\begin{definition}[Definition:Inclusion-Preserving Mapping]
Let $A$ and $B$ be sets.
Let $f : A \to B$ be a mapping.
Then $f$ is '''inclusion-preserving''' {{iff}} for every two sets $a_1, a_2 \in A$:
:$a_1 \subseteq a_2 \implies f(a_1) \subseteq f(a_2)$
\end{definition}