Sorgenfrey Line is Separable

Theorem
The Sorgenfrey line is separable.

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

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

Thus by definition:
 * The Sorgenfrey line is separable.