Upper Closure of Singleton

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

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

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

where:
 * $\left\{ {s}\right\}^\succeq$ denotes the upper closure of $\left\{ {s}\right\}$
 * $s^\succeq$ denotes the upper closure of $s$