test
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@ -78,6 +78,16 @@ is-1-type A = (x y : A) → (p q : x ≡ y) → (r s : p ≡ q) → r ≡ s
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```
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```
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lemma3∙1∙8 : {A : Set} → isSet A → is-1-type A
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lemma3∙1∙8 : {A : Set} → isSet A → is-1-type A
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lemma3∙1∙8 {A} A-set x y p q r s =
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lemma3∙1∙8 {A} A-set x y p q r s =
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let g = λ q → A-set x y p q in
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let
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what : {q' : x ≡ y} (r : q ≡ q') → g q ∙ r ≡ g q'
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what r =
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let what3 = apd g r in
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let what4 = lemma2∙11∙2.i r (g q) in
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let what5 = {! !} in
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sym what4 ∙ what3
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in
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-- let what2 = what r in
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{! !}
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{! !}
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```
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```
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@ -8,8 +8,17 @@ open import HottBook.Chapter3
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## 4.1 Quasi-inverses
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## 4.1 Quasi-inverses
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### Lemma 4.1.1
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```
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```
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-- qinv : {A B : Type} (f : A → B) →
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lemma4∙1∙1 : {A B : Set}
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→ (f : A → B)
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→ qinv f
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→ qinv f ≃ ((x : A) → x ≡ x)
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lemma4∙1∙1 f q = {! !}
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where
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ff : qinv f → (x : A) → x ≡ x
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ff
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```
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```
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### Theorem 4.1.3
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### Theorem 4.1.3
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