In this part of the online supplement, different types of proofs you may encounter are listed in the drop-down menu. On each landing page you will find the following: a description of the proof, some reasons to use them, and a link to a worked out example. It is important to note the the provided examples are not rooted in probability theory concepts. Rather, the concepts in each of the problems are those you may have encountered in algebra or introductory real analysis problems.
The red text in each of the examples are not things you would have to include in the formal proof, but rather things you should consider and think about as you follow through the example. If you would like to challenge yourself, try reading the example problem but work out the solution yourself. You can then compare your solution with the included solution!