A Set Theory Prover Within Theorema

摘要

In this paper, we present the Theorema Set Theory Prover. This prover is designed for proving statements involving notions from set theory using natural deduction inference rules for set theory. Moreover, it applies the PCS paradigm (Proving-Computing-Solving) for generating natural proofs that has already been used in other provers in the Theorema system, notably the prover for automated proofs in elementary analysis. We show some applications of this prover in a case study on equivalence relations and partitions, which also nicely shows the interplay between proving, computing , and solving during an exploration of some mathematical theory.