An exercise in coinduction: Moessner’s theorem

We present a coinductive proof of Moessner’s theorem. This theorem describes the construction of the stream (1n, 2n, 3n, . . .) (for n ≥ 1) out of the stream of natural numbers by repeatedly dropping and summing elements. Our formalisation consists of a direct translation of the operational description of Moessner’s procedure into the equivalence of in essence two functional programs. Our proof fully exploits the circularity that is present in Moessner’s procedure and is more elementary than existing proofs. As such, it serves as a non-trivial illustration of the relevance and power of coinduction.