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_split_post_and_pred {X} (m : Poram X) Pre Post P : poram_lift Pre triv P m -> poram_lift Pre Post triv m -> poram_lift Pre Post P m.