Abstract
We present a new approach to introducing an extensional propositional equality in Intensional Type Theory. Our construction is based on the observation that there is a sound, intensional setoid model in Intensional Type theory with a proof-irrelevant universe of propositions and /spl eta/-rules for /spl Pi/and /spl Sigma/-types. The Type Theory corresponding to this model is decidable, has no irreducible constants and permits large eliminations, which are essential for universes.
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