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.

Help me proofread tau day exercises

In honor of tau day (a math holiday celebrated on June 28 every year), I have written some exercises at wikiproofs.org tau day. If you have a little time to go to that page and try to go through the exercises, I'd appreciate your feedback on writing style, whether they are too easy or too hard, whether they were too long or too short, and any other suggestions. I'm hoping this will be a fun game/exercise for anyone interested in math but I am trying to make it accessible to someone with no experience in formal proofs.

If you are here to read about programming, I intend to keep writing about that too, but the math proofs have been a good part of my hobby activities lately. It is kind of like programming anyway (processed by a computer, needs to follow pretty specific rules to work, can be addictive in some of the same ways).