Finite Set Theory on Ordered Lists in ACL2

We present a finite set theory implementation for ACL2. Our library represents sets as fully ordered lists, and provides efficient implementations of the typical set theory operations such as insertion, deletion, union, intersection, difference, cardinality, and sorting lists to create sets. It also includes facilities for quantifying predicates over sets, filtering sets by some criteria, and taking images of sets. We demonstrate that despite our insistence on full order, it is possible to mirror traditional set theoretic proof techniques and reason through membership. At the same time, we are able to benefit from having a unique representation for each set, which unifies the notions of set and element equality and allows us to handle nested sets trivially.