proposition: Lemma not_divides_lt : forall n m:nat, 0<m -> m<n -> ~ divides n m.
proof: Proof. intros n m H H0 H1. elim H1; intros q Hq. rewrite <- Hq in H. rewrite <- Hq in H0. generalize H H0; case q. simpl. intros; absurd (0 < 0); auto with arith. clear H H0; intros y Hy Hy'. simpl in Hy'. absurd (n <= n + y * n); auto with arith. Qed.
imports: Arith Lia