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)).