  A recent result presented the expansion for the entropy rate of a Hidden
Markov Process (HMP) as a power series in the noise variable $\eps$. The
coefficients of the expansion around the noiseless ($\eps = 0$) limit were
calculated up to 11th order, using a conjecture that relates the entropy rate
of a HMP to the entropy of a process of finite length (which is calculated
analytically). In this communication we generalize and prove the validity of
the conjecture, and discuss the theoretical and practical consequences of our
new theorem.
