Definition triv2 {X Y} : X -> Y -> Prop :=
  fun _ _ => True.Definition pforall {I X} (P : I -> X -> Prop) : X -> Prop :=
  fun x => forall i, P i x.

Lemma plift_triv {X} (m : dist X) (P : X -> Prop) : (forall x, P x) -> plift P m.