Module R := R.
Hint Resolve (@subp_sepcon _ Join_rmap Perm_rmap Sep_rmap): contractive.
unfold identity_rmap; intros.
rewrite R.unsquash_squash.
simpl.
apply extensionality; intro l.
unfold compose; simpl; auto.
Qed.
(* Lemma make_simple_rmap: forall n (f: AV.address -> resource) , AV.valid (fun l => res_option (f l)) -> (forall l, match f l with YES _ _ (SomeP _ _) => False | _ => True end) -> exists phi:rmap, level phi = n /\ resource_at phi = f. *)
Ltac do_map_arg :=
match goal with |- ?a = ?b =>
match a with context [map ?x _] =>
match b with context [map ?y _] => replace y with x; auto end end end.
Implicit Arguments resource_at_empty.
Ltac inj_pair_tac :=
match goal with H: (@existT ?U ?P ?p ?x = @existT _ _ _ ?y) |- _ =>
generalize (@inj_pair2 U P p x y H); clear H; intro; try (subst x || subst y)
end.
Definition no_preds (r: resource) :=
match r with NO => True | YES _ _ pp => pp=NoneP | PURE _ pp => pp=NoneP end.

Lemma join_YES_pfullshare2:
forall pp k p x y, join x (YES  (mk_lifted Share.top pp) k p) y -> (NO, YES pfullshare k p) = (x,y).