proposition: Lemma addsmx_addKl n m1 m2 (A : 'M_(m1, n)) (B C : 'M_(m2, n)) : (B <= A)%MS -> (A + (B + C)%R :=: A + C)%MS.
proof: Proof. move=> sBA; apply/eqmxP; rewrite !addsmx_sub !addsmxSl. by rewrite -{3}[C](addKr B) !addmx_sub_adds ?eqmx_opp. 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)