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https://github.com/Smaug123/agdaproofs
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28 lines
877 B
Agda
28 lines
877 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Groups.Groups
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open import Groups.Homomorphisms.Definition
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open import Groups.Definition
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open import Numbers.Naturals.Naturals
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open import Setoids.Orders
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open import Setoids.Setoids
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open import Functions
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open import Sets.EquivalenceRelations
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open import Rings.Definition
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open import Rings.Homomorphisms.Definition
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open import Groups.Homomorphisms.Lemmas
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open import Rings.IntegralDomains.Definition
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Rings.Associates.Definition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} {R : Ring S _+_ _*_} (intDom : IntegralDomain R) where
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open import Rings.Units.Definition R
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open Setoid S
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open Ring R
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open Equivalence eq
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Associates : Rel A
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Associates x y = Sg A (λ z → Unit z && (x ∼ (y * z)))
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