I'm having trouble following the proof of lemma 1, and I can't tell if it's the notation being different from what I'm used to. Is the expression for gamma pri

I'm having trouble following the proof of lemma 1, and I can't tell if it's the notation being different from what I'm used to. Is the expression for gamma prime equal to negative the square of the distance between x and y, that is, -<x-y,x-y>? I'm curious, because I would have expected a stronger property to be necessary for the parallelogram structure.