PartialOrder - Dr. A's Wiki

Definition: Partial Order (see PoSet for partially ordered set).

A relation $\leq$ is a partial order on a set $S$ if it has:

Reflexivity: $a \leq a$ for all $a \in S$ .
Antisymmetry: $a \leq b$ and $b \leq a \Rightarrow a = b$ .
Transitivity: $a \leq b$ and $b \leq c \Rightarrow a \leq c$ .