Cauchy-Bunyakovsky-Schwarz Inequality/Inner Product Spaces

Theorem
Let $\mathbb K$ be a subfield of $\C$.

Let $V$ be a semi-inner product space over $\mathbb K$.

Let $x, y$ be vectors in $V$.

Then:
 * $\size {\innerprod x y}^2 \le \innerprod x x \innerprod y y$