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https://github.com/Smaug123/agdaproofs
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23 lines
739 B
Agda
23 lines
739 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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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 Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Rings.Ideals.Principal.Definition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} (R : Ring S _+_ _*_) where
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open import Rings.Ideals.Definition R
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open import Rings.Divisible.Definition R
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open Setoid S
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record PrincipalIdeal {c : _} {pred : A → Set c} (ideal : Ideal pred) : Set (a ⊔ b ⊔ c) where
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field
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generator : A
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genIsInIdeal : pred generator
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genGenerates : {x : A} → pred x → generator ∣ x
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