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From Sets and Types to Topology and Analysis
We describe two methods of extracting constructive content from classical proofs, focusing on theorems involving infinite sequences and nonconstructive choice principles. The first method removes any reference to infinite sequences and transforms the theorem into a system of inductive definitions, the other applies a combination of Gödel's negativeand Friedman's A-translation. Both approaches are explained by means of a case study on Higman's Lemma and its well-known classical proof due todoi:10.1093/acprof:oso/9780198566519.003.0008 fatcat:n4z453pujrenfgte7abt4tkjhi