Let $I$ be an D1247: Inner product-normed vector space such that

(i)	$\langle \cdot, \cdot \rangle$ is the D34: Inner product in $I$
(ii)	$\Vert \cdot \Vert$ is the D504: Inner product norm in $I$
(iii)	$x, y \in I$ are each a D1129: Vector in $I$

Then \begin{equation} \Vert x + y \Vert^2 + \Vert x - y \Vert^2 = 2 \Vert x \Vert^2 + 2 \Vert y \Vert^2 \end{equation}