# [Agda] hidden proofs

Liam O'Connor liamoc at cse.unsw.edu.au
Tue Jul 30 19:46:07 CEST 2013

```Hi Sergei,

I was pretty easily able to define "even" using a similar definition to your first one:

open import Data.Nat

mutual
data Even : ℕ → Set
where
even0 : Even 0
even-suc : {n : ℕ} → Even n → Even (suc (suc n))

open import Relation.Nullary

even : (n : ℕ) -> Dec (Even n)
even zero = yes even0
even (suc zero) = no (λ ()) -- absurd pattern :)
even (suc (suc n)) with even n
... | yes p = yes (even-suc p)
... | no p = no (λ { (even-suc x) → p x })

If you wanted to include odd as well the proof is still possible, just a little longer.

Regards,
Liam

On Wednesday, 31 July 2013 at 3:33 AM, Sergei Meshveliani wrote:

> mutual
> data Even : ℕ → Set
> where
> even0 : Even 0
> even-suc : {n : ℕ} → Odd n → Even (suc n)
>
> data Odd : ℕ → Set where
> odd-suc : {n : ℕ} → Even n → Odd (suc n)

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