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 mu_ex_le2 :
forall t be1 be2 : bool_expr,
be_le2 be1 be2 -> be_le2 (mu_ex_eval t be1) (mu_ex_eval t be2).