Module Trashcan.
(* Note: This approach to proving HOcontractive doesn't automate as well as the methods above.*)

Lemma exp_HOcontractive {A}{agA: ageable A}:
forall X Y (G: Y -> X -> X) (F: Y -> X -> pred A -> pred A),
(forall y x, contractive (F y x)) ->
HOcontractive (fun (R: X -> pred A) (x: X) => EX y: Y, F y x (R (G y x))).