Definition rmap'2pre_rmap (f: rmap') : f_pre_rmap (pred rmap) :=
(fun x : address => resource2res (fst f x), ghost2g (snd f)).
Definition pre_rmap2rmap' (f: f_pre_rmap (pred rmap)) : rmap' :=
(fun l : address => res2resource (fst f l), g2ghost (snd f)).

Lemma pre_rmap2rmap'2pre_rmap :
forall x,  pre_rmap2rmap' (rmap'2pre_rmap x) = x.