diff options
| author | Greg Brown <greg.brown@cl.cam.ac.uk> | 2022-04-04 12:34:14 +0100 |
|---|---|---|
| committer | Greg Brown <greg.brown@cl.cam.ac.uk> | 2022-04-04 12:34:14 +0100 |
| commit | e3f5e2a708452c8cde9af7f08ab6f00afe0f859a (patch) | |
| tree | 53f48f4d174b50b5b5f473b6f1d7b77b2033f807 /src/Helium/Algebra/Ordered/StrictTotal/Properties/Group.agda | |
| parent | ba95dc7d15cab1af40da896114b7dd9aad5afda0 (diff) | |
Remove redundant cancel property.
It is in the standard library as `⁻¹-injective`.
Diffstat (limited to 'src/Helium/Algebra/Ordered/StrictTotal/Properties/Group.agda')
| -rw-r--r-- | src/Helium/Algebra/Ordered/StrictTotal/Properties/Group.agda | 11 |
1 files changed, 0 insertions, 11 deletions
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 |