\begin{definition}[Definition:Invariant Mapping Under Equivalence Relation]
Let $S$ and $T$ be sets.
Let $\RR$ be an equivalence relation on $S$.
Let $f: S \to T$ be a mapping.
Then $f$ is '''invariant under $\RR$''' {{iff}}:
:$x \mathrel \RR y \implies \map f x = \map f y$
\end{definition}