mirror of
https://github.com/Smaug123/agdaproofs
synced 2025-10-16 17:08:39 +00:00
26 lines
873 B
Agda
26 lines
873 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
|
|
|
|
open import LogicalFormulae
|
|
open import Groups.Groups
|
|
open import Groups.Definition
|
|
open import Numbers.Naturals.Naturals
|
|
open import Setoids.Orders
|
|
open import Setoids.Setoids
|
|
open import Functions
|
|
open import Sets.EquivalenceRelations
|
|
open import Rings.Definition
|
|
open import Rings.Orders.Partial.Definition
|
|
|
|
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
|
|
|
|
module Rings.Orders.Total.Definition {n m : _} {A : Set n} {S : Setoid {n} {m} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} where
|
|
|
|
open Ring R
|
|
open Group additiveGroup
|
|
open Setoid S
|
|
|
|
record TotallyOrderedRing {p : _} {_<_ : Rel {_} {p} A} {pOrder : SetoidPartialOrder S _<_} (pRing : PartiallyOrderedRing R pOrder) : Set (lsuc n ⊔ m ⊔ p) where
|
|
field
|
|
total : SetoidTotalOrder pOrder
|
|
open SetoidPartialOrder pOrder
|