Linearizability is compositional

[Ibrahim Dalal]

Hi,

This is in regard to Theorem 3.6.1. (Revised Reprint):

Theorem 3.6.1. H is linearizable if, and only if, for each object x, H|x is lin-
earizable.

Our instructor says that there is something wrong with the given proof and has asked the class to figure out what it might be. I went through the proof over and over again but apparently can't find any issues. I also referred to the original paper that discusses this (although it gives a proof by construction as oppose to the proof by induction given in the book). Are there any issues reported with respect to this?

Thanks