Set Difference with Superset is Empty Set

Theorem

 * $S \subseteq T \iff S \setminus T = \O$

where:
 * $S \subseteq T$ denotes that $S$ is a subset of $T$
 * $S \setminus T$ denotes the set difference between $S$ and $T$
 * $\O$ denotes the empty set.