26 lines
769 B
Agda
26 lines
769 B
Agda
module 1FundamentalGroup.Quest1 where
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open import Cubical.Core.Everything
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open import Cubical.HITs.S1
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open import Cubical.Data.Nat
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open import Cubical.Data.Int
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open import Cubical.Data.Empty
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open import Cubical.Foundations.Prelude
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open import Cubical.Foundations.HLevels
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open import 1FundamentalGroup.Quest0Solutions using ( Refl ; Refl≢loop )
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Ω : (A : Type) (a : A) → Type
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Ω A a = a ≡ a
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loop_times : ℤ → Ω S¹ base
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loop pos zero times = refl
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loop pos (suc n) times = loop pos n times ∙ loop
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loop negsuc zero times = sym loop
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loop negsuc (suc n) times = loop negsuc n times ∙ sym loop
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¬isSetS¹ : isSet S¹ → ⊥
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¬isSetS¹ h = Refl≢loop (h base base Refl loop)
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¬isPropS¹ : isProp S¹ → ⊥
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¬isPropS¹ h = ¬isSetS¹ (isProp→isSet h)
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