A theorem concerning the positive metric

It is proved that if then-point correlation functions of a system vanish for alln>N then they vanish for alln>2. The theorem is valid for a wide variety of formalisms and an explicit proof is given for a Bose system with the canonical commutation relations; a proof is sketched out for a relativistic field theory of the Wightman type. The essential property used in the proof is the positive definite metric.