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this paper can still go through (with slightly more technical effort) in case onecan distinguish cases according to whether a specific subterm is a type or kind ina fixed context. The other property of type systems that is really actually requiredfor the constructions in this paper to go through is a slight strengthening of theStripping property (also called Generation). This property says, for example,that if \Gamma ` v:T:M : U has a derivation D, then one can find a subderivation of

A short and flexible proof of strong normalization for the calculus of constructions