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[Coq-Club] Re: trying to use Init.Wf.Fix .


chronological Thread 
  • From: dehlinge AT dpt-info.u-strasbg.fr
  • To: coq-club AT pauillac.inria.fr
  • Subject: [Coq-Club] Re: trying to use Init.Wf.Fix .
  • Date: Thu, 6 May 2004 15:48:20 +0200 (CEST)
  • Importance: Normal
  • List-archive: <http://pauillac.inria.fr/pipermail/coq-club/>

If you tried to run the proof script of the well-foundedness of l that I
provided, you didn't fail to notice there was a slight problem with it.
Here is the corrected version:

Lemma WFL :
        well_founded l.
Proof.
intro n.
apply (lt_wf_ind n (Acc l)).
clear n.
intros n rec.
constructor.
intros y l1.
inversion l1.
generalize l1.
rewrite <- H0.
rewrite H1.
clear H1 H0 n0 l1 y.
intros.
constructor.
intros.
inversion H0.
 elim (not_even_and_odd (S n)); auto with arith.
  apply rec.
    destruct n.
   elim H1.
     auto.
   unfold lt in |- *.
     rewrite minus_Sn_m.
    simpl in |- *.
      rewrite <- minus_n_O.
      apply le_S.
      apply le_n.
    do 2 apply le_n_S.
      destruct n.
     inversion H.
       inversion H6.
     apply le_n_S.
       apply le_O_n.
 apply rec.
   destruct n.
inversion H0.
  unfold lt in |- *.
    apply le_n_S.
    simpl in |- *.
    apply le_minus.
Defined.




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