# Definition:Inclusion-Reversing Mapping

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## Definition

Let $A, B$ be sets of sets and $\phi: A \to B$ be a mapping.

Then $\phi$ is inclusion-reversing if and only if:

for every pair of sets $a_1, a_2 \in A$ such that $a_1 \subseteq a_2$:
$\phi \left({a_2}\right) \subseteq \phi \left({a_1}\right)$