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[ refactor ] deprecate Algebra.Structures.IsGroup.{uniqueˡ-⁻¹|uniqueʳ-⁻¹} with knock-ons for Algebra.Module.* (#2571)
* deprecate: `uniqueˡ-⁻¹` and `uniqueʳ-⁻¹` * refactor: simplify imports * refactor: simplify imports * refactor: export of uniqueness proofs * tweak: remove parentheses * tweak: `import` refinements * tweak: whitespace/alignment * fix: semicolon * refactor: corresponding changes for `Module`s, plus new `module`s to support them * refactor: fix re-exports from `Algebra.Module.Properties` * fix: `CHANGELOG` * fix: names of lemmas, and their types! * fix: whitespace! * fix: names, types, and exports
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‎CHANGELOG.md‎

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@@ -57,6 +57,18 @@ Deprecated names
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*ₗ-assoc+comm⇒*ₗ-*ᵣ-assoc ↦ *ₗ-assoc∧comm⇒*ₗ-*ᵣ-assoc
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```
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* In `Algebra.Modules.Structures.IsLeftModule`:
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```agda
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uniqueˡ‿⁻ᴹ ↦ Algebra.Module.Properties.LeftModule.inverseˡ-uniqueᴹ
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uniqueʳ‿⁻ᴹ ↦ Algebra.Module.Properties.LeftModule.inverseʳ-uniqueᴹ
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```
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* In `Algebra.Modules.Structures.IsRightModule`:
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```agda
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uniqueˡ‿⁻ᴹ ↦ Algebra.Module.Properties.RightModule.inverseˡ-uniqueᴹ
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uniqueʳ‿⁻ᴹ ↦ Algebra.Module.Properties.RightModule.inverseʳ-uniqueᴹ
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```
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* In `Algebra.Properties.Magma.Divisibility`:
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```agda
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∣∣-sym ↦ ∥-sym
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∣-trans ↦ ∣ʳ-trans
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```
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* In `Algebra.Structures.Group`:
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```agda
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uniqueˡ-⁻¹ ↦ Algebra.Properties.Group.inverseˡ-unique
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uniqueʳ-⁻¹ ↦ Algebra.Properties.Group.inverseʳ-unique
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```
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* In `Data.List.Base`:
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```agda
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and ↦ Data.Bool.ListAction.and
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New modules
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-----------
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* `Algebra.Module.Properties.{Bimodule|LeftModule|RightModule}`.
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* `Data.List.Base.{and|or|any|all}` have been lifted out into `Data.Bool.ListAction`.
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* `Data.List.Base.{sum|product}` and their properties have been lifted out into `Data.Nat.ListAction` and `Data.Nat.ListAction.Properties`.
@@ -161,6 +181,12 @@ Additions to existing modules
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commutativeRing : CommutativeRing c ℓ → CommutativeRing (a ⊔ c) (a ⊔ ℓ)
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```
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* In `Algebra.Modules.Properties`:
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```agda
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inverseˡ-uniqueᴹ : x +ᴹ y ≈ 0ᴹ → x ≈ -ᴹ y
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inverseʳ-uniqueᴹ : x +ᴹ y ≈ 0ᴹ → y ≈ -ᴹ x
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```
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* In `Algebra.Properties.Magma.Divisibility`:
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```agda
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∣ˡ-respʳ-≈ : _∣ˡ_ Respectsʳ _≈_

‎src/Algebra/Module/Bundles.agda‎

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@@ -39,7 +39,6 @@ open import Algebra.Module.Definitions
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open import Function.Base using (flip)
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open import Level using (Level; _⊔_; suc)
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open import Relation.Binary.Core using (Rel)
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open import Relation.Nullary using (¬_)
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import Relation.Binary.Reasoning.Setoid as ≈-Reasoning
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private

