Definition:Inflationary Mapping/Subset

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Let $C$ be a set of sets or a class of sets.

Let $f: C \to C$ be a mapping from $C$ to $C$.

Then $f$ is inflationary if and only if:

$\forall x: x \in C \implies x \subseteq f \left({x}\right)$

That is, if and only if for each $x \in C$, $x$ is a subset of $f \left({x}\right)$.