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'.