I was going through the proof in Appendix A and I just want to make sure that something written towards the bottom of pg. 189 is a typo.

Namely,

should read

I'm 99.999999999999% sure this is indeed a typo since the latter case easily follows from reverse triangle inequality and it suffices to show the inequality in (A.3) and I cannot see how one can arrive at the implication in the former case nor how the former case implies the inequality (A.3), but it would ease my mind if I can get a verification that it is a typo. Thank you in advance!