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 poram2_split_post_and_pred {X Y} (m : Poram X) (m' : Poram Y) Pre Post P : poram_lift2 Pre triv2 P m m' -> poram_lift2 Pre Post triv2 m m' -> poram_lift2 Pre Post P m m'.