agda bug
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2022 Oct 10
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===
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# 2022 Oct 10
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```agda
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{-# OPTIONS --cubical #-}
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0
src/2023-08-05-scratchpad.agda
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src/2023-08-05-scratchpad.agda
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@ -11,7 +11,7 @@ path-ind : {A : Set}
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→ (C : (x y : A) → x ≡ y → Set)
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→ (c : (x : A) → C x x refl)
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→ (x y : A) → (p : x ≡ y) → C x y p
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path-ind C c x y p = ?
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path-ind C c x y p = {! !}
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-- Lemma 2.1.1
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@ -52,13 +52,13 @@ ap f p i = f (p i)
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lemma2111 : {A B : Set} → (f : A → B) → (ie : isEquiv f) → {a a′ : A}
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→ isEquiv (ap f)
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lemma2111 f ie .equiv-proof y = ?
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lemma2111 f ie .equiv-proof y = {! !}
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-- Lemma 2.11.2
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lemma2112a : {A : Set} → (a : A) → {x₁ x₂ : A} → (p : x₁ ≡ x₂) → (q : a ≡ x₁)
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→ transport ? p ≡ q ∙ p
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lemma2112a a p q = ?
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→ transport {! !} p ≡ q ∙ p
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lemma2112a a p q = {! !}
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-- Lemma 2.11.3
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@ -1,10 +1,11 @@
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```
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module HottBook.Chapter1 where
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open import Relation.Binary.PropositionalEquality
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open import Data.Empty
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open import Data.Sum
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Type = Set
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open import HottBook.Common
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```
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## 1.7 Coproduct types
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@ -21,3 +22,12 @@ A + B = A ⊎ B
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¬_ : (A : Type) → Type
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¬ A = A → ⊥
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```
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## 1.12.1 Path Induction
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```
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J : {A : Type} → (C : (x y : A) → x ≡ y → Type)
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→ (c : (x : A) → C x x refl)
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→ (x y : A) → (p : x ≡ y) → C x y p
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J C c x x refl = c x
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```
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@ -5,12 +5,14 @@ open import Relation.Binary.PropositionalEquality
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open import Function
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open import Data.Product
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open import Data.Product.Properties
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Type = Set
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infixr 6 _∙_
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_∙_ = trans
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open import HottBook.Common
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open import HottBook.Chapter1
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```
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> An internal error has occurred. Please report this as a bug.
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> Location of the error: `__IMPOSSIBLE__`, called at src/full/Agda/Interaction/Imports.hs:915:15 in Agd-2.6.3-d4728884:Agda.Interaction.Imports
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## 2.2 Functions are functors
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### Lemma 2.2.1
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@ -222,16 +224,16 @@ data 𝟙 : Set where
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-- open import Function.HalfAdjointEquivalence
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-- _is-⋆ : (x : 𝟙) → x ≡ ⋆
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-- ⋆ is-⋆ = refl
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--
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--
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-- theorem281-helper2 : {x : 𝟙} → (p : x ≡ x) → p ≡ refl
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-- theorem281-helper2 {x} p =
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-- theorem281-helper2 {x} p =
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-- let a = sym (x is-⋆) ∙ p ∙ (x is-⋆) in
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-- J (λ the what → p ≡ the) ? ?
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--
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--
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-- theorem281-helper : {x y : 𝟙} → (p : x ≡ y) → (x is-⋆) ∙ sym (y is-⋆) ≡ p
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-- theorem281-helper {x} p =
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-- J (λ the what → (x is-⋆) ∙ sym (the is-⋆) ≡ what) p (theorem281-helper2 _)
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--
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--
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-- theorem281 : (x y : 𝟙) → (x ≡ y) ≃ 𝟙
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-- theorem281 x y = record
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-- { to = λ _ → ⋆
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6
src/HottBook/Common.agda
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6
src/HottBook/Common.agda
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open import Relation.Binary.PropositionalEquality
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Type = Set
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infixr 6 _∙_
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_∙_ = trans
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