Section A.
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.

(** Composition respects weak monotonicity *)
Lemma Comp_wmon: wmonotonic TX TY (Comp G F).