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[Refractor] contradiction over ⊥-elim in Data/List/Fresh/Relation.Unary.Any.Propreties #2669

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Merged
JacquesCarette merged 1 commit into from
Mar 13, 2025
Merged

[Refractor] contradiction over ⊥-elim in Data/List/Fresh/Relation.Unary.Any.Propreties #2669

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2 changes: 0 additions & 2 deletions src/Data/List/Fresh/Relation/Unary/All/Properties.agda
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Expand Up @@ -10,12 +10,10 @@ module Data.List.Fresh.Relation.Unary.All.Properties where

open import Data.List.Fresh using (List#; []; cons; _∷#_; _#_)
open import Data.List.Fresh.Relation.Unary.All using (All; []; _∷_; append)
open import Data.Empty using (⊥; ⊥-elim)
open import Data.Nat.Base using (ℕ; zero; suc)
open import Data.Product.Base using (_,_)
open import Function.Base using (_∘′_)
open import Level using (Level; _⊔_; Lift)
open import Relation.Nullary.Negation.Core using (¬_)
open import Relation.Unary as U using (Pred)
open import Relation.Binary.Core using (Rel)
open import Relation.Binary.PropositionalEquality.Core using (_≡_; refl; cong)
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7 changes: 3 additions & 4 deletions src/Data/List/Fresh/Relation/Unary/Any/Properties.agda
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Expand Up @@ -9,7 +9,6 @@
module Data.List.Fresh.Relation.Unary.Any.Properties where

open import Data.Bool.Base using (true; false)
open import Data.Empty using (⊥; ⊥-elim)
open import Data.List.Fresh using (List#; _∷#_; _#_; NonEmpty; cons; length; [])
open import Data.List.Fresh.Relation.Unary.All using (All; _∷_; append; [])
open import Data.List.Fresh.Relation.Unary.Any using (Any; here; there; _─_)
Expand All @@ -19,12 +18,12 @@ open import Data.Sum.Base as Sum using (_⊎_; inj₁; inj₂)
open import Function.Base using (_∘′_)
open import Level using (Level; _⊔_; Lift)
open import Relation.Nullary.Reflects using (invert)
open import Relation.Nullary.Negation.Core using (¬_)
open import Relation.Nullary.Decidable.Core
open import Relation.Unary as U using (Pred)
open import Relation.Binary.Core using (Rel)
open import Relation.Nary using (∀[_]; _⇒_; ∁; Decidable)
open import Relation.Binary.PropositionalEquality.Core using (_≡_; refl; cong)
open import Relation.Nullary.Negation.Core using (contradiction; ¬_)

private
variable
Expand Down Expand Up @@ -56,15 +55,15 @@ module _ {R : Rel A r} {P : Pred A p} {Q : Pred A q} (P⇒¬Q : ∀[ P ⇒ ∁ Q
module _ {R : Rel A r} {P : Pred A p} {Q : Pred A q} (P? : Decidable P) where

¬All⇒Any : {xs : List# A R} → ¬ (All P xs) → Any (∁ P) xs
¬All⇒Any {xs = []} ¬ps = ⊥-elim (¬ps [])
¬All⇒Any {xs = []} ¬ps = contradiction [] ¬ps
¬All⇒Any {xs = x ∷# xs} ¬ps with P? x
... | true because [p] = there (¬All⇒Any (¬ps ∘′ (invert [p] ∷_)))
... | false because [¬p] = here (invert [¬p])

¬Any⇒All : {xs : List# A R} → ¬ (Any P xs) → All (∁ P) xs
¬Any⇒All {xs = []} ¬ps = []
¬Any⇒All {xs = x ∷# xs} ¬ps with P? x
... | true because [p] = ⊥-elim (¬ps (here (invert [p])))
... | true because [p] = contradiction (here (invert [p])) ¬ps
... | false because [¬p] = invert [¬p] ∷ ¬Any⇒All (¬ps ∘′ there)

------------------------------------------------------------------------
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