Generalization in the presence of free variables: A mechanically-checked correctness proof for one algorithm

We present a case study in which an automated proof assistant was used to show the correctness of an algorithm. Specifically, we document the application of an extension of the Boyer-Moore Theorem Prover to the problem of verifying the correctness of an implementation of generalization, where the proof had surprisingly many details and a previous implementation contained an error. We attempt to provide sufficient detail so that the reader can gain a realistic impression of the nature of this exercise.

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