Sample Space is Union of All Distinct Simple Events

Theorem
Let $\EE$ be an experiment.

Let $\Omega$ denote the sample space of $\EE$.

Then $\Omega$ is the union of the set of simple events in $\EE$.

Proof
By Set is Subset of Itself:
 * $\Omega \subseteq \Omega$

That is, $\Omega$ is itself an event in $\EE$.

The result as an application of Non-Trivial Event is Union of Simple Events.