proposition: Lemma lemc_lt_add m1 m2 n1 n2 : (m1 <= n1 -> m2 < n2 -> (m1 + m2)%MM < (n1 + n2)%MM)%O.
proof: Proof. move=> le lt; apply/(le_lt_trans (y := n1 + m2)%MM). by rewrite lemc_add2l. by rewrite ltmc_add2r. 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