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_fmap_singleton: forall f g k v, ghost_fmap f g (singleton k v) =
singleton k (match v with (a, b) => (a, preds_fmap f g b) end).