Definition bool_fun_impl (bf1 bf2 : bool_fun) : bool_fun :=
fun vb : var_binding => implb (bf1 vb) (bf2 vb).

Lemma bool_fun_impl_is_neg_or_bf2 :
forall bf1 bf2 : bool_fun,
bool_fun_eq (bool_fun_impl bf1 bf2) (bool_fun_or (bool_fun_neg bf1) bf2).