Lower Closure of Singleton

Theorem
Let $\left({S, \preceq}\right)$ be an ordered set.

Let $s$ be an element of $S$.

Then:
 * $\left\{ {s}\right\}^\preceq = s^\preceq$

where:
 * $\left\{ {s}\right\}^\preceq$ denotes the lower closure of $\left\{ {s}\right\}$
 * $s^\preceq$ denotes the lower closure of $s$.