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Re: [Coq-Club] For arbitrary crelations, is symmetry involutive?


Chronological Thread 
  • From: "John Wiegley" <johnw AT newartisans.com>
  • To: Gaetan Gilbert <gaetan.gilbert AT ens-lyon.fr>
  • Cc: coq-club AT inria.fr
  • Subject: Re: [Coq-Club] For arbitrary crelations, is symmetry involutive?
  • Date: Sat, 29 Apr 2017 01:16:15 -0700
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>>>>> "GG" == Gaetan Gilbert
>>>>> <gaetan.gilbert AT ens-lyon.fr>
>>>>> writes:

GG> [symmetry] is not involutive: take [R := fun _ _ => bool] and for the
GG> proof of symmetry [fun x y (H : R x y) => true : R y x].

GG> Then for some x and y, [false : R x y] and [symmetry (symmetry false) =
GG> true <> false].

Hi Gaëtan,

How about relations that are known to be equivalences?

Theorem symmetry_invol `{Setoid A} (x y : A) (R : x === y) :
symmetry (symmetry R) = R.

--
John Wiegley GPG fingerprint = 4710 CF98 AF9B 327B B80F
http://newartisans.com 60E1 46C4 BD1A 7AC1 4BA2



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