Definition liftPCMMixin := 
  PCMMixin (@Lift.joinC A) (@Lift.joinA A) 
           (@Lift.unitL A) (@Lift.validL A) (@Lift.validU A).Canonical liftPCM := Eval hnf in PCM (lift A) liftPCMMixin.

(* Specifications: *)
Lemma valid_down : valid (@down A) = false.