Reference textbook about proof techniques I am looking for some good recommended reference textbooks about proof techniques.
Someone told me "G. Polya - How to solve it" is kind of standard, but quite old.
I am looking for a book that handles both classical (manual work) proofs and modern proof techniques using proof assistants or automated theorem provers. Or two separate books each handling just one of these topics.

The free book An Introduction to Proofs and the Mathematical Vernacular can be interesting. Quote from the author:

The typical university calculus sequence, which serves majors in the physical sciences and engineering as well as mathematics, emphasizes calculational technique.  In upper level mathematics courses, however, students are expected to operate at a more conceptual level, in particular to produce "proofs" of mathematical statements.  To help students make the transition to more advanced mathematics courses, many university mathematics programs include a "bridge course".  Many texts have been written for such a course.  I have taught from a couple of them, and have looked at numerous others. These various texts represent different ideas for what a bridge course should emphasize.  Not having found a text that was a good fit with my own ideas, I decided to try to write one of my own.  I am making the book freely available; a link is provided at the bottom of this page.  But first I want to explain the ideas which I have tried to embody in the book.

