proposition: Lemma matrix_modr m1 m2 m3 n (A : 'M_(m1, n)) (B : 'M_(m2, n)) (C : 'M_(m3, n)) : (C <= A -> (A :&: B) + C :=: A :&: (B + C))%MS.
proof: Proof. by rewrite !(capmxC A) -!(addsmxC C); apply: matrix_modl. 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)