Set is Subset of Union

Theorem
The union of two sets is a superset of each:


 * $$S \subseteq S \cup T$$
 * $$T \subseteq S \cup T$$

General Result
Let $$S$$ be a set.

Let $$\mathcal P \left({S}\right)$$ be the power set of $$S$$.

Let $$\mathbb S \subseteq \mathcal P \left({S}\right)$$.

Then:
 * $$\forall T \in \mathbb S: T \subseteq \bigcup \mathbb S$$

Proof
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Similarly for $$T$$.

Proof of General Result
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