Because g is partial computable, there must be a program e that computes g, by the assumption that the model of computation is Turing-complete. This program is one of all the programs on which the halting function h is defined. The next step of the proof shows that h(e,e) will not have the same value as f(e,e).

It follows from the definition of g that exactly one of the following two cases must hold:
* f(e,e) = 0 and so g(e) = 0. In this case program e halts on input e, so h(e,e) = 1.
* f(e,e) != 0 and so g(e) is undefined.