Below is an excerpt from the proof of Ito's formula in the following post :https://almostsuremath.com/2010/01/25/the-generalized-ito-formula/#scn_genito_eq3
We assume $f$ to be a real $C^2$ function from some open subset $U \subset \mathbb{R}^d$ and $X$ is a $d$-dimensional semimartingale.
The statement below states that the terms inside the sum $$\Delta f(X_t) - D_i f(X_{t-})\Delta X_t^i - \frac{1}{2}D_{ij}f(X_{t-})\Delta X_t^i \Delta X_t^j$$ are all finite variation processes.
Why is this the case? I am not familiar with any thoerem stating that jumps of cadlag functions are of bounded variation. I would greatly appreciate if anyone could clear this up for me.
