{-# OPTIONS --safe --warning=error --without-K #-} open import Groups.Definition open import Setoids.Orders open import Setoids.Setoids open import Functions 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