Upper Closure of Singleton

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

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

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

where:
 * $\set s^\succeq$ denotes the upper closure of $\set s$
 * $s^\succeq$ denotes the upper closure of $s$