(* end hide *)
Section UIter'.
Variable X: Type.
Variable F: function X X.
Hypothesis HF: forall R, eeq (trans (F R)) (F (trans R)) .
Hypothesis HF': increasing F.

Lemma UExp_trans: forall n R, eeq (trans (UExp F R n)) (UExp F (trans R) n).
intros n R; induction n as [ | n IH ]; split; intros x y H; auto; celim H; intro H.