Let \(\mathbf{F} \subset \mathbf{G}\) and let \(G_{t}-\int_{0}^{t} \gamma_{s} d s\) be a G-martingale. Recalling that \({ }^{(o)} X\) is the \(\mathbf{F}\)-optional projection of a process \(X\), prove that \({ }^{(o)} G_{t}-\int_{0}^{t}{ }^{(o)} \gamma_{s} d s\) is an \(\mathbf{F}\)-martingale.