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In this post, Andrej Bauer says:

There is a theorem about normal forms of proofs in intuitionistic logic which tells us that every proof of a negation can be rearranged so that it ends with the inference rule cited above

Can someone point me to a text on "normal forms of proofs in intuitionistic logic" and to this theorem?

user56834
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    The standard texts are Natural Deduction by Dag Prawitz (1965) and Basic Proof Theory by Troelstra & Schwichtenberg (2nd ed., 2000). In particular, you may want to take a look at §IV.1 and §IV.2 of Natural Deduction (theorem 1 and 2, respectively) and chapter 6 of Basic Proof Theory, theorem 6.1.8, and, especially, §6.2, proposition 6.2.4. – Hermógenes Oliveira Apr 12 '19 at 22:30

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