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Re: [Coq-Club] Empty type


Chronological Thread 
  • From: Guillaume Brunerie <guillaume.brunerie AT gmail.com>
  • To: Marco Maggesi <maggesi AT math.unifi.it>
  • Cc: Coq-Club Club <coq-club AT inria.fr>
  • Subject: Re: [Coq-Club] Empty type
  • Date: Wed, 13 Feb 2013 09:12:38 -0500

Note also that you still get the full elimination principle for Type.
This is explained in the section "Empty and singleton elimination" in
the doc.

Guillaume

2013/2/13 Guillaume Brunerie
<guillaume.brunerie AT gmail.com>:
> No, that’s a feature.
> See here http://coq.inria.fr/doc/Reference-Manual006.html#@default353
> (further down), and in particular the sentence:
>
>> […] More precisely, an empty or small singleton inductive definition is
>> set in Prop, a small non-singleton inductive family is set in Set, and
>> otherwise in the Type hierarchy.
>
> Guillaume
>
> On 2013/2/12 Marco Maggesi
> <maggesi AT math.unifi.it>
> wrote:
>> When I try to define in Coq 8.4 the empty Type but I get an empty Prop.
>> Is this a bug?
>> M.
>>
>> Welcome to Coq 8.4 (September 2012)
>>
>> Coq < Inductive empty : Type := .
>> empty is defined
>> empty_rect is defined
>> empty_ind is defined
>> empty_rec is defined
>>
>> Coq < Check empty.
>> empty
>> : Prop



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