\begin{definition}[Definition:Operation Compatible with Set Equivalence]
Let $F$ be a (unary) operation which can be applied to sets.
Then $F$ is '''compatible with set equivalence''' {{iff}}:
:$F \sqbrk A = F \sqbrk B \iff A \sim B$
where:
:$A$ and $B$ are arbitrary sets
:$F \sqbrk A$ denotes the image of $A$ under $F$
:$\sim$ denotes set equivalence.
\end{definition}