proposition: Lemma lem_add m1 m2 n1 n2 : (m1 <= n1 -> m2 <= n2 -> (m1 + m2)%MM <= (n1 + n2)%MM)%O.
proof: Proof. move=> le1 le2; apply/(le_trans (y := m1 + n2)%MM). by rewrite lemc_add2r. by rewrite lemc_add2l. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq path) mathcomp(choice fintype tuple finfun bigop finset binomial) mathcomp(order fingroup perm ssralg zmodp poly ssrint) mathcomp(matrix vector) mathcomp(bigenough) ssrcomplements freeg