\begin{definition}[Definition:Continuous Lattice Subframe]
Let $L = \left({X, \preceq}\right)$ be an ordered set.
Let $S = \left({Y, \preceq'}\right)$ be an ordered subset of $L$.
Then $S$ is '''continuous lattice subframe''' of $L$ {{iff}}
:$S$ inherits infima and directed suprema.
\end{definition}