Definition is_resource_pred (p: address -> pred rmap) (q: resource -> address -> nat -> Prop) :=
forall l w, (p l) w = q (w @ l) l (level w).
Definition resource_stable (p: address -> pred rmap) :=
forall l w w', w @ l = w' @ l -> level w = level w' -> (p l) w = (p l) w'.

Lemma is_resource_pred_resource_stable: forall {p},
(exists q, is_resource_pred p q) -> resource_stable p.