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Re: [Coq-Club] Why is it wrong to declare a proven theorem as axiom?


chronological Thread 
  • From: Pierre-Yves Strub <pierre-yves AT strub.nu>
  • To: <coq-club AT inria.fr>
  • Subject: Re: [Coq-Club] Why is it wrong to declare a proven theorem as axiom?
  • Date: Fri, 24 Jun 2011 15:40:19 +0200

You proved:

False -> Q and False -> ~Q

because VAR is discharged when you close the section.

Pierre-Yves.

On Fri, 24 Jun 2011 16:35:43 +0300, Georgi Guninski wrote:

i am somewhat surprised why you don't print False->stuff here:

Section S.
Lemma T : Prop.
exact False.
Defined.

Variable VAR : T.

Lemma L_2: exists a : T, a = VAR.
eexists. instantiate (1:=VAR). reflexivity.
Defined.


Lemma L_1: ~(exists a : T, a = VAR).

change ((exists a : T, a = VAR) -> False); intro H; refine (ex_ind _ H);
       clear H; intro x; intro H; auto with *.
Defined.

End S.




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