\begin{definition}[Definition:Boolean Lattice/Definition 2]
An ordered structure $\left({S, \vee, \wedge, \preceq}\right)$ is a '''Boolean lattice''' {{iff}}:
$(1): \quad \left({S, \vee, \wedge}\right)$ is a Boolean algebra
$(2): \quad$ For all $a, b \in S$: $a \wedge b \preceq a \vee b$
\end{definition}