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The cut-elimination theorem is the central result establishing the significance of the sequent calculus. It was originally proved by Gerhard Gentzen in part I of his landmark 1935 paper "Investigations in Logical Deduction" for the systems LJ and LK formalising intuitionistic and classical logic respectively. The cut-elimination theorem states that any sequent that possesses a proof in the sequent calculus making use of the cut rule also possesses a cut-free proof, that is, a proof that does not make use of the cut rule. The natural deduction version of cut-elimination, known as the normalization theorem, was first proved for a variety of logics by Dag Prawitz in 1965.
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