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https://github.com/Smaug123/agdaproofs
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20 lines
743 B
Agda
20 lines
743 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import Rings.Definition
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open import Rings.Orders.Partial.Definition
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open import Rings.Orders.Total.Definition
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open import Setoids.Setoids
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open import Setoids.Orders.Partial.Definition
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open import Functions
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open import Fields.Fields
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Fields.Orders.Total.Definition {m n : _} {A : Set m} {S : Setoid {m} {n} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} (F : Field R) where
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open Ring R
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record TotallyOrderedField {p} {_<_ : Rel {_} {p} A} {pOrder : SetoidPartialOrder S _<_} (pRing : PartiallyOrderedRing R pOrder) : Set (lsuc (m ⊔ n ⊔ p)) where
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field
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oRing : TotallyOrderedRing pRing
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