[Agda] Re: problem using "with"

[Guillermo Calderón]

On 11/05/12 16:24, Ulf Norell wrote:
>
> On Fri, May 11, 2012 at 7:36 PM, Guillermo Calderón
> <calderon at fing.edu.uy
> <mailto:calderon at fing.edu.uy>> wrote:
>
>     hello,
>
>     I have a problem using "with".  The  code below  is a simplified
>     version to illustrate the case:
>
>      > g :  ℕ  → ℕ
>      > g a with  a ≤? 5
>      > ... |  yes _  = a
>      > ... |  no  _  = suc a
>      >
>      > prop-g  : ∀ n  -> (R :  ℕ  → Set)
>      >                -> (∀ m -> R (suc m))
>      >                -> (∀ n -> n ≤ 5 -> R (g n))
>      >                -> R (g n)
>      > prop-g n R f1 f2  with n ≤? 5
>      > ... | no  ¬p   =  f1 n
>      > ... | yes p    =  f2 n p- -*** ERROR here ***
>      >
>
>
> The problem is that the abstraction happens at the point of the
> with. At that point you haven't applied f2 yet, so the n in the type
> of f2 is a different n from the one in n ≤? 5, thus it doesn't abstract.
>

Ulf,
Thanks for your answer.
As far as i known, the same problem should happen for the case (no  ¬p).

        > ... | no  ¬p   =  f1 n

However,  no error is reported by agda at this level and  (f1 n)  is 
accepted as well typed.
¿what is the difference between   both cases?