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https://github.com/Smaug123/agdaproofs
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22 lines
709 B
Agda
22 lines
709 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.Primes.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.Divisible.Definition R
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open Ring R
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open Setoid S
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open import Rings.Units.Definition R
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record Prime (x : A) : Set (a ⊔ b) where
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field
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isPrime : (r s : A) → (x ∣ (r * s)) → ((x ∣ r) → False) → (x ∣ s)
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nonzero : (x ∼ 0R) → False
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nonunit : Unit x → False
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