mirror of
https://github.com/Smaug123/agdaproofs
synced 2025-10-11 06:38:39 +00:00
18 lines
651 B
Agda
18 lines
651 B
Agda
{-# OPTIONS --safe --warning=error #-}
|
||
|
||
open import LogicalFormulae
|
||
open import Groups
|
||
open import Naturals
|
||
open import Orders
|
||
open import Setoids
|
||
open import Functions
|
||
open import Rings
|
||
|
||
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
|
||
|
||
module IntegralDomains where
|
||
record IntegralDomain {n m : _} {A : Set n} {S : Setoid {n} {m} A} {_+_ : A → A → A} {_*_ : A → A → A} (R : Ring S _+_ _*_) : Set (lsuc m ⊔ n) where
|
||
field
|
||
intDom : {a b : A} → Setoid._∼_ S (a * b) (Ring.0R R) → (Setoid._∼_ S a (Ring.0R R)) || (Setoid._∼_ S b (Ring.0R R))
|
||
nontrivial : Setoid._∼_ S (Ring.1R R) (Ring.0R R) → False
|