\begin{definition}[Definition:Minimal/Set]
Let $S$ be a set.
Let $\powerset S$ be the power set of $S$.
Let $\TT \subseteq \powerset S$ be a subset of $\powerset S$.
Let $\struct {\TT, \subseteq}$ be the ordered set formed on $\TT$ by $\subseteq$ considered as an ordering.
Then $T \in \TT$ is a '''minimal set''' of $\TT$ {{iff}} $T$ is a minimal element of $\struct {\TT, \subseteq}$.
That is:
:$\forall X \in \TT: X \subseteq T \implies X = T$
\end{definition}