Definition rmap_fmap (f g:(pred rmap)->(pred rmap)) (x:rmap') : rmap' :=
              (resource_fmap f g oo fst x, ghost_fmap f g (snd x)).

(* Specifications: *)
Lemma rmap_fmap_id : rmap_fmap (id (pred rmap)) (id (pred rmap)) = id rmap'.
Lemma rmap_fmap_comp : forall f1 f2 g1 g2, rmap_fmap g1 g2 oo rmap_fmap f1 f2 = rmap_fmap (g1 oo f1) (f2 oo g2).