patrick/agdaproofs
1
0
Fork 0
mirror of https://github.com/Smaug123/agdaproofs synced 2025-10-18 17:48:40 +00:00
Code Issues Packages Projects Releases Wiki Activity

Z is a Euclidean domain (#86)

Browse Source
This commit is contained in:
Patrick Stevens
2019-12-07 13:00:18 +00:00
committed by GitHub
parent cfd9787bb8
commit e192f0e1f1
38 changed files with 1018 additions and 486 deletions
Download Patch File Download Diff File Expand all files Collapse all files

9
Rings/IntegralDomains/Examples.agda
View File

@@ -17,12 +17,3 @@ open import Fields.Fields
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Rings.IntegralDomains.Examples where
fieldIsIntDom : {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} {R : Ring S _+_ _*_} (F : Field R) → (Setoid._∼_ S (Ring.1R R) (Ring.0R R) → False) → IntegralDomain R
IntegralDomain.intDom (fieldIsIntDom F 1!=0) {a} {b} ab=0 a!=0 with Field.allInvertible F a a!=0
IntegralDomain.intDom (fieldIsIntDom {S = S} {R = R} F _) {a} {b} ab=0 a!=0 | 1/a , prA = transitive (symmetric identIsIdent) (transitive (*WellDefined (symmetric prA) reflexive) (transitive (symmetric *Associative) (transitive (*WellDefined reflexive ab=0) timesZero)))
where
open Setoid S
open Equivalence eq
open Ring R
IntegralDomain.nontrivial (fieldIsIntDom F 1!=0) = 1!=0