Has anyone ever applied the Ito formula on $|X^+|^2$ for $X^+ = \max(X,0)$ with

$X(t) = X(0) + M(t) + V(t)$, where $M(t)$ is a local martingale and $V(t)$ is bounded variation process. I found it in a lemma for $M$ continuous local martingale but the proof was not provided either.

Thanks for any hint.