A D286: Partial ordering relation ${\preceq} \subseteq X \times X$ on $X$ is a lattice order relation on $X$ if and only if
\begin{equation}
\forall \, x, y \in X :
\inf \{ x, y \}, \sup \{ x, y \} \in X
\end{equation}
A D286: Partial ordering relation ${\preceq} \subseteq X \times X$ on $X$ is a partial lattice-ordering relation on $X$ if and only if
\begin{equation}
\forall \, x, y \in X :
x \land y, x \lor y \in X
\end{equation}
