Consistency of Equations for the Single Scalar Field Case in
  Second-order Gauge-invariant Cosmological Perturbation Theory
  We derived the second-order perturbations of the Einstein equations and the
Klein-Gordon equation for a generic situation in terms of gauge-invariant
variables. The consistency of all the equations is confirmed. This confirmation
implies that all the derived equations of the second order are self-consistent
and these equations are correct in this sense. We also discuss the physical
implication of these equations.
