Scott Topology equals to Scott Sigma

Theorem
Let $\left({T, \preceq, \tau}\right)$ be a up-complete topological lattice with Scott topology.

Then $\tau = \sigma\left({\left({T, \preceq}\right)}\right)$

where $\sigma\left({L}\right)$ denotes the Scott sigma of $L$.

Proof
This follows by Open iff Upper and with Property (S) in Scott Topological Lattice and definition Scott sigma.