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[Adam Koprowski <adam.koprowski AT gmail.com>]

   Dear Dimitri,
  Sure, you can do the same thing without Program, but it gets slightly more complicated as you need to manually get the equality for the pattern-matched variable:

Section testing.

Variable P : forall i, i < 10 -> nat -> nat.

Definition check (i : nat) (H : i < 10) : nat.
Proof.
  refine (fix check (i : nat) (H : i < 10) {struct i} : nat :=
    match i as j return i = j -> nat with
    | 0 => fun _ => 0
    | S n => fun ij => P n _ (check n _)
    end refl); subst; auto with arith.
Defined.

End testing.

  Hope that helps,
  Adam

On Tue, Apr 21, 2009 at 14:57, dimitrisg7 <dvekris AT hotmail.com> wrote:

Thanks Adam. But I am not familiar with the new features of Coq. I still use
the previous version. I am wondering if there is still something that can be
done with "old" Coq. If not, I might consider seriously to switch to the new
version.

-----
Never say never.
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-- 
=====================================================
Adam.Koprowski AT gmail.com, http://www.cs.ru.nl/~Adam.Koprowski

The difference between impossible and possible
lies in determination (Tommy Lasorda)
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