Definition gname := nat.
Definition own {RA: Ghost} (n: gname) (a: G) (pp: preds) :=
EX v : _, Own (singleton n (existT _ RA (exist _ a v), pp)).
Definition list_set {A} (m : list (option A)) k v : list (option A) :=
firstn k m ++ repeat None (k - length m) ++ Some v :: skipn (S k) m.

Lemma ghost_valid_2: forall {RA: Ghost} g a1 a2 pp,
own g a1 pp * own g a2 pp |-- !!ghost.valid_2 a1 a2.