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[Refractor] contradiction over ⊥-elim in commutes-with-∪ def #2663

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Merged
jamesmckinna merged 2 commits into from
Mar 15, 2025
Merged

[Refractor] contradiction over ⊥-elim in commutes-with-∪ def #2663

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[Refractor] contradiction over ⊥-elim in commutes-with-∪ def
jmougeot Mar 12, 2025
25dfbaa
Merge branch 'master' into contradiciton11
jamesmckinna Mar 15, 2025
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8 changes: 4 additions & 4 deletions src/Data/Nat/InfinitelyOften.agda
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Original file line number Diff line number Diff line change
Expand Up @@ -8,18 +8,18 @@

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)
open import Data.Sum.Base using (inj₁; inj₂; _⊎_)
open import Effect.Monad using (RawMonad)
open import Function.Base using (_∘_; id)
open import Level using (Level; 0ℓ)
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.Unary using (Pred; _∪_; _⊆_)
open import Relation.Nullary.Negation.Core using (contradiction)

open RawMonad (¬¬-Monad {a = 0ℓ})

Expand Down Expand Up @@ -62,7 +62,7 @@ _∪-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.
Expand Down