\begin{definition}[Definition:Heyting Algebra]
Let $\left({L, \wedge, \vee, \preceq}\right)$ be a lattice.
Then $\left({L, \wedge, \vee, \preceq}\right)$ is a '''Heyting algebra''' {{iff}}:
: $(1): \quad \left({L, \wedge, \vee, \preceq}\right)$ is a Brouwerian lattice
: $(2): \quad L$ has a smallest element.
\end{definition}