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arXiv · 2507.19008

A Proof of the Schr\"oder-Bernstein Theorem in ACL2

Grant Jurgensen
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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.

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Grant Jurgensen. 2025-07-25. A Proof of the Schr\"oder-Bernstein Theorem in ACL2. https://doi.org/10.4204/eptcs.423.3

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