To prove an algorithm's correctness, I need to show that
$|x|+|x+\Delta h+\Delta s| \geq |x + \Delta s|+|x+\Delta h|$
when $\Delta h > 0$ and $\Delta s > 0$. Mathematica simplifies this to True, but I don't see how. The only tools I know are the triangle inequality and arithmetic/geometric mean inequality.
How can I prove this inequality?