If a string $s$ contains $t$ as an internal substring, then $s$ can be written as $s_1 t s_2$,
where $s_1$ and $s_2$ are nonempty. A t-prefix contains all of $s_1$ and none of $s_2$, so that
its corresponding suffix contains all of $s_2$ and none of $s_1$. The corresponding cut will
therefore fall somewhere in $t$.