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.