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Using structural induction, I need to prove that some set S possesses a property P. I understand the basic concept of structural induction, that is prove the basis is true and prove that for successive iterations of the recursive rule, the property P holds for new elements built from “smaller” elements that also have property P. However, I’m not sure if I’m doing this proof correctly:

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I don't see any mistakes. I think the proof is correct as is.

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