Proposition: Order Relation for Integers is Strict Total
The order relation for integers "$<$" defines a strict total order on the set $\mathbb Z$ of integers, i.e. for any integers \(x,y,z\in\mathbb Z\), we have
 Only one of the following cases can be true: either \(x=y\), or \(x > y\), or \(x < y\) trichotomy).
 If $x < y$ and $y < z$, then $x < z$ transitivity).
 The same applies for the relation "$ > $".
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