Lambda the Ultimate

Hello everybody !,

Can somebody help me to understand some basic stuff about substitution of equal by equal formulas ?

Some things to consider about me or background:

- English is not my first language and although I can manage to read a book the effort is considerable if I want to get the most of it.
- I'm reading Richard Bornat's "Programming from first principles (Prentice Hall international, 1987)"
- I only have a technical degree on computer programming and I graduated 3 yeard ago. Never worked in software developing nor anything related to IT.
- I never felt that I had really learnt because they taught "coding" rather that what I fell programming is (I learnt first C, then VB, and then databases)
- In the following years after my graduation I decided to took of to lose practice and forget the things that they taught, in the meanwhile searching for publications to start on my own.

After some reads I came to Bornat's book (it seemed to me an introduction in the way I like it, not language-centered and focused on concepts/principles that I could apply to any imperative programming language).
The thing is, I can not understand it and I feel really bad !, I am reading chapter 2 and when it comes to proofs or proving I cant get "it". I cant also explain it so I would like to upload that part of chapter 2 (I have the book in dead-tree form and I also have it in electronic format, but I dont know if uploading it isnt correct -its on the net though-.
I google search for -Programming equals by equals substitution- but cant find such stuff, so maybe, some of you have read the book or know other resources -or maybe have the answers to the book exercises !- .

Well, thats all, thank you for your time.

Warmest regards,
Sebastian.