\begin{definition}[Definition:Meet Irreducible]
Let $\left({S, \wedge, \preceq}\right)$ be a meet semilattice.
Let $g \in S$.
Then $g$ is '''meet irreducible''' {{iff}}:
:$\forall x, y \in S: g = x \wedge y \implies g = x$ or $g = y$
\end{definition}