I have a question about ordered integral domains. What do I need to do to prove that for $a \in D^p$, $-a \in D^p$, or $a = 0$ and $b \in D^p$, $-b \in D^p$ or $b = 0$ then
1) $\mathrm{abs}(a) \geq a \geq -\mathrm{abs}(a)$
and
2) $\mathrm{abs}(a) + \mathrm{abs}(b) \geq \mathrm{abs}(a+b)$.
Do I need to split each equation by switching the inequality sign?