Q:

Beginning Haskell - cannot understand proof

I've just started reading "Thinking Functionally with Haskell" by Richard Bird
In the preface he states : 

And after stating the proof he also states the proof will be used throughout the book.
What is this proof ? I do not understand this proof or why it will be used throughout this book ?
What background reading should I use in order to understand this proof ?

A:

It’s not the proof itself that will be used throughout the book: it’s the format of the proof, in which the justification for each equality is given in curly braces immediately after the equals sign. For instance, the third step,
$$\sin2\alpha\cos\alpha+\cos2\alpha\sin\alpha=2\sin\alpha\cos^2\alpha+\cos2\alpha\sin\alpha\;,$$
is justified by the reason
$$\{\text{since }\sin2\alpha=2\sin\alpha\cos\alpha\}\;.$$
Apply this double angle formula to $\sin2\alpha\cos\alpha$, and you get
$$(2\sin\alpha\cos\alpha)\cos\alpha\;,$$
which simplifies to $2\sin\alpha\cos^2\alpha$.

