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 split_post_and_pred {S X Y} (m : StateT S dist X) (m' : StateT S dist Y) Pre Post P : state_plift2 Pre triv2 P m m' -> state_plift2 Pre Post triv2 m m' -> state_plift2 Pre Post P m m'.