I have to prove some monotonic laws for ordinals. It's quite comfortable for me to show monotonic laws of ordinal addition (e.g. $\beta\leq\gamma\Rightarrow\alpha+\beta\leq\alpha+\gamma$). But when it comes to laws with subtraction, then I'm not sure where to start.
Maybe it's because of definition of subtraction for ordinals $\alpha-\beta=\gamma$, if $\alpha=\beta+\gamma$, which is not constructive.
So, maybe someone can give me a hint on how to prove those:
$\alpha,\beta,\gamma$ - ordinals.
$\alpha>\beta>\gamma \Rightarrow \alpha-\gamma>\beta-\gamma$