Automated element-wise reasoning with sets

Abstract

Operational reasoning with sets is important for software engineering methods like B or Z and a longstanding challenge in automated deduction. A proof-search procedure for atomic distributive lattices is presented that captures an interesting fragment of set theory. In contrast to a previous procedure [21], atomicity is extensively used. This yields short and confined expressions and inference rules. It makes the approach particularly suited for small problems and strongly element-wise specifications.