Element equals to Supremum of Infima of Open Sets that Element Belongs implies Topological Lattice is Continuous

Theorem
Let $L = \left({S, \preceq, \tau}\right)$ be a complete Scott topological lattice.

Let
 * $\forall x \in S: x = \sup \left\{ {\inf X: x \in X \in \sigma\left({L}\right)}\right\}$

Then $L$ is continuous.