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Re: [Coq-Club] A couple of simple proofs.


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  • From: Gaëtan Gilbert <gaetan.gilbert AT skyskimmer.net>
  • To: coq-club AT inria.fr
  • Subject: Re: [Coq-Club] A couple of simple proofs.
  • Date: Tue, 28 Aug 2018 18:06:57 +0200
  • Authentication-results: mail2-smtp-roc.national.inria.fr; spf=None smtp.pra=gaetan.gilbert AT skyskimmer.net; spf=Pass smtp.mailfrom=gaetan.gilbert AT skyskimmer.net; spf=None smtp.helo=postmaster AT relay1-d.mail.gandi.net
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The first one can't be proven, either add it as an axiom or live without it.

For the second one:

Theorem xverif: (forall q, q+1=3->q+1=4)<->False.
Proof.
split.
(* get rid of the False -> ... goal *)
2:intros [].

intros H.
specialize H with 2. (* or pose proof (H 2) as H' then work with H' *)
discriminate H.
reflexivity.
Qed.

for instance

I don't know why you're trying with (q:=0), that won't give anything interesting.

Gaëtan Gilbert

On 28/08/2018 18:00, Kenneth Roe wrote:
How can I complete the following two proofs:


Theorem bicond:

  forall (x y :Prop), (x <-> y) -> x=y.

Proof.

  ...

Qed.


And the second proof:


Theorem xverif: (forall q, q+1=3->q+1=4)=False.

Proof.

  eapply bicond.

  split. intros.


  elim H with (q := 0).

  generalize H.

  intros.

  ...

Qed.


What gets filled in for the "..." in each of the above proofs?


                  - Ken




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