\begin{definition}[Definition:Renaming Mapping]
Let $f: S \to T$ be a mapping.
The '''renaming mapping''' $r: S / \RR_f \to \Img f$ is defined as:
:$r: S / \RR_f \to \Img f: \map r {\eqclass x {\RR_f} } = \map f x$
where:
:$\RR_f$ is the equivalence induced by the mapping $f$
:$S / \RR_f$ is the quotient set of $S$ determined by $\RR_f$
:$\eqclass x {\RR_f}$ is the equivalence class of $x$ under $\RR_f$.
\end{definition}