diff --git a/src/Data/Nat/InfinitelyOften.agda b/src/Data/Nat/InfinitelyOften.agda index a5c8fb6dcd..e4d59e7830 100644 --- a/src/Data/Nat/InfinitelyOften.agda +++ b/src/Data/Nat/InfinitelyOften.agda @@ -10,7 +10,6 @@ module Data.Nat.InfinitelyOften where open import Effect.Monad using (RawMonad) open import Level using (Level; 0ℓ) -open import Data.Empty using (⊥-elim) open import Data.Nat.Base using (ℕ; _≤_; _⊔_; _+_; suc; zero; s≤s) open import Data.Nat.Properties open import Data.Product.Base as Prod hiding (map) @@ -18,7 +17,7 @@ open import Data.Sum.Base using (inj₁; inj₂; _⊎_) open import Function.Base using (_∘_; id) open import Relation.Binary.PropositionalEquality.Core using (_≢_) open import Relation.Nullary.Negation using (¬¬-Monad; call/cc) -open import Relation.Nullary.Negation.Core using (¬_) +open import Relation.Nullary.Negation.Core using (¬_; contradiction) open import Relation.Unary using (Pred; _∪_; _⊆_) open RawMonad (¬¬-Monad {a = 0ℓ}) @@ -62,7 +61,7 @@ _∪-Fin_ {P = P} {Q} (i , ¬p) (j , ¬q) = (i ⊔ j , helper) commutes-with-∪ : ∀ {P Q} → Inf (P ∪ Q) → ¬ ¬ (Inf P ⊎ Inf Q) commutes-with-∪ p∪q = call/cc λ ¬[p⊎q] → - (λ ¬p ¬q → ⊥-elim (p∪q (¬p ∪-Fin ¬q))) + (λ ¬p ¬q → contradiction (¬p ∪-Fin ¬q) p∪q) <$> ¬[p⊎q] ∘ inj₁ ⊛ ¬[p⊎q] ∘ inj₂ -- Inf is functorial.