[Agda] Re: eta expansion

[Altenkirch Thorsten]

From: Thorsten Altenkirch <psztxa at exmail.nottingham.ac.uk<mailto:psztxa at exmail.nottingham.ac.uk>>
To: Peter Hancock <hancock at spamcop.net<mailto:hancock at spamcop.net>>, Agda List <agda at lists.chalmers.se<mailto:agda at lists.chalmers.se>>
Subject: Re: [Agda] Re: eta expansion

Indeed the universe of finite sets (U=Nat,T=Fin) is univalent and this is easily provable in vanilla type theory (without univalence).

I have to correct myself:

This is incorrect while isomorphism is logically equivalent to equality of the codes (natural numbers), this is not an isomorphism since the equality of numbers is propositional but the isomorphism is obviously not. Indeed, the only univalent universe in vanilla type theory is (Bool,isTrue).

To construct a univalent universe of finite sets one would need to use a higher inductive type.

Thorsten


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