left; exact (proj1 IH _ _ H).
right; apply (HF' (proj1 IH)); apply (proj1 (HF (UExp F R n))); auto.
left; exact (proj2 IH _ _ H).
right; apply (proj2 (HF (UExp F R n))); apply (HF' (proj2 IH) H).
Qed.

(* Specifications: *)
Lemma UIter_trans: forall R, eeq (trans (UIter F R)) (UIter F (trans R)).
intro R; split; intros x y H; destruct H as [ i H ]; exists i.