The Coq mailing list

[Thorsten Altenkirch <Thorsten.Altenkirch AT nottingham.ac.uk>]

Hi Jonathan,

>
>On 09/12/2016 01:57 PM, Thorsten Altenkirch wrote:
>> The proof by Hedberg only requires that there is a constant endofunction
>>
>> Pi x,y:A. x=y -> x=y
>>
>> However, this already follows from stability
>>
>> Pi x,y:A ~~(x = y) -> x=y
>>
>> by composing with x=y -> ~~(x = y) [see lemma 3.5 in our paper
>> http://www.cs.nott.ac.uk/~psztxa/publ/jhedberg.pdf)
>
>But, in Coq, is this true?:  "There is, for any x, y : X, a canonical
>map x=y -> ~~(x = y) ."

I think you got confused: actually for any P we have P -> ~~P.

>
>which, if I understand this correctly, means:
>
>Goal forall X (x y:X) (e1 e2 : ~~(x = y)), e1=e2.
>
>which I don't see how to prove in Coq for arbitrary X.

I never said anything like this.

>
>-- Jonathan
>





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