\begin{definition}[Definition:Inclusion-Reversing Mapping]
Let $A, B$ be sets of sets and $\phi: A \to B$ be a mapping.
Then $\phi$ is '''inclusion-reversing''' {{iff}}:
: for every pair of sets $a_1, a_2 \in A$ such that $a_1 \subseteq a_2$:
:: $\phi \left({a_2}\right) \subseteq \phi \left({a_1}\right)$
\end{definition}