proof methods

[Buday Gergely]

Dear FOMers,

my question is not strictly foundational, but related.

Do you know some reference that writes about proof methods, giving a 
taxonomy of them?

I think of basic proof methods like indirect proof, proof by cases, 
proof by symmetry, induction

and advanced ones like transfinite induction or forcing.

Some of these have formalization in mathematical logic, some others don't.

Some of these connections are direct and easy, like reductio ad 
absurdum, some others like symmetry have a detailed theory, namely, 
nominal sets.

What I look for is what working mathematicians use in their publications.

Is there a survey paper or book on this?

- Gergely