Trichotomy Law


 * Trichotomy Law (Ordering): An ordering $\preceq$ is a total ordering iff:
 * $\forall a, b \in S: a \prec b \lor a = b \lor a \succ b$


 * Trichotomy Law (Integral Domains): in an ordered integral domain, the positivity property $P$ is such that:
 * $\forall a \in D: P \left({a}\right) \lor P \left({-a}\right) \lor a = 0_D$