Variables F G: function X Y.
Hypothesis HF: monotonic TX TY F.
Hypothesis HG: monotonic TX TY G.

(* Specifications: *)
(** Composition respect monotonicity *)
Lemma Comp_mon: monotonic TX TY (Comp G F).
(** Binary union respect monotonicity *)
Lemma Union2_mon: monotonic TX TY (Union2 F G).
Section Union.