Definition rmap'2pre_rmap (r: rmap') : pre_rmap (pred rmap).Definition pre_rmap2rmap' (r: pre_rmap (pred rmap)) : rmap'.

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