  We give an explicit proof of equivalence of the two-point function to
one-loop order in the two formalisms of thermal $\lambda \phi^3$ theory based
on the expressions in the real-time formalism. It is indicated that the
key-point of completing the proof is to separate carefully the imaginary part
of the zero-temperature loop integral from relevant expressions and this fact
will certainly be very useful for examination of the equivalence problem of the
two formalisms of thermal field theory in other theories, including the one of
the propagators for scalar bound states in a NJL model.
