(* Lemma BDDex_var_le : (Nleb (node_height (Fst BDDex) (Snd BDDex)) (node_height cfg node))=true. *)
Fixpoint BDDunivl (cfg : BDDconfig) (ul : list ad)
(node : ad) (ly : list BDDvar) {struct ly} : BDDconfig * ad :=
match ly with
| nil => (cfg, node)
| y :: ly' =>
match BDDunivl cfg ul node ly' with
| (cfg1, node1) => BDDuniv cfg1 (node1 :: ul) y node1
end
end.

Lemma BDDunivl_lemma :
forall (ly : list BDDvar) (cfg : BDDconfig) (ul : list ad) (node : ad),
BDDconfig_OK cfg ->
used_list_OK cfg ul ->
used_node' cfg ul node ->
BDDconfig_OK (fst (BDDunivl cfg ul node ly)) /\
config_node_OK (fst (BDDunivl cfg ul node ly))
(snd (BDDunivl cfg ul node ly)) /\
used_nodes_preserved cfg (fst (BDDunivl cfg ul node ly)) ul /\
bool_fun_eq
(bool_fun_of_BDD (fst (BDDunivl cfg ul node ly))
(snd (BDDunivl cfg ul node ly)))
(bool_fun_univl (bool_fun_of_BDD cfg node) ly).