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_forall {I X} (P : I -> X -> Prop) (m : dist X) : (forall i, plift (P i) m) -> plift (pforall P) m.