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finished rewind

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Jlh18 2021-11-13 00:43:32 +00:00
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1FundamentalGroup/Quest3Solutions.agda
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@ -19,68 +19,6 @@ pathToFun→ A B f =
{-
private
variable
ℓ : Level
transport→ : {A B : I → Type ℓ} (f : A i0 → B i0) (x : A i0) →
transport (λ i → A i → B i) f (transport (λ i → A i) x) ≡ transport (λ i → B i) (f x)
transport→ {A = A} {B = B} f x =
J
(λ A1 A →
transport (λ i → A i → B i) f (transport (λ i → A i) x) ≡ transport (λ i → B i) (f x))
(J
(λ B1 B →
transport (λ i → A i0 → B i) f (transport (λ i → A i0) x) ≡ transport (λ i → B i) (f x))
(
transport (λ i → A i0 → B i0) f (transport (λ i → A i0) x)
≡⟨ cong (transport (λ i → A i0 → B i0) f) (transportRefl x) ⟩
transport (λ i → A i0 → B i0) f x
≡⟨ cong (λ g → g x) (transportRefl f) ⟩
f x
≡⟨ sym (transportRefl (f x)) ⟩
transport (λ i → B i0) (f x) ∎
)
λ i → B i
)
λ i → A i
-- J (λ A1 A → transport (λ i → A i → B i) f ≡ λ a1 → transport B (f (transport (sym A) a1)))
-- (funExt (λ a1 → refl)) A
transport→' : {A0 A1 B0 B1 : Type} {A : A0 ≡ A1} {B : B0 ≡ B1} (f : A0 → B0) →
transport (λ i → A i → B i) f ≡ λ a1 → transport B (f (transport (sym A) a1))
transport→' {A = A} {B = B} f =
J (λ A1 A → transport (λ i → A i → B i) f ≡ λ a1 → transport B (f (transport (sym A) a1)))
refl A
pathToFun→ : {A0 A1 B0 B1 : Type} {A : A0 ≡ A1} {B : B0 ≡ B1} (f : A0 → B0) →
pathToFun (λ i → A i → B i) f ≡ λ a1 → pathToFun B (f (pathToFun (sym A) a1))
pathToFun→ {A = A} {B = B} f =
J (λ A1 A → pathToFun (λ i → A i → B i) f ≡ λ a1 → pathToFun B (f (pathToFun (sym A) a1)))
refl A
pathToFun→' : {A0 A1 B0 B1 : Type} {A : A0 ≡ A1} {B : B0 ≡ B1} (f : A0 → B0) →
pathToFun (λ i → A i → B i) f ≡ λ a1 → pathToFun B (f (pathToFun (sym A) a1))
pathToFun→' {A0} {A1} {B0} {B1} {A} {B} f =
J (λ A1 A → pathToFun (λ i → A i → B i) f ≡ λ a1 → pathToFun B (f (pathToFun (sym A) a1)))
(
J (λ B1 B → pathToFun (λ i → A0 → B i) f ≡ λ a → pathToFun B (f (pathToFun refl a)))
(
funExt λ a →
pathToFun refl f a
≡⟨ cong (λ g → g a) (pathToFunRefl f) ⟩
f a
≡⟨ sym (pathToFunRefl (f a)) ⟩
pathToFun refl (f a)
≡⟨ cong (λ x → pathToFun refl (f x)) (sym (pathToFunRefl a)) ⟩
pathToFun refl (f (pathToFun refl a)) ∎
)
B
)
A -}
open ℤ open ℤ
loopSucℤtimes : (n : ℤ) → loop n times ∙ loop ≡ loop sucℤ n times loopSucℤtimes : (n : ℤ) → loop n times ∙ loop ≡ loop sucℤ n times