Definition bool_fun_if (x : BDDvar) (bf bf' : bool_fun) : bool_fun :=
  fun vb : var_binding => ifb (vb x) (bf vb) (bf' vb).

Lemma bool_fun_or_one : forall bf : bool_fun, bool_fun_eq (bool_fun_or bf bool_fun_one) bool_fun_one.