I am trying to learn the amalgamation of two cluster seeds and I am reading the paper https://arxiv.org/pdf/math/0508408.pdf written by V.V. Fock and A. B. Goncharov. I am at a loss for the Lemma 2.2. on page 9.
My question is (a) I don't find a function $c$ on $K$.
(b) I don't understand the proof of Lemma 2.2, who can explain it clearly? Or offer me some relative papers. Any help will be appreciated.