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I find it's very strange that you can write equalities between universe levels, as it sounds to me Level should live in some metalevel. Why I in cubical agda lives in Set omega but Level only lives in Set?<br>
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<font size="3"><b>Thanks,</b></font></div>
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<font size="3"><b>Jason Hu</b></font></div>
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<font size="3"><b><a href="https://hustmphrrr.github.io/">https://hustmphrrr.github.io/</a></b></font><br>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Agda <agda-bounces@lists.chalmers.se> on behalf of Siek, Jeremy <jsiek@indiana.edu><br>
<b>Sent:</b> May 20, 2021 10:32 AM<br>
<b>To:</b> Agda List <agda@lists.chalmers.se><br>
<b>Subject:</b> Re: [Agda] another level problem</font>
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Chuckle... and just minutes later I find a solution:</div>
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⊔-cong : ∀{a b c d : Level} → (a ≡ b) → (c ≡ d) → a ⊔ c ≡ b ⊔ d
<div>⊔-cong refl refl = refl</div>
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<div>EQ : ∀ {ℓᵛ₁ ℓᵛ₂ ℓᶜ₁ ℓᶜ₂ : Level} → (ℓᵛ₁ ⊔ ℓᶜ₁ ≡ ℓᶜ₁) → (ℓᵛ₂ ⊔ ℓᶜ₂ ≡ ℓᶜ₂) → (ℓᵛ₁ ⊔ ℓᵛ₂ ⊔ ℓᶜ₁ ⊔ ℓᶜ₂ ≡ ℓᶜ₁ ⊔ ℓᶜ₂)</div>
EQ eq1 eq2 = ⊔-cong eq1 eq2</div>
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Cheers,</div>
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Jeremy</div>
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<div id="x_divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> Agda <agda-bounces@lists.chalmers.se> on behalf of Siek, Jeremy <jsiek@indiana.edu><br>
<b>Sent:</b> Thursday, May 20, 2021 10:16 AM<br>
<b>To:</b> Agda List <agda@lists.chalmers.se><br>
<b>Subject:</b> [Agda] another level problem</font>
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I'd like to prove:<br>
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EQ : ∀ {ℓᵛ₁ ℓᵛ₂ ℓᶜ₁ ℓᶜ₂ : Level} → (ℓᵛ₁ ⊔ ℓᶜ₁ ≡ ℓᶜ₁) → (ℓᵛ₂ ⊔ ℓᶜ₂ ≡ ℓᶜ₂) → (ℓᵛ₁ ⊔ ℓᵛ₂ ⊔ ℓᶜ₁ ⊔ ℓᶜ₂ ≡ ℓᶜ₁ ⊔ ℓᶜ₂)<br>
<span>EQ eq1 eq2 = ?</span></div>
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<span>From earlier threads it sounds like reasoning about equality of levels is mostly automated</span></div>
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<span>in Agda.</span></div>
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<span>So my question is how to use assumptions such as ℓᵛ₁ ⊔ ℓᶜ₁ ≡ ℓᶜ₁?</span></div>
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<span>Cheers,</span></div>
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<span>Jeremy<br>
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