proposition: Lemma Umult_lt_compat : forall x y z t, x < y -> z < t -> x * z < y * t.
proof: Proof. intros. assert (0<y); auto. apply Ule_lt_trans with x; auto. assert (0<t); auto. apply Ule_lt_trans with z; auto. apply (Ueq_orc 0 z); auto; intros. rewrite <- H3. rewrite Umult_zero_right; auto. apply Ult_trans with (y * z); auto. Qed.
imports: ALEA(Utheory)