One small thing is that in the proof they use n-1 instead of n as the denominator for sample variance which is different from my/Kevin's settings. Although this

One small thing is that in the proof they use n-1 instead of n as the denominator for sample variance which is different from my/Kevin's settings. Although this might be trivial, I will further look into that to see if it makes any difference. Overall this (full) derivation I would say is non-trivial, although it is not some discoveries.