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: monotonic TX TY F.
Hypothesis HG: monotonic TX TY G.

(** Iteration respect monotonicity *)
Lemma UExp_mon: forall n, monotonic TX TY (fun R => UExp F R n).