proposition: Lemma sqr_ascend : forall n : nat, n > 1 -> n < n * n.
proof: Proof. simple induction n. intros. elim (lt_n_O 1). assumption. intros m IHm. intro. unfold gt in H. unfold lt in H. elim (le_lt_or_eq 1 m). intros. simpl in |- *. apply lt_n_S. rewrite <- (mult_n_Sm m m). rewrite plus_comm. apply lt_plus_trans. apply lt_plus_trans. apply IHm. assumption. intros. rewrite <- H0. simpl in |- *. unfold lt in |- *. apply le_S. apply le_n. apply le_S_n. assumption. Qed.
imports: ZArith EqNat