proposition: Lemma genmx_adds m1 m2 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) : (<<(A + B)%MS>> = <<A>> + <<B>>)%MS.
proof: Proof. rewrite -(eq_genmx (adds_eqmx (genmxE A) (genmxE B))). by rewrite [@addsmx]unlock !addsmx_nop_id !(fun_if (@genmx _ _ _)) !genmx_id. 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)