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_commute : forall bf bf' : bool_fun, bool_fun_eq (bool_fun_or bf bf') (bool_fun_or bf' bf).