On Friday, November 8, 2013 2:05:19 AM UTC, fom wrote: > On 11/5/2013 6:10 PM, David Hartley wrote: > > > In message <email@example.com>, Paul > > > <firstname.lastname@example.org> writes > > >> Of course, the below is irrelevant to understanding the proof. > > >> However, I am completely mystified by the page 1 sentences: "We now > > >> show that f is L-canonical. We shall apply the definition of f > > >> repeatedly without referring to this fact." It's only the second of > > >> those sentences that confuses me. The first sentence is given for > > >> context. > > > > > > I can't make sense of it either. The whole section is rather odd. > > > Firstly he hasn't actually defined L-canonical, only L-canonical on B, > > > presumably he means here L-canonical on A. The actual theorem is trivial > > > yet he devotes several lines to a proof. > > > > Your presumption is correct. > > > > The theorem is trivial, but, its > > purpose is not. > > > > He has given a definition. He is > > demonstrating that the definition > > is not vacuous before proceeding to > > the main theorem.
You are absolutely correct about the purpose of the theorem. David and I are of the opinion that the non-vacuity of the definition is sufficiently obvious to the intended readership, as not to be worth stating.
A longer paper, for an undergraduate audience, could be given, which simplifies the proof along the lines found by David, and which gives more details. This suggested longer paper might well contain such details.