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_ex_is_mu_ex : bool_fun_eq (bool_fun_of_BDD (fst (BDDmu_ex gc cfg ul nodet nodeg)) (snd (BDDmu_ex gc cfg ul nodet nodeg))) (bool_fun_mu_ex (bool_fun_of_BDD cfg nodet) (bool_fun_of_BDD cfg nodeg)).