patrick/agdaproofs
1
0
Fork 0
mirror of https://github.com/Smaug123/agdaproofs synced 2025-10-17 09:28:40 +00:00
Code Issues Packages Projects Releases Wiki Activity

Irreducible and maximal (#87)

Browse Source
This commit is contained in:
Patrick Stevens
2019-12-07 18:53:08 +00:00
committed by GitHub
parent e192f0e1f1
commit 99c38495ce
9 changed files with 123 additions and 19 deletions
Download Patch File Download Diff File Expand all files Collapse all files

6
Rings/Units/Definition.agda
View File

@@ -1,17 +1,11 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Homomorphisms.Definition
open import Groups.Definition
open import Numbers.Naturals.Naturals
open import Setoids.Orders
open import Setoids.Setoids
open import Functions
open import Sets.EquivalenceRelations
open import Rings.Definition
open import Rings.Homomorphisms.Definition
open import Groups.Homomorphisms.Lemmas
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

22
Rings/Units/Lemmas.agda Normal file
View File

@@ -0,0 +1,22 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions
open import Sets.EquivalenceRelations
open import Rings.Definition
open import Rings.Homomorphisms.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Rings.Units.Lemmas {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} (R : Ring S _+_ _*_) where
open import Rings.Units.Definition R
open import Rings.Ideals.Definition R
open Ring R
open Setoid S
open Equivalence eq
unitImpliesGeneratedIdealEverything : {x : A} → Unit x → {y : A} → generatedIdealPred x y
unitImpliesGeneratedIdealEverything {x} (a , xa=1) {y} = (a * y) , transitive *Associative (transitive (*WellDefined xa=1 reflexive) identIsIdent)