Cardinality Less One

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