Section BDDsubst_results.
Variable cfg : BDDconfig.
Variable ul : list ad.
Variable node1 node2 : ad.
Variable x : ad.
Hypothesis cfg_OK : BDDconfig_OK cfg.
Hypothesis ul_OK : used_list_OK cfg ul.
Hypothesis used1 : used_node' cfg ul node1.
Hypothesis used2 : used_node' cfg ul node2.
Hypothesis node2_ind : bool_fun_independent (bool_fun_of_BDD cfg node2) x.

Lemma BDDsubst_is_subst :
bool_fun_eq
(bool_fun_of_BDD (fst (BDDsubst cfg ul node1 x node2))
(snd (BDDsubst cfg ul node1 x node2)))
(bool_fun_subst x (bool_fun_of_BDD cfg node2) (bool_fun_of_BDD cfg node1)).