Lemma Generation Method in Rewriting Induction for Constrained Term Rewriting Systems

Recently, rewriting induction, which is one of the induction principles for proving inductive theorems in equational theory, has been extended to deal with constrained term rewriting systems. Rewriting induction has been applied to developing a method for proving the equivalence of imperative programs. To prove inductive theorems, there are many cases where appropriate lemmas need to be added. To this end, several methods for lemma generation in term rewriting have been studied. However, these existing methods are not effective for cases in constrained term rewriting. In this paper, we propose a framework of lemma generation for constrained term rewriting systems, in which we formalize the correspondences of terms in diverging equations by means of given constrained rewrite rules. We show an instance of the formalization, and also show that due to the framework with the instance, there is no necessity to give lemmas in advance for the examples shown by previous works.