\begin{definition}[Definition:Complete Distributive Lattice]
Let $\left({S, \vee, \wedge, \preceq}\right)$ be a lattice.
Then $S$ is a '''complete distributive lattice''' {{iff}}
:$(1): \quad S$ is a complete lattice
:$(2): \quad S$ is a distributive lattice.
Category:Definitions/Lattice Theory
\end{definition}