{-# OPTIONS --safe --warning=error --without-K #-}

open import LogicalFormulae
open import Setoids.Setoids
open import Rings.Definition

open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

module Rings.Units.Definition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} (R : Ring S _+_ _*_) where

open Setoid S
open Ring R

Unit : A → Set (a ⊔ b)
Unit r = Sg A (λ s → (r * s) ∼ 1R)