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https://github.com/Smaug123/agdaproofs
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21 lines
678 B
Agda
21 lines
678 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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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.Irreducibles.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 Setoid S
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open Ring R
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open import Rings.Units.Definition R
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record Irreducible (r : A) : Set (a ⊔ b) where
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field
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nonzero : (r ∼ 0R) → False
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nonunit : (Unit r) → False
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irreducible : (x y : A) → (x * y) ∼ r → (Unit x → False) → Unit y
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