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Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities

From: Abhishek Anand <abhishek.anand.iitg AT gmail.com>
To: coq-club <coq-club AT inria.fr>
Subject: Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities
Date: Fri, 15 Apr 2016 19:36:12 -0400
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Thanks, Daniel, Pierre-Marie, and Laurent.

I am missing one piece of the puzzle.

My boolean ring (say B) has infinitely many elements.

How do I justify changing the types of the variables from B to bool, or to Z/2Z?

More formally, How do I prove:

(forall (b1 b2 ... bn : B), h1l=h1r -> h2l=h2r ->..... hml=hmr -> cl=cr)

<->(forall (b1 b2 ... bn : bool), h1l=h1r -> h2l=h2r ->..... hml=hmr -> cl=cr),

where hil, hir, cl and cr are ring expressions over the variables bi.

Thanks,

-- Abhishek

http://www.cs.cornell.edu/~aa755/

On Fri, Apr 15, 2016 at 6:24 AM, Laurent Thery <Laurent.Thery AT inria.fr> wrote:

Maybe I am missing something here but as

x = y can be encoded as x + y + 1
and
x -> y as x * y + y + 1

Oops

x * y + x + 1

[Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities, Abhishek Anand, 04/13/2016
- Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities, Laurent Thery, 04/13/2016
  - Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities, Laurent Thery, 04/13/2016
    - Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities, Abhishek Anand, 04/15/2016
      - Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities, Daniel Schepler, 04/15/2016
        
        Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities, Abhishek Anand, 04/15/2016
        
        Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities, Daniel Schepler, 04/15/2016
        
        Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities, Pierre-Marie Pédrot, 04/15/2016
      - Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities, Laurent Thery, 04/15/2016
        
        Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities, Laurent Thery, 04/15/2016
        
        Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities, Abhishek Anand, 04/16/2016
        
        Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities, Daniel Schepler, 04/16/2016
- Re: [Coq-Club] ring tactic: boolean rings and completeness when supplied with equalities, Assia Mahboubi, 04/19/2016