(* NOT TRUE, because the shares might not match Lemma extensionally_yesat: forall pp k sh l, extensionally (yesat pp k sh l) = yesat pp k sh l. *)
Program Definition noat (l: AV.address) : pred rmap :=
fun m => identity (m @ l).
Next Obligation.
intros; intro; intros.
apply (age1_resource_at_identity _ _ l H); auto.
Qed.
Definition resource_share (r: resource) : option share :=
match r with
| YES sh _ _ _ => Some sh
| NO sh _ => Some sh
| PURE _ _ => None
end.
Definition nonlock (r: resource) : Prop :=
match r with
| YES _ _ k _ => isVAL k \/ isFUN k
| NO _ _ => True
| PURE _ _ => False
end.

Lemma resource_share_join: forall r1 r2 r sh1 sh2 sh,
resource_share r1 = Some sh1 ->
resource_share r2 = Some sh2 ->
join r1 r2 r ->
join sh1 sh2 sh ->
resource_share r = Some sh.