Definition resource_fmap (f:(pred rmap)->(pred rmap)) (x:resource) : resource :=
    match x with
    | NO => NO
    | YES sh k p => YES sh k (preds_fmap f p)
    | PURE k p => PURE k (preds_fmap f p)
    end.

Lemma resource_fmap_id : resource_fmap (id (pred rmap)) = id resource.