proposition: Lemma liveness : forall (x : Z) (c : Config), legal x c -> (co c > 0)%Z -> exists t : transition c, legal x (next_config c t).
proof: Proof. intros. generalize (Zeven.Zeven_odd_dec (co c)). intro. elim H1. intro. split with (divide c H0 a). apply after. auto. intro. split with (decrement c H0 b). apply after. auto. Qed.
imports: ZArith Omega