The Frank–Wolfe duality gap certificate

Show that the quantity $\mathrm{gap}_t = \langle\nabla f(x_t), x_t - s_t\rangle$ computed at each Frank–Wolfe step, where $s_t = \arg\min_{s\in\mathcal C}\langle\nabla f(x_t),s\rangle$, is an upper bound on $f(x_t)-f^\star$. Explain why this makes Frank–Wolfe self-certifying.