In the context of Proposition 6.12, let \(t \in\{0,1, \ldots, T-1\}\) and \(A_{t} \in \mathscr{F}_{t}\) and suppose that, for some \(s \in\{t+1, \ldots, T\}\), there exists an event \(A_{s} \in \mathscr{F}_{s}\) such that \(A_{s} \subseteq A_{t}\) and \(q_{A_{s} \mid A_{t}}^{*} eq q_{A_{s}}^{*} / q_{A_{t}}^{*}\). Prove that such a price system admits arbitrage opportunities and, hence, cannot correspond to an equilibrium.