Definition initBDDconfig :=
(initBDDstate, (initBDDsharing_map, ad_S (ad_S N0))).
Definition BDDconfig_OK (cfg : BDDconfig) :=
match cfg return Prop with
| (bs, (share, counter)) =>
BDDstate_OK bs /\
BDDsharing_OK bs share /\
(forall a : ad, Nleb counter a = true -> MapGet _ bs a = None) /\
Nleb (ad_S (ad_S N0)) counter = true
end.

Lemma config_OK_zero :
forall cfg : BDDconfig,
BDDconfig_OK cfg -> MapGet _ (fst cfg) BDDzero = None.