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Re: [Coq-Club] Prop vs Type


Chronological Thread 
  • From: Herman Geuvers <herman AT cs.ru.nl>
  • To: coq-club AT inria.fr
  • Subject: Re: [Coq-Club] Prop vs Type
  • Date: Thu, 15 Nov 2012 10:27:22 +0100

Hi,

That's a nice proof Hugo. I was wondering whether one could show _directly_ that there is a retract from Prop into a small type, from the assumption that Prop = Type.

BTW the link in the Coq StdLib to my note on this is wrong; it should be
http://www.cs.ru.nl/~herman/PUBS/newnote.ps.gz

Best

Herman Geuvers

On 11/15/2012 04:30 AM, Hugo Herbelin wrote:
Hi,

Attached is a proof relying on Hurkens' paradox (not without pain)!

Hugo

On Thu, Nov 15, 2012 at 12:16:52AM +0100, Andreas Abel wrote:
You could try to adopt Hurkens' Paradox (inconsistency of Prop :
Prop). I do not know whether it will work, because under the
assumption

H : Type = Prop

you only get something like

cast H Prop : Prop

but it might work nevertheless.

Andreas

On 14.11.12 4:15 PM, Daniel Schepler wrote:
On Tue, Nov 13, 2012 at 4:54 PM, Jonas Oberhauser
<s9joober AT gmail.com>
wrote:
Can I prove

Goal Prop <> Type.

In coq?

Kind regards,
Jonas

Well, Prop has impredicative constructions, which in Type would lead
to contradictions. That's where I'd start looking for something to
distinguish between the two. Though I couldn't immediately think of
any way to exploit this...


--
Andreas Abel <>< Du bist der geliebte Mensch.

Theoretical Computer Science, University of Munich
Oettingenstr. 67, D-80538 Munich, GERMANY

andreas.abel AT ifi.lmu.de
http://www2.tcs.ifi.lmu.de/~abel/



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