Definition BDDordered (bs : BDDstate) (node : ad) :=
match MapGet _ bs node with
| None => True
| Some (n, _) => BDDbounded bs node (ad_S n)
end.
Definition BDD_OK (bs : BDDstate) (node : ad) := BDDordered bs node.
Definition BDDstate_OK (bs : BDDstate) :=
MapGet _ bs BDDzero = None /\
MapGet _ bs BDDone = None /\
(forall a : ad, in_dom _ a bs = true -> BDD_OK bs a).

Lemma initBDDstate_OK : BDDstate_OK initBDDstate.
Definition BDDsharing_map := Map (Map (Map ad)).