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Progress towards UFDs (#88)

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Patrick Stevens
2019-12-08 11:18:39 +00:00
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parent 99c38495ce
commit 33098e94b0
20 changed files with 462 additions and 253 deletions
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Rings/UniqueFactorisationDomains/Definition.agda Normal file
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Rings.Definition
open import Rings.IntegralDomains.Definition
open import Lists.Lists
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Rings.UniqueFactorisationDomains.Definition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} {R : Ring S _+_ _*_} (intDom : IntegralDomain R) where
open import Rings.Units.Definition R
open import Rings.Irreducibles.Definition intDom
open Ring R
open Setoid S
record Factorisation {r : A} (nonzero : (r ∼ 0R) → False) (nonunit : (Unit r) → False) : Set (a ⊔ b) where
field
factorise : List A
factoriseIsFactorisation : fold (_*_) 1R factorise ∼ r
factoriseIsIrreducibles : allTrue Irreducible factorise
record UFD : Set (a ⊔ b) where
field
factorisation : {r : A} → (nonzero : (r ∼ 0R) → False) → (nonunit : (Unit r) → False) → Factorisation nonzero nonunit
uniqueFactorisation : {r : A} → (nonzero : (r ∼ 0R) → False) → (nonunit : (Unit r) → False) → (f1 f2 : Factorisation nonzero nonunit) → {!Sg !}