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)).

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).