Suffix of String is Substring

Theorem
Let $S$ be a string.

Let $T$ be a suffix of $S$.

Then $T$ is a substring of $S$.

Proof
By definition of substring, there exists a string $T'$ such that:


 * $S = T'T$

Hence $S$ is the concatenation of the null string, $T'$, and $T$.

Thus by definition of substring, $T$ is a substring of $S$.