A Proof of the Schr\"oder-Bernstein Theorem in ACL2
Logic in Computer Science
2025-07-28 v1
Abstract
The Schr\"oder-Bernstein theorem states that, for any two sets P and Q, if there exists an injection from P to Q and an injection from Q to P, then there must exist a bijection between the two sets. Classically, it follows that the ordering of the cardinal numbers is antisymmetric. We describe a formulation and verification of the Schr\"oder-Bernstein theorem in ACL2 following a well-known proof, introducing a theory of chains to define a non-computable witness.
Cite
@article{arxiv.2507.19008,
title = {A Proof of the Schr\"oder-Bernstein Theorem in ACL2},
author = {Grant Jurgensen},
journal= {arXiv preprint arXiv:2507.19008},
year = {2025}
}
Comments
In Proceedings ACL2 2025, arXiv:2507.18567