‎src/Algebra/Module/Properties.agda‎

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{-# OPTIONS --cubical-compatible --safe #-}
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open import Algebra using (CommutativeRing; Involutive)
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open import Algebra.Bundles using (CommutativeRing)
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open import Algebra.Module.Bundles using (Module)
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open import Level using (Level)
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open Module mod
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open import Algebra.Module.Properties.Semimodule semimodule public
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open import Algebra.Properties.Group using (⁻¹-involutive)
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-ᴹ-involutive : Involutive _≈ᴹ_ -ᴹ_
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-ᴹ-involutive = ⁻¹-involutive +ᴹ-group
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open import Algebra.Module.Properties.Bimodule bimodule public
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using (inverseˡ-uniqueᴹ; inverseʳ-uniqueᴹ; -ᴹ-involutive)

‎src/Algebra/Module/Properties/Bimodule.agda‎

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------------------------------------------------------------------------
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-- The Agda standard library
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--
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-- Properties of bimodules.
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------------------------------------------------------------------------
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{-# OPTIONS --cubical-compatible --safe #-}
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open import Algebra.Bundles using (Ring)
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open import Algebra.Module.Bundles using (Bimodule)
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open import Level using (Level)
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module Algebra.Module.Properties.Bimodule
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{r ℓr s ℓs m ℓm : Level}
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{ringR : Ring r ℓr} {ringS : Ring s ℓs}
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(mod : Bimodule ringR ringS m ℓm)
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where
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open Bimodule mod
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open import Algebra.Module.Properties.LeftModule leftModule public
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using (inverseˡ-uniqueᴹ; inverseʳ-uniqueᴹ; -ᴹ-involutive)

‎src/Algebra/Module/Properties/LeftModule.agda‎

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------------------------------------------------------------------------
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-- The Agda standard library
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--
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-- Properties of left modules.
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------------------------------------------------------------------------
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{-# OPTIONS --cubical-compatible --safe #-}
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open import Algebra.Bundles using (Ring)
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open import Algebra.Module.Bundles using (LeftModule)
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open import Level using (Level)
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module Algebra.Module.Properties.LeftModule
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{r ℓr m ℓm : Level}
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{ring : Ring r ℓr}
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(mod : LeftModule ring m ℓm)
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where
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open Ring ring
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open LeftModule mod
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open import Algebra.Properties.AbelianGroup +ᴹ-abelianGroup public
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using ()
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renaming (inverseˡ-unique to inverseˡ-uniqueᴹ
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; inverseʳ-unique to inverseʳ-uniqueᴹ
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; ⁻¹-involutive to -ᴹ-involutive)

‎src/Algebra/Module/Properties/RightModule.agda‎

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------------------------------------------------------------------------
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-- The Agda standard library
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--
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-- Properties of right modules.
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------------------------------------------------------------------------
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{-# OPTIONS --cubical-compatible --safe #-}
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open import Algebra.Bundles using (Ring)
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open import Algebra.Module.Bundles using (RightModule)
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open import Level using (Level)
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module Algebra.Module.Properties.RightModule
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{r ℓr m ℓm : Level}
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{ring : Ring r ℓr}
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(mod : RightModule ring m ℓm)
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where
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open Ring ring
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open RightModule mod
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open import Algebra.Properties.AbelianGroup +ᴹ-abelianGroup public
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using ()
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renaming (inverseˡ-unique to inverseˡ-uniqueᴹ
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; inverseʳ-unique to inverseʳ-uniqueᴹ
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; ⁻¹-involutive to -ᴹ-involutive)

‎src/Algebra/Module/Properties/Semimodule.agda‎

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{-# OPTIONS --cubical-compatible --safe #-}
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open import Algebra using (CommutativeSemiring)
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open import Algebra.Bundles using (CommutativeSemiring)
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open import Algebra.Module.Bundles using (Semimodule)
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open import Level using (Level)
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open CommutativeSemiring semiring
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open Semimodule semimod
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open import Relation.Nullary.Negation using (contraposition)
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open import Relation.Binary.Reasoning.Setoid ≈ᴹ-setoid
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open import Relation.Nullary.Negation using (contraposition)
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x≈0⇒x*y≈0 : ∀ {x y} → x ≈ 0# → x *ₗ y ≈ᴹ 0ᴹ
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x≈0⇒x*y≈0 {x} {y} x≈0 = begin

