Computer-assisted proofs in analysis and programming in logic: A case study

In this paper we present a computer-assisted proof of the existence of a solution for the Feigenbaum equation phi(x) = 1/lambda phi(phi(lambda x)). There exist by now various such proofs in the literature. Although the one presented here is new, the main purpose of this paper is not to provide yet another version, but to give an easy-to-read and self-contained introduction to the technique of computer-assisted proofs in analysis. Our proof is written in Prolog (Programming in logic), a programming language which we found to be well suited for this purpose. In this paper we also give an introduction to Prolog, so that even a reader without prior exposure to programming should be able to verify the correctness of the proof.