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 poram_lift2_forall {I X Y} Pre
(Post : I -> state -> state -> Prop)
(P : X -> Y -> Prop) (m : Poram X) (m' : Poram Y) : I ->
(forall i, poram_lift2 Pre (Post i) P m m') ->
poram_lift2 Pre (fun x y => forall i, Post i x y) P m m'.