On 11/5/2013 6:10 PM, David Hartley wrote: > In message <firstname.lastname@example.org>, Paul > <email@example.com> 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.