From ddfecdd209b953831f28848aee24aa4d32091230 Mon Sep 17 00:00:00 2001 From: Jlh18 Date: Tue, 28 Sep 2021 14:40:40 +0100 Subject: [PATCH] quest1 prepped with solutions added --- 1FundamentalGroup/Quest1.agda | 11 ++++------ 1FundamentalGroup/Quest1Solutions.agda | 19 ++++++++++++++++++ .../1FundamentalGroup/Quest1Solutions.agdai | Bin 0 -> 49337 bytes 3 files changed, 23 insertions(+), 7 deletions(-) create mode 100644 1FundamentalGroup/Quest1Solutions.agda create mode 100644 _build/2.6.2/agda/1FundamentalGroup/Quest1Solutions.agdai 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 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