What does "cavallier extension claim" in The Algorithm Design Manual mean I have been reading the Algorithm Design Manual by Steven S. Skienna and on page 15 it mentions a term called "cavallier extension claim" and I have been desperately trying to find a definition for this. A search in Google just returns quotes of the same book.

Possibly my confusion lies in the misspelling of the word "cavallier", which seems like it should be spelled "cavalier", unless it was the name of some French mathematician or some other concept that I am missing.

Update

As requested here is the context. First he talks about boundary errors in inductive proofs and then this:


  The second and more common class of inductive proof errors concerns cavallier extension claims. Adding an extra item to a given problem instance might cause the entire optimal solution to change.
The phrase means "cavalier" in the ordinary English sense of the word, i.e., it is talking about a claim in a proof that is made carelessly.  Without more context or examples I'm not sure exactly what pattern of flawed proof it is referring to, but it has something to do with making an assumption/claim (without justifying it) that the solution for $n+1$ is related to the solution for $n$ in a particular way.

"Cavallier extension claim" is not a technical phrase.  It's just some English that the author is using.