When I said identities I was actually referring to the rules "elim" and "intro", I forgot that identity means = (there are way too many new terms in this subject). I still can't figure out how to apply them this question though.
In the end I just stated my reasoning without using the given "rules", something like.
The function Between(x,y,z) means that the variables x,y,z is arranged in such a way that they are either arranged horisontally, diagonaly or vertical ...... etc.
Hope that is what is expected as I can't see the rules applied here, although I do get the feeling that we basically have to prove between is transitive.