proposition: Lemma leq_mul m1 m2 n1 n2 : m1 <= n1 -> m2 <= n2 -> m1 * m2 <= n1 * n2.
proof: Proof. move=> le_mn1 le_mn2; apply (@leq_trans (m1 * n2)). by rewrite leq_mul2l le_mn2 orbT. by rewrite leq_mul2r le_mn1 orbT. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype) BinNat Ring