Abstract
We consider the (&, ⊃)-fragment of the intuitionistic propositional calculus. It is proved that under the standard transformation of a Gentzen derivation α into a natural derivationϕ(α), the length of (ϕ(α))≤22·length(α). There is constructed a sequence of Gentzen derivations of length αi, for which the length of (ϕ(α i))≥21/3·length(αi), which shows that the upper bound obtained is not too weak.
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 192–196, 1979.
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Solov'ev, S.V. Growth of length of sequential derivation transformed into natural one. J Math Sci 20, 2367–2369 (1982). https://doi.org/10.1007/BF01629448
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DOI: https://doi.org/10.1007/BF01629448