diff --git a/1FundamentalGroup/Quest1.agda b/1FundamentalGroup/Quest1.agda index 4ab21d0..5b93ee6 100644 --- a/1FundamentalGroup/Quest1.agda +++ b/1FundamentalGroup/Quest1.agda @@ -4,16 +4,13 @@ open import 1FundamentalGroup.Preambles.P1 Ω : (A : Type) (a : A) → Type -Ω A a = a ≡ a +Ω A a = a ≡ a loop_times : ℤ → Ω S¹ base -loop pos zero times = refl -loop pos (suc n) times = loop pos n times ∙ loop -loop negsuc zero times = sym loop -loop negsuc (suc n) times = loop negsuc n times ∙ sym loop +loop n times = {!!} ¬isSetS¹ : isSet S¹ → ⊥ -¬isSetS¹ h = Refl≢loop (h base base Refl loop) +¬isSetS¹ = {!!} ¬isPropS¹ : isProp S¹ → ⊥ -¬isPropS¹ h = ¬isSetS¹ (isProp→isSet h) +¬isPropS¹ = {!!} diff --git a/1FundamentalGroup/Quest1Solutions.agda b/1FundamentalGroup/Quest1Solutions.agda new file mode 100644 index 0000000..9fbf1ab --- /dev/null +++ b/1FundamentalGroup/Quest1Solutions.agda @@ -0,0 +1,19 @@ +-- ignore +module 1FundamentalGroup.Quest1Solutions where +open import 1FundamentalGroup.Preambles.P1 + + +Ω : (A : Type) (a : A) → Type +Ω A a = a ≡ a + +loop_times : ℤ → Ω S¹ base +loop pos zero times = refl +loop pos (suc n) times = loop pos n times ∙ loop +loop negsuc zero times = sym loop +loop negsuc (suc n) times = loop negsuc n times ∙ sym loop + +¬isSetS¹ : isSet S¹ → ⊥ +¬isSetS¹ h = Refl≢loop (h base base Refl loop) + +¬isPropS¹ : isProp S¹ → ⊥ +¬isPropS¹ h = ¬isSetS¹ (isProp→isSet h) diff --git a/_build/2.6.2/agda/1FundamentalGroup/Quest1Solutions.agdai b/_build/2.6.2/agda/1FundamentalGroup/Quest1Solutions.agdai new file mode 100644 index 0000000..0605090 Binary files /dev/null and b/_build/2.6.2/agda/1FundamentalGroup/Quest1Solutions.agdai differ