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[Coq-Club] question about universes and equalities

From: Jonathan Leivent <jonikelee AT gmail.com>
To: Coq Club <coq-club AT inria.fr>
Subject: [Coq-Club] question about universes and equalities
Date: Sun, 8 May 2016 14:10:11 -0400
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I'm hitting some problems that I think are related to equalities in different universes. For example, consider:

Goal forall S1 S2:Set, @eq Type S1 S2 -> @eq Set S1 S2.

Is this provable in Coq? If not, then does that mean it is possible to have two Sets in Coq such that they are (@eq Type) but not (@eq Set)? What would that possibly mean?

-- Jonathan

[Coq-Club] question about universes and equalities, Jonathan Leivent, 05/08/2016
- Re: [Coq-Club] question about universes and equalities, Jason Gross, 05/08/2016
  - Re: [Coq-Club] question about universes and equalities, Jonathan Leivent, 05/08/2016
    - Re: [Coq-Club] question about universes and equalities, Jason Gross, 05/08/2016
      - Re: [Coq-Club] question about universes and equalities, Jonathan Leivent, 05/09/2016
        
        Re: [Coq-Club] question about universes and equalities, Matthieu Sozeau, 05/09/2016
        
        Re: [Coq-Club] question about universes and equalities, Jonathan Leivent, 05/09/2016
        
        Re: [Coq-Club] question about universes and equalities, Jonathan Leivent, 05/09/2016
        Re: [Coq-Club] question about universes and equalities, Jason Gross, 05/09/2016
        Re: [Coq-Club] question about universes and equalities, Jonathan Leivent, 05/09/2016
      - Re: [Coq-Club] question about universes and equalities, Stefan Monnier, 05/09/2016