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<math>
<math>
I(\overrightarrow{Z_t})
\begin{aligned}
I(\overrightarrow{Z_t}; \overleftarrow{X_t} | \overleftarrow{Z_t}) & = H(\overrightarrow{Z_t} | \overleftarrow{Z_t}) - H(\overrightarrow{Z_t} | \overleftarrow{X_t} , \overleftarrow{Z_t}) \\
& = H(\overrightarrow{Z_t} | \overleftarrow{Z_t}) - H(\overrightarrow{Z_t} | \overleftarrow{X_t}) \\
& = \sum_{l = t+1}^{t+L} \left ( H(Z_l | Z_{l-1}) - H(Z_l | \overrightarrow{Z_{t+1}}, X_t) \right ) \\
\leq = \sum_{l = t+1}^{t+L} \left ( H(Z_l | Z_{l-1}) - H(Z_l | \overrightarrow{Z_{t+1}}, X_t) \right ) \\
= 0
\end{aligned}
</math>
</math>