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This paper studies a formalisation of intuitionistic logic by Negri and vonPlato which has general introduction and elimination rules. The philosophicalimportance of the system is expounded. Definitions of `maximal formula',`segment' and `maximal segment' suitable to the system are formulated andcorresponding reduction procedures for maximal formulas and permutativereduction procedures for maximal segments given. Alternatives to the mainmethod used are also considered. It is shown that deductions in the systemconvert into normal form and that deductions in normal form have the subformulaproperty.

Normalisation and subformula property for a system of intuitionistic logic with general introduction and elimination rules