Definition node_OK (bs : BDDstate) (node : ad) :=
    node = BDDzero \/ node = BDDone \/ in_dom _ node bs = true.

Lemma BDDalloc_adjusts_counter : forall (cfg : BDDconfig) (x : BDDvar) (l r a : ad), BDDconfig_OK cfg -> (forall a : ad, Nleb (snd (snd (fst (BDDalloc cfg x l r)))) a = true -> MapGet _ (fst (fst (BDDalloc cfg x l r))) a = None) /\ Nleb (ad_S (ad_S N0)) (snd (snd (fst (BDDalloc cfg x l r)))) = true.