proposition: Lemma ofnat_lt : forall n m : nat, [n]<[m] <-> (n<m)%nat.
proof: Proof. induction n as [|n IH]; destruct m; repeat rewrite ofnat_zero; split. - intro H; elim (lt_irrefl _ H). - inversion 1. - intros _; apply Nat.lt_0_succ. - intros; apply ofnat_S_gt_0. - intro H; elim (lt_asymm _ _ H); apply ofnat_S_gt_0. - inversion 1. - rewrite !ofnat_succ, <- succ_lt_mono, IH; apply Nat.succ_lt_mono. - rewrite !ofnat_succ, <- succ_lt_mono, IH; apply Nat.succ_lt_mono. Qed.
imports: NumPrelude NZAxioms NZBase NZOrder NZAddOrder PeanoNat