Definition:Smallest Set by Set Inclusion/Class Theory

Definition
Let $\mathcal A$ be a set of sets or a class of sets.

Then a set $M$ is the least element of $\mathcal A$ (with respect to the subset relation) :


 * $(1): \quad M \in \mathcal A$
 * $(2): \quad \forall S: \left({S \in \mathcal A \implies M \subseteq S}\right)$