Cover Relation

The transitive reflexive reduction of a Partial Order. An element $z$ of a Poset $(X, \leq)$ covers another element $x$ provided that there exists no third element $y$ in the poset for which $x \leq y \leq z$. In this case, $z$ is called an ``upper cover'' of $x$ and $x$ a ``lower cover'' of $z$.