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Re: [Coq-Club] proof with nat_ind


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  • From: Pierre Casteran <pierre.casteran AT labri.fr>
  • To: coq-club AT inria.fr
  • Subject: Re: [Coq-Club] proof with nat_ind
  • Date: Wed, 02 Dec 2015 18:58:17 +0100
  • Authentication-results: mail3-smtp-sop.national.inria.fr; spf=None smtp.pra=pierre.casteran AT labri.fr; spf=Pass smtp.mailfrom=pierre.casteran AT labri.fr; spf=Pass smtp.helo=postmaster AT iona.labri.fr
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Perhaps it's just a syntax error, if you put nat_ind at a place where a tactic is expected.

You should try to write something like :

exact (nat_ind ... ...)
or
apply nat_ind with ...
or
intros n; pattern; apply nat_ind.

Pierre


Quoting Patricia Peratto
<psperatto AT vera.com.uy>:

I want to prove (using nat_ind) the following proposition.
I adjoin the proof I have written myself.

Definition aux1b (n:nat) : forall m:nat,
forall (e:n=m),S n = S m.
nat_ind (fun n:nat =>
(forall m:nat, forall e:n=m, S n = S m))

(fun m:nat, fun e:O=m,
(f_equal nat nat S O m e))

(fun p:nat, fun q:(forall m:nat,
forall e:p = m, S p = S m) =>
(fun m2:nat =>
(fun e2:(S p)=m2 =>
(f_equal nat nat S (S p) m2 e2))))
n.

I have proved it using "induction" but I want to
find the proof using nat_ind.

I have gotten the following message:

Error: The reference nat_ind was not found in the current environment.

Someone can say me where I'm wrong?

Regards

Patricia






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