  We apply a generalized version of the Lieb-Schultz-Mattis Theorem to
fermionic ladder systems to show the existence of a low-lying excited state
(except for some special fillings). This can be regarded as a non-perturbative
proof for the conservation under interaction of the sum of the Fermi wave
vectors of the individual channels, corresponding to a generalized version of
the Luttinger Theorem to fermionic ladder systems. We conclude by noticing that
the Lieb-Schultz-Mattis Theorem is not applicable in this form to show the
existence of low-lying excitations in the limit that the number of legs goes to
infinity, e.g. in the limit of a 2D plane.
