Let $R$ be an endorelation with domain $(X, X)$ and $P$ be
the asymmetric part of $R$ for which $x P y$ iff $x R y$
and not $y R x$. (If $R$ is a $\le$ order relation,
$P$ is the associated strict order.) We say that $x$ is
covered by $y$ if $x P y$ and there is no $z$ such that
$x P z$ and $z P y$. One also says that $y$ covers
$x$, or that it is a successor of $x$. The covering relation of $R$ consists of all pairs $(x, y)$
for which $x$ is covered by $y$.