As in equation (7.4), define \(\varepsilon_{t}^{\mathbb{F}}:=s_{t}^{\mathbb{P}}+d_{t}-r_{f} s_{t-1}^{\mathbb{F}}\), for all \(t \in \mathbb{N}\), with an analogous definition for the information flow \(\mathbb{G}\). Suppose that \(r_{f}>1\) and that

\[\operatorname{Var}\left(\varepsilon_{t+s}^{\mathbb{F}}\right)=\operatorname{Var}\left(\varepsilon_{t}^{\mathbb{F}}\right) \quad \text { and } \quad \operatorname{Var}\left(\varepsilon_{t+s}^{\mathbb{G}}\right)=\operatorname{Var}\left(\varepsilon_{t}^{\mathbb{G}}\right), \quad \text { for all } t, s \in \mathbb{N} \text {. }\]

Under this assumption, show that inequality (7.12) holds.