> It would be nice if everyone could master these > "abstractions" and the basic methods of proof, but few > are motivated to do so. I hope my little video and my > software will help a bit in this regard.
I'm not sure why students at large would be interested in formal predicate calculus based proofs, but for the smaller populations that are, it seems a shame to not include the fundamental fact that once a formal system is adopted, the very act of generating proofs can be automated - you can write a "function" that given a number, hands back a proof corresponding to that number. (Of course, many mathematician's balk at the notion that what they do is "computational" yuck!...)
For anyone actually motivated to study formal proofs in the first place, that much would seem to be entirely digestible in itself. Once that was done I would certainly at least briefly discuss "Godel's Lost Letter" (with help from the teacher in translating jargon into concepts)and muse about the connections between mathematical theories and automated processes.