Definition bool_fun_eq (bf1 bf2 : bool_fun) :=
  forall vb : var_binding, bool_fun_eval bf1 vb = bool_fun_eval bf2 vb.

Lemma bool_fun_eq_trans : forall bf1 bf2 bf3 : bool_fun, bool_fun_eq bf1 bf2 -> bool_fun_eq bf2 bf3 -> bool_fun_eq bf1 bf3.