Definition: Partial Order (see PoSet for partially ordered set).
A relation $$\le$$ is a partial order on a set $$S$$ if it has:
- Reflexivity: $$a \le a$$ for all $$a \in S$$.
- Antisymmetry: $$a \le b$$ and $$b \le a \Rightarrow a=b$$.
- Transitivity: $$a \le b$$ and $$b \le c \Rightarrow a \le c$$.