Abstract
In this paper we describe a method for proving the normalization property for a large variety of typed lambda calculi of first and second order, which is based on a proof of equivalence of two deduction systems. We first illustrate the method on the elementary example of simply typed lambda calculus, and then we show how to extend it to a more expressive dependent type system. Finally we use it to prove the normalization theorem for Girard's system F.
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