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

Lemma BDDalloc_preserves_zero : forall (cfg : BDDconfig) (l r : ad) (x : BDDvar), BDDconfig_OK cfg -> MapGet _ (fst (fst (BDDalloc cfg x l r))) BDDzero = None.