= Solution
A unit <zero-coupon bond> pays one at its maturity, so $P_t(t)=1$. Monotonicity in maturity gives $P_t(t+1)\le1$. Using the <state-price density> representation with $T=t+1$,
$$
\boxed{\mathbb E(Z_{t+1}\mid\mathcal F_t)=Z_tP_t(t+1)\le Z_t.}
$$
The process is positive and integrable, as noted in part (a), and adapted. Thus it is a <supermartingale>. Strictly decreasing maturity prices yield a strict one-step conditional inequality; weak decrease is already enough for the conclusion.
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