I strongly agree there's a lack of text along the lines of "theorem proving for regular programmers". The majority I ever read assumed a strong background in maths, logic and functional programming and were really off-putting.
Well, have a look at the two tutorials to which I link in readme.md of the github project. The first is very suitable for programmers with minimal prior knowledge of maths, the second is aimed at the opposite audience (mathematicians without much CS knowlede) (and I think is actually even simpler).