Abstract
In [1] Girard gives a procedure, by which all derivations in the “calculus of natural deductions” of Prawitz [4] are transformed into normal derivations. Exploiting his idea we give a syntactical proof of the admissibility of the cut rule in Schutte's formal system of intuitionistic type theory. We obtain a normal form theorem but not a normalization theorem. Our “Berechnungspradikate” are different from the “candidats de reductibilite” of Girard. In the case of second order logic “Berechnungspradikate fur Terme t(O)” are not defined for derivations ending with rO e t(O) which are normalizable, but for finite formula sets Γ with the property, that Γ→rO e t(O) is derivable without cut.
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