Product of Negative Real Numbers is Positive

Theorem
Let $a, b \in \R_{\le 0}$ be negative real numbers.

Then:
 * $a \times b \in \R_{\ge 0}$

That is, their product $a \times b$ is a positive real number.

Proof
From Real Numbers form Ring, the set $\R$ of real numbers forms a ring.

The result then follows from Product of Ring Negatives.