\begin{definition}[Definition:Preimage/Mapping/Subset]
Let $f: S \to T$ be a mapping.
Let $f^{-1} \subseteq T \times S$ be the inverse of $f$, defined as:
:$f^{-1} = \set {\tuple {t, s}: \map f s = t}$
Let $Y \subseteq T$.
\end{definition}