Proof of Wald's equation by stopping indicators

If $M$ is a stopping time for independent identically distributed integrable variables $X_i$ and $\mathbb{E}M<\infty$, then $\{M\ge i\}$ depends only on $X_1,\dots ,X_{i-1}$ and is independent of $X_i$. HenceThe interchange is justified because the same calculation with $|X_i|$ gives finite expected absolute sum.