. 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)