A logic for specification and verification is derived from the axioms of Zermelo-Fraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the flexibility to adapt to variants of set theory. Its higher-order syntax supports the definition of new binding operators. Unknowns in subgoals can be instantiated incrementally. The paper describes the derivation of rules for descriptions, relations and functions, and discusses interactive proofs of Cantor’s Theorem, the Composition of Homomorphisms challenge [9], and Ramsey’s Theorem [5]. A generic proof assistant can stand up against provers dedicated to particular logics. Key words. Isabelle, set theory, generic theorem proving, Ramsey’s Theorem,

Zermelo-Fraenkel (ZF) set theory is widely regarded as unsuitable for automated reasoning. But a computational logic has been formally derived from the ZF axioms using Isabelle. The library of theorems and derived rules, with Isabelle's proof tools, support a natural style of proof. The paper describes the derivation of rules for descriptions, relations and functions, and discusses interactive proofs of Cantor's Theorem, the Composition of Homomorphisms challenge [3], and Ramsey's Theorem [2].