From e3f5e2a708452c8cde9af7f08ab6f00afe0f859a Mon Sep 17 00:00:00 2001 From: Greg Brown Date: Mon, 4 Apr 2022 12:34:14 +0100 Subject: Remove redundant cancel property. MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit It is in the standard library as `⁻¹-injective`. --- src/Helium/Algebra/Ordered/StrictTotal/Properties/Group.agda | 11 ----------- 1 file changed, 11 deletions(-) (limited to 'src/Helium/Algebra/Ordered/StrictTotal/Properties/Group.agda') diff --git a/src/Helium/Algebra/Ordered/StrictTotal/Properties/Group.agda b/src/Helium/Algebra/Ordered/StrictTotal/Properties/Group.agda index d72ae10..cf8e4f2 100644 --- a/src/Helium/Algebra/Ordered/StrictTotal/Properties/Group.agda +++ b/src/Helium/Algebra/Ordered/StrictTotal/Properties/Group.agda @@ -94,17 +94,6 @@ open import Helium.Relation.Binary.Properties.StrictTotalOrder strictTotalOrder ---- Cancellative --- _≈_ - -⁻¹-cancel : Injective _≈_ _≈_ _⁻¹ -⁻¹-cancel {x} {y} x⁻¹≈y⁻¹ = begin-equality - x ≈⟨ inverseˡ-unique x (y ⁻¹) (begin-equality - x ∙ y ⁻¹ ≈˘⟨ ∙-congˡ x⁻¹≈y⁻¹ ⟩ - x ∙ x ⁻¹ ≈⟨ inverseʳ x ⟩ - ε ∎) ⟩ - y ⁻¹ ⁻¹ ≈⟨ ⁻¹-involutive y ⟩ - y ∎ - -- _<_ ⁻¹-anti-cancel-< : Injective _<_ _>_ _⁻¹ -- cgit v1.2.3