A Proof of the Schröder-Bernstein Theorem in ACL2
arXiv:2507.19008 · doi:10.4204/EPTCS.423.3
Abstract
The Schröder-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 Schröder-Bernstein theorem in ACL2 following a well-known proof, introducing a theory of chains to define a non-computable witness.
In Proceedings ACL2 2025, arXiv:2507.18567