Admitted.

Lemma state_plift_P_split :
forall {C : Config} {S M X} `{PredLift M}
(P Q : X -> Prop) (Pre Post: S -> Prop)
(s : StateT S M X),
state_plift Pre Post P s /\
state_plift Pre Post Q s ->
state_plift Pre Post (fun x => (P x /\ Q x)) s.