Reduction Free Normalisation for a proof irrelevant type of propositions
arXiv:2103.04287 · doi:10.46298/lmcs-19(3:5)2023
Abstract
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.