Open Real Interval is Subset of Closed Real Interval

Theorem
Let $a, b \in \R$ be real numbers.

Then:
 * $\openint a b \subseteq \closedint a b$

where:
 * $\openint a b$ is the open interval between $a$ and $b$
 * $\closedint a b$ is the closed interval between $a$ and $b$.

Proof
Let $x \in \openint a b$.

Then by definition of open interval:
 * $a < x < b$

Thus:
 * $a \le x \le b$

and so by definition of closed interval:
 * $x \in \closedint a b$