Small-step semantics: for-loops

Question

I'm trying to construct the small-step semantic rules involving the for-loops, but I can't find anything about it in the literature (only about while-loops).

I was wondering if anyone could help me out with this? This is a first attempt, where $s$ represents a statement and $e$ an expression:

$\quad \displaystyle\sigma, \text{for } s_1 \, e_1 \, e_2 \, s_2 \, \rightarrow \, \sigma, \text{if } e_1 \text{ then (} s_2 ; \, e_2; \, \text{for } s_1 \, e_1 \, e_2 \, s_2 \text{ ) else } skip$

Where $\sigma$ is a local value store, $s_1$ is for example $i = 0$, $e_1$ could equal $i < 4$ and $e_2$ $i=i+1$.