mirror of
https://github.com/Smaug123/agdaproofs
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22 lines
902 B
Agda
22 lines
902 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.Lemmas
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open import Groups.Definition
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open import Setoids.Setoids
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open import Rings.Definition
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open import Rings.Lemmas
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open import Sets.EquivalenceRelations
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open import Rings.Ideals.Definition
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Rings.Ideals.Maximal.Definition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} {R : Ring S _+_ _*_} {c : _} {pred : A → Set c} (i : Ideal R pred) where
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record MaximalIdeal {d : _} : Set (a ⊔ b ⊔ c ⊔ lsuc d) where
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field
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notContained : A
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notContainedIsNotContained : (pred notContained) → False
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isMaximal : {bigger : A → Set d} → Ideal R bigger → ({a : A} → pred a → bigger a) → (Sg A (λ a → bigger a && (pred a → False))) → ({a : A} → bigger a)
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