Abstract
This paper starts with a brief exploration of the history of Higman's lemma with emphasis on Veldman's recent intuitionistic proof, which established the lemma in its most general form. The rest of the paper is devoted to the description of a type-theoretic proof of such a general form of Higman's lemma. This involves considering type-theoretic formulations of bar induction, fan theorem, Ramsey theorem, and Higman's lemma. The proof was formalized in Martin-Löf's type theory without universes, and edited and checked in the proof editor ALF.
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Fridlender, D. (1998). Higman's lemma in type theory. In: Giménez, E., Paulin-Mohring, C. (eds) Types for Proofs and Programs. TYPES 1996. Lecture Notes in Computer Science, vol 1512. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0097789
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DOI: https://doi.org/10.1007/BFb0097789
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