proposition: Theorem iter_app: forall l1 l2, iter (app l1 l2) = g (iter l1) (iter l2).
proof: Proof. intros l1; elim l1; simpl; auto. intros l2; rewrite g_sym; auto. intros a l H l2; rewrite H. rewrite g_trans; auto. Qed.
imports: List Permutation Arith