@@ -56,7 +56,7 @@ open import Relation.Nullary.Negation.Core public
5656¬¬-Monad : RawMonad {a} DoubleNegation
5757¬¬-Monad = mkRawMonad
5858 DoubleNegation
59- ¬¬-eta
59+ ¬¬-η
6060 (λ x f → negated-stable (¬¬-map f x))
6161
6262¬¬-push : DoubleNegation Π[ P ] → Π[ DoubleNegation ∘ P ]
@@ -72,7 +72,7 @@ open import Relation.Nullary.Negation.Core public
7272-- ⊥).
7373
7474call/cc : ((A → Whatever) → DoubleNegation A) → DoubleNegation A
75- call/cc hyp ¬a = hyp (flip contradiction ¬a) ¬a
75+ call/cc hyp ¬a = hyp (λ a → contradiction a ¬a) ¬a
7676
7777-- The "independence of premise" rule, in the double-negation monad.
7878-- It is assumed that the index set (A) is inhabited.
@@ -81,17 +81,17 @@ independence-of-premise : A → (B → Σ A P) → DoubleNegation (Σ[ x ∈ A ]
8181independence-of-premise {A = A} {B = B} {P = P} q f = ¬¬-map helper ¬¬-excluded-middle
8282 where
8383 helper : Dec B → Σ[ x ∈ A ] (B → P x)
84- helper (yes p ) = Product.map₂ const (f p )
85- helper (no ¬p ) = (q , flip contradiction ¬p )
84+ helper (yes b ) = Product.map₂ const (f b )
85+ helper (no ¬b ) = (q , λ b → contradiction b ¬b )
8686
8787-- The independence of premise rule for binary sums.
8888
8989independence-of-premise-⊎ : (A → B ⊎ C) → DoubleNegation ((A → B) ⊎ (A → C))
9090independence-of-premise-⊎ {A = A} {B = B} {C = C} f = ¬¬-map helper ¬¬-excluded-middle
9191 where
9292 helper : Dec A → (A → B) ⊎ (A → C)
93- helper (yes p ) = Sum.map const const (f p )
94- helper (no ¬p ) = inj₁ (flip contradiction ¬p)
93+ helper (yes a ) = Sum.map const const (f a )
94+ helper (no ¬a ) = inj₁ λ a → contradiction a ¬a
9595
9696private
9797
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