Definition nodes_preserved (cfg cfg' : BDDconfig) :=
  forall (x : BDDvar) (l r node : ad),
  MapGet _ (fst cfg) node = Some (x, (l, r)) ->
  MapGet _ (fst cfg') node = Some (x, (l, r)).

Lemma nodes_preserved_1 : forall (cfg : BDDconfig) (node : ad) (n m : nat) (x : BDDvar) (l r : ad), BDDconfig_OK cfg -> MapGet _ (fst cfg) node = Some (x, (l, r)) -> n = S m -> nat_of_N (var cfg node) < n -> nodes_preserved (fst (BDDneg_2 (fst (BDDneg_2 cfg l m)) r m)) (fst (BDDneg_2 cfg node n)).