End A.
Section B.
Variables X Y: Type.
Variable TX: reduction_t A X.
Variable TY: reduction_t A Y.
Variables F G: function X Y.
Hypothesis HF: wmonotonic TX TY F.
Hypothesis HG: wmonotonic TX TY G.

(* Specifications: *)
(** Iteration respects weak monotonicity *)
Lemma UExp_wmon: forall n, wmonotonic TX TY (fun R => UExp F R n).
Lemma UIter_wmon: wmonotonic TX TY (UIter F).
End B.