diff options
| author | Greg Brown <greg.brown@cl.cam.ac.uk> | 2022-04-02 11:41:51 +0100 |
|---|---|---|
| committer | Greg Brown <greg.brown@cl.cam.ac.uk> | 2022-04-02 11:59:21 +0100 |
| commit | 2167866c53aa7f9cbb52e776bfb64f53acf3fa2c (patch) | |
| tree | d9422bd08ee318b3fad90d03210f6a02a4c30783 /src/Helium/Algebra/Ordered/StrictTotal/Properties/Semigroup.agda | |
| parent | 23e8afe152a84551491594aea133488523525410 (diff) | |
Add more properties for ordered structures.
Diffstat (limited to 'src/Helium/Algebra/Ordered/StrictTotal/Properties/Semigroup.agda')
| -rw-r--r-- | src/Helium/Algebra/Ordered/StrictTotal/Properties/Semigroup.agda | 31 |
1 files changed, 31 insertions, 0 deletions
diff --git a/src/Helium/Algebra/Ordered/StrictTotal/Properties/Semigroup.agda b/src/Helium/Algebra/Ordered/StrictTotal/Properties/Semigroup.agda new file mode 100644 index 0000000..17228ac --- /dev/null +++ b/src/Helium/Algebra/Ordered/StrictTotal/Properties/Semigroup.agda @@ -0,0 +1,31 @@ +------------------------------------------------------------------------ +-- Agda Helium +-- +-- Algebraic properties of ordered semigroups +------------------------------------------------------------------------ + +{-# OPTIONS --safe --without-K #-} + +open import Helium.Algebra.Ordered.StrictTotal.Bundles + +module Helium.Algebra.Ordered.StrictTotal.Properties.Semigroup + {ℓ₁ ℓ₂ ℓ₃} + (semigroup : Semigroup ℓ₁ ℓ₂ ℓ₃) + where + +open Semigroup semigroup + renaming + ( trans to <-trans + ; irrefl to <-irrefl + ; asym to <-asym + ) + +open import Helium.Algebra.Ordered.StrictTotal.Properties.Magma magma public + using + ( ∙-mono-<; ∙-monoˡ-<; ∙-monoʳ-< + ; ∙-mono-≤; ∙-monoˡ-≤; ∙-monoʳ-≤ + ; ∙-cancelˡ; ∙-cancelʳ; ∙-cancel + ; ∙-cancelˡ-<; ∙-cancelʳ-<; ∙-cancel-< + ; ∙-cancelˡ-≤; ∙-cancelʳ-≤; ∙-cancel-≤ + ) +open import Helium.Relation.Binary.Properties.StrictTotalOrder strictTotalOrder public |