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https://github.com/Smaug123/agdaproofs
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28 lines
1.1 KiB
Agda
28 lines
1.1 KiB
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 Lists.Lists
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Rings.UniqueFactorisationDomains.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.Units.Definition R
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open import Rings.Irreducibles.Definition intDom
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open Ring R
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open Setoid S
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record Factorisation {r : A} (nonzero : (r ∼ 0R) → False) (nonunit : (Unit r) → False) : Set (a ⊔ b) where
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field
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factorise : List A
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factoriseIsFactorisation : fold (_*_) 1R factorise ∼ r
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factoriseIsIrreducibles : allTrue Irreducible factorise
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--record UFD : Set (a ⊔ b) where
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-- field
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-- factorisation : {r : A} → (nonzero : (r ∼ 0R) → False) → (nonunit : (Unit r) → False) → Factorisation nonzero nonunit
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-- uniqueFactorisation : {r : A} → (nonzero : (r ∼ 0R) → False) → (nonunit : (Unit r) → False) → (f1 f2 : Factorisation nonzero nonunit) → {!Sg !}
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