Celebrate tau day with a few proofs

What better way to celebrate Tau Day than by trying your hand at writing a few proofs? Wikiproofs is a wiki which anyone can edit, and the goal is to build a library of proofs. They are written in a formal language, so the web site can check their correctness, and that is what makes it good for the tau day exercise: you get feedback about whether your proof is correct from the site as you go. The tau day exercises are intended to be of modest length and difficulty (so you can get them done on tau day) and explain everything you need to know about wikiproofs. Go to Wikiproofs tau day to play.