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Re: [Coq-Club] Re: Coq-club digest, Vol 1 #1172 - 3 msgs


chronological Thread 
  • From: Adam Chlipala <adamc AT hcoop.net>
  • To: Cedric.Auger AT lri.fr
  • Cc: coq-club AT pauillac.inria.fr
  • Subject: Re: [Coq-Club] Re: Coq-club digest, Vol 1 #1172 - 3 msgs
  • Date: Fri, 05 Sep 2008 10:47:47 -0400
  • List-archive: <http://pauillac.inria.fr/pipermail/coq-club/>

AUGER Cédric wrote:
I may be wrong, but there is also cardinal impossibility for that
isomorphism:

cnat is a lot bigger than nat and even bigger than reals (true reals, not
floating ones), since for each real x, there exists a cnat c such that "c
real 0 _ = x", and as there is no bijection between nat and reals, there
is no bijection between nat and cnat.

Isn't every type not provably bigger than [nat] in Coq, since every nameable value of every type (and thus every value that we're sure exists in every model of CIC) corresponds to a finite string of Coq syntax? I'm not so up on the meta-theoretic issues here, but it seems like constructivity should break the usual cardinality arguments.





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