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Normalisation by evaluation for type theory, in type theory

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Figure

Figure 1: Normalisation by evaluation.
Figure 2: The type of quote and unquote for a type A in NBE for simple types. We useprimed notations for the unquote and quote functions to denote that they includethe completeness proof
Figure 3: The types of quote and unquote for a context Γ in our proof.
Figure 4: Proof of injectivity of ΠTy in the domain. The dashed lines are given by the fillersof the squares

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