Lemma Discovery for Induction: A Survey

Abstract

Automating proofs by induction can be challenging, not least because proofs might need auxiliary lemmas, which themselves need to be proved by induction. In this paper we survey various techniques for automating the discovery of such lemmas, including both top-down techniques attempting to generate a lemma from an ongoing proof attempt, as well as bottom-up theory exploration techniques trying to construct interesting lemmas about available functions and datatypes, thus constructing a richer background theory