  The Lieb-Schultz-Mattis theorem for spin chains is generalized to a wide
range of models of interacting electrons and localized spins in one-dimensional
lattice. The existence of a low-energy state is generally proved except for
special commensurate fillings where a gap may occur. Moreover, the crystal
momentum of the constructed low-energy state is $2k_F$, where $k_F$ is the
Fermi momentum of the non-interacting model, corresponding to Luttinger's
theorem. For the Kondo lattice model, our result implies that $k_F$ must be
calculated by regarding the localized spins as additional electrons.
