Einstein notation (Einstein summation convention)

www.maths.cam.ac.uk/postgrad/part-iii/files/misc/index-notation.pdf gives a definition that does not consider upper and lower indexes, it only counts how many times the indices appear

Their definition of the Laplacian is a bit wrong as only one $i$ appears in it, they likely meant to have written $\frac{\partial }{\partial x_i}\frac{\partial F}{\partial x_i}$ instead of $\frac{{\partial }^{2}F}{\partial x_i^2}$, related: