Definition bool_fun_neg (bf : bool_fun) : bool_fun :=
fun vb : var_binding => negb (bf vb).
Definition bool_fun_or (bf1 bf2 : bool_fun) : bool_fun :=
fun vb : var_binding => bf1 vb || bf2 vb.

Lemma bool_fun_neg_zero : bool_fun_neg bool_fun_zero = bool_fun_one.