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[Refractor] contradiction over ⊥-elim in ¬-not def #2661

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Mar 15, 2025
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[Refractor] contradiction over ⊥-elim in ¬-not def #2661

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6 changes: 3 additions & 3 deletions src/Data/Bool/Properties.agda
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Original file line number Diff line number Diff line change
Expand Up @@ -16,7 +16,6 @@ import Algebra.Lattice.Properties.BooleanAlgebra as BooleanAlgebraProperties
open import Data.Bool.Base
using (Bool; true; false; not; _∧_; _∨_; _xor_ ; if_then_else_; T; _≤_; _<_
; b≤b; f≤t; f<t)
open import Data.Empty using (⊥; ⊥-elim)
open import Data.Product.Base using (_×_; _,_; proj₁; proj₂)
open import Data.Sum.Base using (_⊎_; inj₁; inj₂; [_,_])
open import Function.Base using (_⟨_⟩_; const; id)
Expand All @@ -42,6 +41,7 @@ open import Relation.Binary.PropositionalEquality.Properties
using (module ≡-Reasoning; setoid; decSetoid; isEquivalence)
open import Relation.Nullary.Decidable.Core
using (True; yes; no; fromWitness ; toWitness)
open import Relation.Nullary.Negation.Core using (contradiction)
import Relation.Unary as U

open import Algebra.Definitions {A = Bool} _≡_
Expand Down Expand Up @@ -657,10 +657,10 @@ not-¬ {true} refl ()
not-¬ {false} refl ()

¬-not : ∀ {x y} → x ≢ y → x ≡ not y
¬-not {true} {true} x≢y = ⊥-elim (x≢y refl)
¬-not {true} {true} x≢y = contradiction refl x≢y
¬-not {true} {false} _ = refl
¬-not {false} {true} _ = refl
¬-not {false} {false} x≢y = ⊥-elim (x≢y refl)
¬-not {false} {false} x≢y = contradiction refl x≢y

------------------------------------------------------------------------
-- Properties of _xor_
Expand Down