Set Difference of Larger Set with Smaller is Not Empty

Theorem
Let $S$ and $T$ be finite sets.

Let $\card S > \card T$.

Then:
 * $S \setminus T \ne \O$

Proof
From Cardinality of Subset of Finite Set:
 * $S \not \subseteq T$

From the contrapositive statement of Set Difference with Superset is Empty Set:
 * $S \setminus T \ne \O$.