Refined program extraction form classical proofs

The paper presents a re"ned method of extracting reasonable and sometimes unexpected programs from classical proofs of formulas of the form ∀x∃yB. We also generalize previously known results, since B no longer needs to be quanti"er-free, but only has to belong to a strictly larger class of so-called “goal formulas”. Furthermore we allow unproven lemmas D in the proof of ∀x∃yB, where D is a so-called “de"nite” formula. c � 2002 Elsevier Science B.V. All rights reserved. MSC: 03F10; 03F50

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