\begin{definition}[Definition:Injection/Definition 3]
Let $f$ be a mapping.
Then $f$ is an injection {{iff}}:
:$f^{-1} {\restriction_{\Img f} }: \Img f \to \Dom f$ is a mapping
where $f^{-1} {\restriction_{\Img f} }$ is the restriction of the inverse of $f$ to the image set of $f$.
\end{definition}