Definition ext_ref {Z} (ora : Z) : {g : ghost.Ghost & {a : ghost.G | ghost.valid a}} :=
  existT _ (ext_PCM _) (exist _ _ (valid_ext_ref ora)).

Lemma valid_ext_both : forall {Z} (ora : Z), @valid (ext_PCM _) (Some (Tsh, Some ora), Some (Some ora)).