Cardinality Less One

Theorem
Let $\left|{S}\right| = n + 1$, where $\left|{S}\right|$ is the cardinality of the finite set $S$.

Let $a \in S$.

Then:
 * $\left|{S - \left\{{a}\right\}}\right| = n$

Proof
This follows as an immediate consequence of Set Equivalence Less One Element.