proposition: Lemma Ndiv_le : forall n p, 0 < p -> (n | p) -> n <= p.
proof: Proof. intros. destruct H0. destruct p. apply Nat.lt_irrefl in H. contradiction. destruct n. auto with arith. destruct q. simpl in H0. discriminate H0. replace (S n) with (1*S n). rewrite H0. apply Nat.mul_le_mono. auto with arith. auto with arith. rewrite Nat.mul_1_l. trivial. Qed.
imports: Coq(Arith Euclid Compare Lia)