Reduction Free Normalisation for a proof irrelevant type of propositions

03/07/2021

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by   Thierry Coquand, et al.

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We show normalisation and decidability of convertibility for a type theory with a hierarchy of universes and a proof irrelevant type of propositions, close to the type system used in the proof assistant Lean. Contrary to previous arguments, the proof does not require explicitly to introduce a notion of neutral and normal forms.