proposition: Lemma next_n_S: forall n m, next_n S n m = plus n m.
proof: Proof. intros n m; generalize n; elim m; clear n m; simpl; auto with arith. intros m H n; case n; simpl. - rewrite H; auto with arith. - intros n1; rewrite H; simpl; auto with arith. Qed.
imports: List Permutation Arith