@@ -12,7 +12,7 @@ open import Haskell.Prim.Applicative
1212--------------------------------------------------
1313-- _∷_
1414
15- module _ {x y : a} {xs ys : List a} where
15+ module _ {x y : a} {xs ys : List a} where
1616 ∷-injective-left : x ∷ xs ≡ y ∷ ys → x ≡ y
1717 ∷-injective-left refl = refl
1818
@@ -40,14 +40,14 @@ map-∘ g f (x ∷ xs) = cong (_ ∷_) (map-∘ g f xs)
4040
4141map-concatMap : ∀ (f : a → b) (xs : List a) → (map f xs) ≡ concatMap (λ g → f g ∷ []) xs
4242map-concatMap f [] = refl
43- map-concatMap f (x ∷ xs)
43+ map-concatMap f (x ∷ xs)
4444 rewrite map-concatMap f xs
4545 = refl
4646
47- map-<*>-recomp : {a b c : Type} → (xs : List (a → b)) → (ys : List a) → (u : (b → c))
47+ map-<*>-recomp : {a b c : Type} → (xs : List (a → b)) → (ys : List a) → (u : (b → c))
4848 → ((map (u ∘_) xs) <*> ys) ≡ map u (xs <*> ys)
4949map-<*>-recomp [] _ _ = refl
50- map-<*>-recomp (x ∷ xs) ys u
50+ map-<*>-recomp (x ∷ xs) ys u
5151 rewrite map-∘ u x ys
5252 | map-++ u (map x ys) (xs <*> ys)
5353 | map-<*>-recomp xs ys u
@@ -102,7 +102,7 @@ lengthNat-++ (x ∷ xs) = cong suc (lengthNat-++ xs)
102102++-cancel-right [] [] eq = refl
103103++-cancel-right (x ∷ xs) [] eq = ++-identity-left-unique (x ∷ xs) (sym eq)
104104++-cancel-right [] (y ∷ ys) eq = sym $ ++-identity-left-unique (y ∷ ys) eq
105- ++-cancel-right (x ∷ xs) (y ∷ ys) eq
105+ ++-cancel-right (x ∷ xs) (y ∷ ys) eq
106106 rewrite ∷-injective-left eq = cong (y ∷_) $ ++-cancel-right xs ys (∷-injective-right eq)
107107
108108++-conical-left : (xs ys : List a) → xs ++ ys ≡ [] → xs ≡ []
@@ -114,7 +114,7 @@ lengthNat-++ (x ∷ xs) = cong suc (lengthNat-++ xs)
114114∷-not-identity : ∀ x (xs ys : List a) → (x ∷ xs) ++ ys ≡ ys → ⊥
115115∷-not-identity x xs ys eq = []≠∷ x xs (sym $ ++-identity-left-unique (x ∷ xs) (sym eq))
116116
117- concatMap-++-distr : ∀ (xs ys : List a) (f : a → List b) →
117+ concatMap-++-distr : ∀ (xs ys : List a) (f : a → List b) →
118118 ((concatMap f xs) ++ (concatMap f ys)) ≡ (concatMap f (xs ++ ys))
119119concatMap-++-distr [] ys f = refl
120120concatMap-++-distr (x ∷ xs) ys f
@@ -129,7 +129,7 @@ foldr-universal : ∀ (h : List a → b) f e → (h [] ≡ e) →
129129 (∀ x xs → h (x ∷ xs) ≡ f x (h xs)) →
130130 ∀ xs → h xs ≡ foldr f e xs
131131foldr-universal h f e base step [] = base
132- foldr-universal h f e base step (x ∷ xs) rewrite step x xs = cong (f x) (foldr-universal h f e base step xs)
132+ foldr-universal h f e base step (x ∷ xs) rewrite step x xs = cong (f x) (foldr-universal h f e base step xs)
133133
134134foldr-cong : ∀ {f g : a → b → b} {d e : b} →
135135 (∀ x y → f x y ≡ g x y) → d ≡ e →
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