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: *)
Axiom rmap_fmap_id : rmap_fmap (id _) = id rmap'.
Axiom rmap_fmap_comp : forall f g, rmap_fmap g oo rmap_fmap f = rmap_fmap (g oo f).
Parameter squash : (nat * rmap') -> rmap.