Definition no_preds (r: resource) :=
   match r with NO => True | YES _ _ pp => pp=NoneP | PURE _ pp => pp=NoneP end.

(* Specifications: *)
Lemma rmap_unage_age: forall r, age (rmap_unage r) r.
Lemma join_YES_pfullshare1: forall pp k p x y, join (YES (mk_lifted Share.top pp) k p) x y -> (NO, YES pfullshare k p) = (x,y).
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).