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[ refactor ] remove redundant private lemma in Data.Sum.Algebra #2908

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Merged
jamesmckinna merged 1 commit into from
Jan 23, 2026
Merged

[ refactor ] remove redundant private lemma in Data.Sum.Algebra #2908

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11 changes: 4 additions & 7 deletions src/Data/Sum/Algebra.agda
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Original file line number Diff line number Diff line change
Expand Up @@ -14,11 +14,11 @@ open import Algebra.Definitions
using (Associative; LeftIdentity; RightIdentity; Identity)
open import Algebra.Structures
using (IsMagma; IsSemigroup; IsMonoid; IsCommutativeMonoid)
open import Data.Empty.Polymorphic using (⊥)
open import Data.Empty.Polymorphic using (⊥; ⊥-elim)
open import Data.Product.Base using (_,_)
open import Data.Sum.Base using (_⊎_; inj₁; inj₂; map; [_,_]; swap; assocʳ; assocˡ)
open import Data.Sum.Properties using (swap-involutive)
open import Data.Unit.Polymorphic.Base using (⊤; tt)
open import Data.Unit.Polymorphic.Base using (⊤)
open import Function.Base using (id; _∘_)
open import Function.Properties.Inverse using (↔-isEquivalence)
open import Function.Bundles using (_↔_; Inverse; mk↔ₛ′)
Expand All @@ -36,9 +36,6 @@ private
a b c d : Level
A B C D : Set a

♯ : {B : ⊥ {a} → Set b} → (w : ⊥) → B w
♯ ()

------------------------------------------------------------------------
-- Algebraic properties

Expand All @@ -62,10 +59,10 @@ module _ (ℓ : Level) where

-- ⊥ is an identity for ⊎
⊎-identityˡ : LeftIdentity {ℓ = ℓ} _↔_ ⊥ _⊎_
⊎-identityˡ A = mk↔ₛ′ [ ♯ , id ] inj₂ cong′ [ ♯ , cong′ ]
⊎-identityˡ A = mk↔ₛ′ [ ⊥-elim , id ] inj₂ cong′ [ ⊥-elim , cong′ ]

⊎-identityʳ : RightIdentity {ℓ = ℓ} _↔_ ⊥ _⊎_
⊎-identityʳ _ = mk↔ₛ′ [ id , ♯ ] inj₁ cong′ [ cong′ , ♯ ]
⊎-identityʳ _ = mk↔ₛ′ [ id , ⊥-elim ] inj₁ cong′ [ cong′ , ⊥-elim ]

⊎-identity : Identity _↔_ ⊥ _⊎_
⊎-identity = ⊎-identityˡ , ⊎-identityʳ
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