Definition rmap_fmap (f:(pred rmap)->(pred rmap)) (x:rmap') : rmap' :=
    match x with exist m H => exist (fun m => valid m) (resource_fmap f oo m) (valid_res_map f m H) end.

(* Specifications: *)
Lemma rmap_fmap_id : rmap_fmap (id (pred rmap)) = id rmap'.
Lemma rmap_fmap_comp : forall f g, rmap_fmap g oo rmap_fmap f = rmap_fmap (g oo f).