I have an Agda formalization of canonicity in a similar manner, although with non-cumulative Coquand universes, if you're interested (the repo is a mess though sorry) github.com/AndrasKovacs/g
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wooooow - some impressive type signatures in Pi.agda! :O
Oh wait - every file has impressive type signatures in it
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Type signatures are copied from UnfoldedDepModelTemplate.agda where they are given by printing everything with implicit params shown. My current "best practice" in Agda looks like this unfortunately.
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