End Snapshot.
Definition pos_PCM := ghost_PCM.pos_PCM.
Definition ref_PCM := ghost_PCM.ref_PCM.
Notation completable := ghost_PCM.completable.
Section Reference.
Context {P : Ghost}.
Definition ghost_reference g a := own(RA := ref_PCM P) g (None, Some a) NoneP.
Definition ghost_part g sh a := own(RA := ref_PCM P) g (Some (sh, a), None) NoneP.
Definition ghost_part_ref g sh a r :=
own(RA := ref_PCM P) g (Some (sh, a), Some r) NoneP.

Lemma self_completable : forall a, completable (Some (Tsh, a)) a.
End Reference.