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

Lemma orp_HOcontractive {A}{agA: ageable A}: forall X (P Q: (X -> pred A) -> (X -> pred A)),
HOcontractive P -> HOcontractive Q -> HOcontractive (fun R x => P R x || Q R x).