Section A'.
Variable R: relation2 X Y.
Variable E: relation2 X X.
Variable T: relation2 Y Y.
End A'.
Variables F G: function X Y.
Hypothesis HF: monotonic TX TY F.
Hypothesis HG: monotonic TX TY G.

(** Binary union respect monotonicity *)
Lemma Union2_mon: monotonic TX TY (Union2 F G).