Proofs of VC theorem I am collecting VC-theorem's proofs
I've found three distinct proofs of VC-theorem ( also called Saur-Shelah lemma or shatter function lemma )
http://www.cse.buffalo.edu/~hungngo/classes/2010/711/lectures/sauer.pdf
here is the theorem:

 "Lectures on discrete geometry
  Jiri Matousek"

Does any one know another proof??

It is an old question... for the record, the shortest proof I know goes via a lemma of Alain Pajor. 
Gil Kalai credits Noga Alon while R. P. Anstee, Lajos Rónyai, and Attila Sali credit others.
P.S. I realize a proof is also in the Wikipedia article on Sauer–Shelah lemma.
