Definition bool_fun_and (bf1 bf2 : bool_fun) : bool_fun :=
  fun vb : var_binding => bf1 vb && bf2 vb.

Lemma bool_fun_and_is_neg_or_neg_neg : forall bf1 bf2 : bool_fun, bool_fun_eq (bool_fun_and bf1 bf2) (bool_fun_neg (bool_fun_or (bool_fun_neg bf1) (bool_fun_neg bf2))).