Complement Union with Superset is Universe

Theorem

 * $$S \subseteq T \iff \complement \left({S}\right) \cup T = \mathbb U$$

where:
 * $$S \subseteq T$$ denotes that $$S$$ is a subset of $$T$$;
 * $$S \cup T$$ denotes the union of $$S$$ and $$T$$;
 * $$\complement$$ denotes set complement;
 * $$\mathbb U$$ denotes the universal set.

Proof
$$ $$ $$ $$ $$

Also see

 * Intersection of Complement with Subset is Empty