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We use G\"odel's Dialectica interpretation to analyse Nash-Williams' elegantbut non-constructive "minimal bad sequence" proof of Higman's Lemma. The resultis a concise constructive proof of the lemma (for arbitrary decidablewell-quasi-orders) in which Nash-Williams' combinatorial idea is clearlypresent, along with an explicit program for finding an embedded pair insequences of words.

Applying G\"odel's Dialectica Interpretation to Obtain a Constructive Proof of Higman's Lemma