Let $x_1, x_2,...,x_n$ be random variable defined on a finite probability space $(\Omega, \mathcal{P}(\Omega), P)$. For an arbitrary possible $k$ suppose that $x_k$ is measurable with respect to decomposition $\mathcal{F}_k.$ In addition, suppose that $\mathcal{F}_1 \preceq \mathcal{F}_2 \preceq ... \preceq \mathcal{F}_k. $ Show that $(x_k, \mathcal{F}_k)$, $k=1,2,...,n$ is a martingale if and only if $\mathbb{E}x_{\tau}=\mathbb{E}x_1$ for an arbitrary stopping time $\tau$ (with respect to $\mathcal{F}_k$).
I know that sequence $x_k$ is a martingale because
1) $x_n$ is $\mathcal{F}_n$ measurable random variable.
2) $\mathbb{E}|x_n|<\infty$
3) $\mathbb{E}(x_{n+1}|\mathcal{F}_n=x_n)$
but what about $\tau$? I have no idea how to use it...