Hi Aditya,
Great talk! You did a great job presenting a difficult system in an easy-to-understand way :)
Just wanna point out a detail. Proofs are dynamic terms (of sort "prop"). So they are not really "type-level". But I guess it is ok to say "type-level" in the talk since they will be erased after proof-checking and you didn't really go into the details about the proof language.
Again, thank you very much for the presentation!