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delete-trailing-whitespace
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owen-milner committed Oct 19, 2023
1 parent af97ed5 commit e0756ca
Showing 1 changed file with 4 additions and 4 deletions.
8 changes: 4 additions & 4 deletions Cubical/Homotopy/WhiteheadsLemma.agda
Original file line number Diff line number Diff line change
Expand Up @@ -156,7 +156,7 @@ private
( (e3 ∘ e1) , (snd (compEquiv (e1 , e1Eq) (e3 , e3Eq))))))
-- end of the long private block of helper lemmas

-- some useful paths between different maps
-- some useful paths between different maps

{-
Expand Down Expand Up @@ -275,7 +275,7 @@ private
| |
| |
v |
πₙ₊₁ (A, a) ---------> πₙ₊₁ (B, f a)
πₙ₊₁ (A, a) ---------> πₙ₊₁ (B, f a)
-}
πHomπHomCongSquare : {A B : Type ℓ} {a : A} {n : ℕ} (f : A B)
Expand Down Expand Up @@ -404,13 +404,13 @@ WhiteheadsLemma : {A B : Type ℓ} {n : ℕ}
isEquiv f
WhiteheadsLemma {n = zero} hA hB f hf0 hf = isContr→isContr→isEquiv f hA hB
WhiteheadsLemma {A = A} {B = B} {n = suc n} hA hB f hf0 hf =
ΩEquiv→Equiv
ΩEquiv→Equiv
( f)
( hf0)
( λ a WhiteheadsLemma
( isOfHLevelPath' n hA a a)
( isOfHLevelPath' n hB (f a) (f a))
( fst (Ω→ {A = (A , a)} {B = (B , f a)} (f , refl)))
( fst (Ω→ {A = (A , a)} {B = (B , f a)} (f , refl)))
( hf a 0)
( ΩWhiteheadHyp a))
where
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