Off-Diagonal Long-Range Order in Bose Liquids: Irrotational Flow and Quantization of Circulation

On the basis of gauge invariance, it is proven in an elementary and straightforward manner, but without invoking any {\it ad hoc} assumption, that the existence of off-diagonal long-range order in one-particle reduced density matrix in Bose liquids implies both the irrotational flow in a simply connected region and the quantization of circulation in a multiply connected region, the two fundamental properties of a Bose superfluid. The origin for both is the phase coherence of condensate wave-functions. Some relevant issues are also addressed.