Sorgenfrey Line is Separable

Theorem
Sorgenfrey line is separable.

Proof
By Rationals Dense in Sorgenfrey Line:
 * $\Q$ is dense in Sorgenfrey line.

By Rational Numbers are Countably Infinite:
 * $\Q$ is countable.

Thus by definition:
 * Sorgenfrey line is separable.