Definition be_le2 (be1 be2 : bool_expr) :=
forall ve : var_env,
bool_fun_of_bool_expr be1 ve = true -> bool_fun_of_bool_expr be2 ve = true.

Lemma BDDmu_all_lemma :
forall gc : BDDconfig -> list ad -> BDDconfig,
gc_OK gc ->
forall (cfg : BDDconfig) (ul : list ad) (nodet nodeg : ad),
BDDconfig_OK cfg ->
used_list_OK cfg ul ->
used_node' cfg ul nodet ->
used_node' cfg ul nodeg ->
BDDconfig_OK (fst (BDDmu_all gc cfg ul nodet nodeg)) /\
config_node_OK (fst (BDDmu_all gc cfg ul nodet nodeg))
(snd (BDDmu_all gc cfg ul nodet nodeg)) /\
used_nodes_preserved cfg (fst (BDDmu_all gc cfg ul nodet nodeg)) ul /\
bool_fun_eq
(bool_fun_of_BDD (fst (BDDmu_all gc cfg ul nodet nodeg))
(snd (BDDmu_all gc cfg ul nodet nodeg)))
(bool_fun_mu_all (bool_fun_of_BDD cfg nodet) (bool_fun_of_BDD cfg nodeg)).