Definition singleton_rmap  (v v': adr) (m: rmap) : rmap :=
proj1_sig
(make_rmap (fun i => if eq_dec i v then YES pfullshare (VAL v') NoneP  else core m @ i )
I (level m) (singleton_rmap_OK _ _ m)).

(* Specifications: *)
Lemma singleton_rmap_level: forall x y m,
level (singleton_rmap x y m) = level m.
Lemma singleton_rmap_mapsto:
forall x y n, app_pred (mapsto x y) (singleton_rmap x y n).