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code formatting
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martinescardo committed Sep 3, 2023
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3 changes: 3 additions & 0 deletions source/Fin/Omega.lagda
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Expand Up @@ -116,8 +116,10 @@ Fin-to-Ω-embedding-is-equiv-iff-2-and-EM {𝓤} fe pe 2 (e , e-is-embedding) =
where
p : Ω 𝓤
p = (P , P-is-prop)

I₁ : is-decidable (e⁻¹ p = e⁻¹ ⊤)
I₁ = Fin-is-discrete (e⁻¹ p) (e⁻¹ ⊤)

I₂ : is-decidable (e⁻¹ p = e⁻¹ ⊤) → is-decidable (p holds)
I₂ = map-is-decidable
(λ (r : e⁻¹ p = e⁻¹ ⊤)
Expand All @@ -136,6 +138,7 @@ Fin-to-Ω-embedding-is-equiv-iff-2-and-EM {𝓤} fe pe 2 (e , e-is-embedding) =
(e 𝟏 =⟨ holds-gives-equal-⊤ pe fe (e 𝟏) h₁ ⟩
⊤ =⟨ (holds-gives-equal-⊤ pe fe (e 𝟎) h₀)⁻¹ ⟩
e 𝟎 ∎))

II₁ : ¬ (e 𝟎 holds) → e 𝟏 holds
II₁ ν₀ = ¬¬-elim (em (e 𝟏 holds) (holds-is-prop (e 𝟏))) II₂
where
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