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).