Is this a typical way of doing proofs?

[Shackleford]

It looks like memorization plays a key component of recognizing/remembering when to use certain "rewriting" tricks to get the desired result in the string of deduction. I had to think for a minute about some of the equations involving absolute values.

http://i111.photobucket.com/albums/n149/camarolt4z28/untitled.jpg?t=1293038613

 

[The_Duck]

If I have a problem that asks me to prove something like this, I just play around with numbers for a bit until I see why it is true. Then I take that understanding and figure out how to express it formally. The formal proof is less intuitive and less informative than my original understanding: its benefit is that it is rigorous. To write down a formal proof I have to justify each step, and if there is in fact some hole in my understanding I will come across it. It is sometimes hard to go the other way: to read a formal proof and develop from it an intuitive understanding of why the proposition is true, but it's something I try to do or I won't remember the proposition or be able to reproduce the proof later.

Of course, sometimes to prove some complicated formula you just use rewriting tricks. You've got to be good with your algebra.