Global Instance Pred_Dist_Lift : PredLift dist :=
  {|
    plift := @dist_lift;
    plift_ret := dist_lift_ret;
    plift_bind := dist_lift_bind;
    plift_weaken := @dist_lift_weaken;
    plift_split := @dist_split;
    plift_true := @dist_true;
    plift_comm := @dist_comm;
  |}.

Lemma coin_flip_triv : plift (fun _ => True) coin_flip.