>>13#1 does not need to be proven. It is a definition. Not being shit is as intrinsic to a Lisp as being unmarried is to being a bachelor.
#2 has been proven many, many times. It is accessible easily, and I do not need to do so here again myself. I do not need to quote an entire copy of Russell's
Principia Mathematica just to do basic arithmetic either. For us to get anywhere, I have to be able to trust you to at least make an attempt to stay informed on the subject independently instead of shifting the burden of your education onto me.