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Re: [Coq-Club] Stuck on a proof of div2 (n + n) = n.


chronological Thread 
  • From: frank maltman <frank.maltman AT googlemail.com>
  • To: Chris Dams <chris.dams.nl AT gmail.com>
  • Cc: <coq-club AT inria.fr>
  • Subject: Re: [Coq-Club] Stuck on a proof of div2 (n + n) = n.
  • Date: Sat, 21 May 2011 11:39:08 +0000
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On Sat, 21 May 2011 13:22:27 +0200
Chris Dams 
<chris.dams.nl AT gmail.com>
 wrote:

> Dear Frank,
> 
> The idea is to get something of the form div2 (S (S m)) because div2
> has been recursively defined as becomes apparent when you do Print
> div2.

Right.

> I found the following proof that utilizes this. The first S in (S n +
> S n) moves to the front automatically because addition is recursive in
> the first argument. The second one needs to helped a bit by using
> plus_n_Sm.

I see. I don't think I would have spotted that.

I guess the trick in general is to spot familiar patterns.

> Lemma divplus : forall n, div2 (n + n) = n.
> intro n.
> induction n as [|n IH]; [tauto|].
> simpl.
> rewrite <- plus_n_Sm.
> f_equal.
> assumption.
> Qed.

Thanks!

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