mirror of
https://github.com/Smaug123/agdaproofs
synced 2025-10-20 10:38:39 +00:00
18 lines
632 B
Agda
18 lines
632 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
|
|
|
|
open import Groups.Definition
|
|
open import Setoids.Orders.Partial.Definition
|
|
open import Setoids.Setoids
|
|
open import Functions.Definition
|
|
|
|
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
|
|
|
|
module Groups.Orders.Partial.Definition {n m : _} {A : Set n} {S : Setoid {n} {m} A} {_+_ : A → A → A} (G : Group S _+_) where
|
|
|
|
open Group G
|
|
open Setoid S
|
|
|
|
record PartiallyOrderedGroup {p : _} {_<_ : Rel {_} {p} A} (pOrder : SetoidPartialOrder S _<_) : Set (lsuc n ⊔ m ⊔ p) where
|
|
field
|
|
orderRespectsAddition : {a b : A} → (a < b) → (c : A) → (a + c) < (b + c)
|