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_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_ex gc cfg ul nodet nodeg)) /\ config_node_OK (fst (BDDmu_ex gc cfg ul nodet nodeg)) (snd (BDDmu_ex gc cfg ul nodet nodeg)) /\ used_nodes_preserved cfg (fst (BDDmu_ex gc cfg ul nodet nodeg)) ul /\ 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)).