[Agda] excluded-middle
Katsutoshi Itoh
cutsea110 at gmail.com
Mon Jun 20 22:23:59 CEST 2016
Hi all.
I'd like to use excluded-middle like below:
```
A∪Aᶜ≈U : ∀ {ℓ} {X : Set ℓ} {A : Pred X lzero} → A ∪ A ᶜ ≈ U
A∪Aᶜ≈U {A = A} = record { eql = A∪Aᶜ⊆U A , A∪Aᶜ⊇U A }
where
A∪Aᶜ⊆U : ∀ {ℓ} {X : Set ℓ} (A : Pred X lzero) → A ∪ A ᶜ ⊆ U
A∪Aᶜ⊆U A x∈A∪Aᶜ = tt
A∪Aᶜ⊇U : ∀ {ℓ} {X : Set ℓ} (A : Pred X lzero) → A ∪ A ᶜ ⊇ U
A∪Aᶜ⊇U A {x} tt = excluded-middle
where
postulate
excluded-middle : ∀ {a} {P : Set a} → P ⊎ ¬ P
```
On the other hand, in standard library,
I found excluded-middle at Relation.Nullary.Negation module.
but, I didn't understand how to use it.
```
excluded-middle : ∀ {p} {P : Set p} → ¬ ¬ Dec P
excluded-middle ¬h = ¬h (no (λ p → ¬h (yes p)))
```
Please teach me how to apply it in my case.
--
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いとう かつとし
cutsea110 at gmail.com
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