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

Lemma BDDalloc_no_new_node : forall (cfg : BDDconfig) (l l1 r r1 a : ad) (x x1 : BDDvar), MapGet _ (fst (fst (BDDalloc cfg x l r))) a = Some (x1, (l1, r1)) -> a = snd (snd cfg) \/ MapGet _ (fst cfg) a = Some (x1, (l1, r1)).