proposition: Lemma chain_none_pred : forall f n p, chain option_cpo f -> p <= n -> f n = None -> f p = None.
proof: Proof. intros f n p Hch Hpn. elim Hpn. auto. intros m Hpm Hfmfp Hfsm. apply Hfmfp. assert (Hcpo : option_cpo (f m) (f (S m))) by apply Hch. inversion Hcpo; auto; rewrite <- Hfsm; auto. Qed.
imports: Relations Classical ClassicalEpsilon Zwf Compare_dec List ZArith