Definition:Operation Compatible with Set Equivalence

Definition
Let $F$ be a (unary) operation which can be applied to sets.

Then $F$ is compatible with set equivalence :


 * $F \sqbrk A = F \sqbrk B \iff A \sim B$

where:
 * $A$ and $B$ are arbitrary sets
 * $F \sqbrk A$ denotes the image of $A$ under $F$
 * $\sim$ denotes set equivalence.