I did not understand how the equation below is obtained. Ie, how is the first line obtained and where is the information $v_{\pi}(x_k)=v_{\pi'}(x_k)$ used in the derivation regarding greedy policy?

where $\pi^{\prime}(x_k)=argmax_{u_k \in \mathcal{U}}q_{\pi}(x_k, u_k)$.

Note: the source of the above equation is slide 22, at the follwing link: https://groups.uni-paderborn.de/lea/share/lehre/reinforcementlearning/lecture_slides/built/Lecture03.pdf