Please have a look at the proof, first of all I don't understand the parts of the proof where one is refering to the Definition of G.
In the inductionbase one Claims that $(1,x)$ is an element of G
In the inductionstep we define $x_{n+1}:= f_n(x_1,..,x_n)$ and claim that $(n+1,x_{n+1})$ is also an element G. Can please someone explain me why these two assertions are true due to the Definition of G?
