Journal of Automated Reasoning

, Volume 11, Issue 3, pp 353–389

# Set theory for verification: I. From foundations to functions

• Lawrence C. Paulson
Article

## Abstract

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 higher-order syntax

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