I'm trying to understand how the Rips Construction works.
In particular, I'd like to understand why the presentation cooked up by the Rips construction (which if I'm not mistaken is not explicitly written out in Rips's 1982 paper) satisfies the small cancellation condition.
Baumslag, Miller and Short (Unsolvable Problems About Small Cancellation...) give explicit words for the presentation, and refer to Lyndon and Schupp's Combinatorial Group Theory for proof that it satisfies the small cancellation hypothesis. They don't give a page number (and my understanding is Lyndon Schupp was published before Rips's paper), and I'm not sure which result they refer to (possibly Theorem 10.3?).
I am aware of Arzhantseva's result (in Rips Construction Without Unique Product), which gives an explicit presentation, but I would like to understand the original construction.
Any references much appreciated :)