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_eq_neg :
forall bf1 bf2 : bool_fun,
bool_fun_eq (bool_fun_neg bf1) (bool_fun_neg bf2) -> bool_fun_eq bf1 bf2.