Lower Closure of Singleton

Theorem
Let $\struct {S, \preceq}$ be an ordered set.

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

Then:
 * $\set s^\preceq = s^\preceq$

where:
 * $\set s^\preceq$ denotes the lower closure of $\set s$
 * $s^\preceq$ denotes the lower closure of $s$.