Talk:Schwarz–Ahlfors–Pick theorem

Doubt
I have a doubt.

An automorphism f has an inverse g. Applying the theorem for both f and g, the inequality becomes an equality. Am I right? What is wrong with this?
 * True, automorphisms preserve distance in this case. I think "automorphism" should have been endomorphism. Jowa fan (talk) 22:59, 1 February 2010 (UTC)