‎src/Algebra/Module/Structures.agda‎

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{-# OPTIONS --cubical-compatible --safe #-}
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open import Relation.Binary.Core using (Rel)
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open import Relation.Binary.Bundles using (Setoid)
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open import Relation.Binary.Structures using (IsEquivalence)
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module Algebra.Module.Structures where
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open import Algebra.Bundles
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open import Algebra.Structures using (IsCommutativeMonoid; IsAbelianGroup)
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open import Data.Product.Base using (_,_; proj₁; proj₂)
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open import Level using (Level; _⊔_)
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open import Relation.Binary.Core using (Rel)
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open import Relation.Binary.Bundles using (Setoid)
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open import Relation.Binary.Structures using (IsEquivalence)
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private
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variable
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; uniqueˡ-⁻¹ to uniqueˡ‿-ᴹ
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; uniqueʳ-⁻¹ to uniqueʳ‿-ᴹ
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)
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{-# WARNING_ON_USAGE uniqueˡ‿-ᴹ
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"Warning: uniqueˡ‿-ᴹ was deprecated in v2.3.
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Please use Algebra.Module.Properties.LeftModule.inverseˡ-uniqueᴹ instead."
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#-}
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{-# WARNING_ON_USAGE uniqueʳ‿-ᴹ
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"Warning: uniqueʳ‿-ᴹ was deprecated in v2.3.
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Please use Algebra.Module.Properties.LeftModule.inverseʳ-uniqueᴹ instead."
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#-}
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record IsRightModule (*ᵣ : Opᵣ R M) : Set (r ⊔ m ⊔ ℓr ⊔ ℓm) where
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open Defs ≈ᴹ
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; uniqueˡ-⁻¹ to uniqueˡ‿-ᴹ
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; uniqueʳ-⁻¹ to uniqueʳ‿-ᴹ
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)
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{-# WARNING_ON_USAGE uniqueˡ‿-ᴹ
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"Warning: uniqueˡ‿-ᴹ was deprecated in v2.3.
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Please use Algebra.Module.Properties.RightModule.inverseˡ-uniqueᴹ instead."
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#-}
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{-# WARNING_ON_USAGE uniqueʳ‿-ᴹ
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"Warning: uniqueʳ‿-ᴹ was deprecated in v2.3.
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Please use Algebra.Module.Properties.RightModule.inverseʳ-uniqueᴹ instead."
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#-}
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module _ (R-ring : Ring r ℓr) (S-ring : Ring s ℓs)
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(≈ᴹ : Rel {m} M ℓm) (+ᴹ : Op₂ M) (0ᴹ : M) (-ᴹ : Op₁ M)

‎src/Algebra/Morphism.agda‎

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import Algebra.Morphism.Definitions as MorphismDefinitions
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open import Algebra
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import Algebra.Properties.Group as GroupP
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open import Function.Base
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open import Level
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open import Relation.Binary.Core using (Rel; _Preserves_⟶_)

‎src/Algebra/Structures.agda‎

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@@ -323,10 +323,18 @@ record IsGroup (_∙_ : Op₂ A) (ε : A) (_⁻¹ : Op₁ A) : Set (a ⊔ ℓ) w
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uniqueˡ-⁻¹ : ∀ x y → (x ∙ y) ≈ ε → x ≈ (y ⁻¹)
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uniqueˡ-⁻¹ = Consequences.assoc∧id∧invʳ⇒invˡ-unique
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setoid ∙-cong assoc identity inverseʳ
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{-# WARNING_ON_USAGE uniqueˡ-⁻¹
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"Warning: uniqueˡ-⁻¹ was deprecated in v2.3.
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Please use Algebra.Properties.Group.inverseˡ-unique instead. "
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#-}
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uniqueʳ-⁻¹ : ∀ x y → (x ∙ y) ≈ ε → y ≈ (x ⁻¹)
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uniqueʳ-⁻¹ = Consequences.assoc∧id∧invˡ⇒invʳ-unique
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setoid ∙-cong assoc identity inverseˡ
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{-# WARNING_ON_USAGE uniqueʳ-⁻¹
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"Warning: uniqueʳ-⁻¹ was deprecated in v2.3.
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Please use Algebra.Properties.Group.inverseʳ-unique instead. "
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#-}
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isInvertibleMagma : IsInvertibleMagma _∙_ ε _⁻¹
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isInvertibleMagma = record

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