Re: [Agda] What is wrong about this proof for A ⊆ A ∪ B

[Andreas Abel]

This works:

   A⊆A∪B' : ∀ {ℓ₀ ℓ₁} {X : Set ℓ₀} {A B : Pred X ℓ₁} → A ⊆ A ∪ B
   A⊆A∪B' x∈A = inj₁ x∈A

On 15.06.2016 02:31, Katsutoshi Itoh wrote:
> Hi all.
>
> I'm studying sets theory by using agda(2.5.1).
> Now, I've proved a theorem A ⊆ A ∪ B by 2 kind of solutions,
> and I get warnings(yellow highlight) occured around both codes,
> But I couldn't understand what's happen.
> Please teach me what is wrong about these?
>
> ```
>    A⊆A∪B : ∀ A B → A ⊆ A ∪ B

Just a short in the dark:  I would guess that Agda cannot infer the 
universe levels for A and B, so you should write

   (A B : FILLMEIN) -> A \subseteq A \cup B

instead.

>    A⊆A∪B x∈A B x = inj₁ x
>
>    A⊆A∪B' : ∀ {ℓ₀ ℓ₁ X} {A : Pred X ℓ₀} {B : Pred X ℓ₁} → A ⊆ A ∪ B
>    A⊆A∪B' x∈A = inj₁ x∈A
> ```
>
> I attach all my program file.
>
> Regards.
>
>
>
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