Instance list_order A : @PCM_order (list_PCM (discrete_PCM A)) list_incl.Instance set_PCM A : Ghost := { valid := fun _ : Ensemble A => True;
   Join_G a b c := Disjoint a b /\ c = Union a b }.Definition ghost_set {A} g s := own(RA := set_PCM A) g s NoneP.

Lemma ghost_set_subset : forall {A} g (s s' : Ensemble A) (Hdec : forall a, In s' a \/ ~In s' a), Included s' s -> ghost_set g s = ghost_set g s' * ghost_set g (Setminus s s').