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https://github.com/Smaug123/agdaproofs
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23 lines
806 B
Agda
23 lines
806 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import Groups.Definition
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open import Setoids.Orders.Partial.Definition
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open import Setoids.Orders.Total.Definition
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open import Setoids.Setoids
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open import Functions
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open import Rings.Definition
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open import Rings.Orders.Partial.Definition
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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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
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open Ring R
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open Group additiveGroup
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open Setoid S
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record TotallyOrderedRing {p : _} {_<_ : Rel {_} {p} A} {pOrder : SetoidPartialOrder S _<_} (pRing : PartiallyOrderedRing R pOrder) : Set (lsuc n ⊔ m ⊔ p) where
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field
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total : SetoidTotalOrder pOrder
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open SetoidPartialOrder pOrder
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