Definition get_val_equiv s s' : Prop :=
  forall k, get_val k s = get_val k s'.

Lemma state_plift_pre {S X} (Pre Pre' Post : S -> Prop) (P : X -> Prop) (m : StateT S dist X) : (forall s, Pre' s -> Pre s) -> state_plift Pre Post P m -> state_plift Pre' Post P m.