Wolff's proof of Wolff's inequality (in the dyadic setting)

In 1983 Tom Wolff proved a surprising inequality which proved to be a pivotal tool in Nonlinear Potential Theory. I will go through Wolff's proof, but in the dyadic setting. Hedberg, L. I.; Wolff, Th. H. Thin sets in nonlinear potential theory. Ann. Inst. Fourier (Grenoble) 33 (1983), no. 4, 161–187.