From: Jason Gross <jason...@gmail.com>
To: Andrew Polonsky <andrew....@gmail.com>,
Homotopy Type Theory <HomotopyT...@googlegroups.com>
Subject: Re: [HoTT] Re: Meta-conjecture about MLTT
Date: Mon, 12 Sep 2016 05:59:12 +0000 [thread overview]
Message-ID: <CAKObCaooaVyFoh-Xr5S8gMj--35FQNUGwQZ8t0CejRQhhRnNJA@mail.gmail.com> (raw)
In-Reply-To: <ca38369f-7691-46f7-8d00-2c944ec6e489@googlegroups.com>
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I suspect "one of them provably has but the other doesn't" should mean "one
of them provably has but the other provably does not have".
On Sun, Sep 11, 2016 at 10:20 PM Andrew Polonsky <andrew....@gmail.com>
wrote:
> The meta-task is to either produce two isomorphic types in an empty
>> context, together with a property that one of them provably has but the
>> other doesn't, or to show that this is impossible.
>>
>
> What do you mean by a "property", exactly?
>
> If you mean a type family, e.g.,
>
> X : U |- P(X) : Type
>
> then a counterexample is
>
> A = Nat x Bool
> B = Bool x Nat
> P(X) = Id(U;X,A)
>
> Cheers,
> Andrew
>
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next prev parent reply other threads:[~2016-09-12 5:59 UTC|newest]
Thread overview: 17+ messages / expand[flat|nested] mbox.gz Atom feed top
2016-09-11 20:47 Martin Escardo
2016-09-11 22:08 ` [HoTT] " Peter LeFanu Lumsdaine
2016-09-11 22:26 ` Martin Escardo
2016-09-12 9:11 ` Thomas Streicher
2016-09-12 5:20 ` Andrew Polonsky
2016-09-12 5:59 ` Jason Gross [this message]
2016-09-12 9:55 ` [HoTT] " Andrew Polonsky
2016-09-12 10:07 ` Andrew Polonsky
2016-09-12 10:35 ` Nicolai Kraus
2016-09-12 10:16 ` Peter LeFanu Lumsdaine
2016-09-12 10:44 ` [HoTT] " Nicolai Kraus
2016-09-12 11:02 ` Andrej Bauer
2016-09-12 11:14 ` Thomas Streicher
2016-09-12 11:23 ` Andrew Polonsky
2016-09-12 11:41 ` Thomas Streicher
2016-09-12 12:47 ` Thomas Streicher
2016-09-12 13:01 ` Martin Escardo
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