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16 lines
635 B
Agda
16 lines
635 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import Setoids.Setoids
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open import Rings.Definition
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open import Rings.IntegralDomains.Definition
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Rings.PrincipalIdealDomains.Definition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} {R : Ring S _+_ _*_} (intDom : IntegralDomain R) where
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open import Rings.Ideals.Principal.Definition R
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open import Rings.Ideals.Definition R
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PrincipalIdealDomain : {c : _} → Set (a ⊔ b ⊔ lsuc c)
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PrincipalIdealDomain {c} = {pred : A → Set c} → (ideal : Ideal pred) → PrincipalIdeal ideal
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