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More rings stuff (#83)

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Patrick Stevens
2019-11-23 13:53:54 +00:00
committed by GitHub
parent 660d7aa27c
commit 2ed7bd8044
12 changed files with 260 additions and 17 deletions
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7
Rings/Ideals/Prime/Definition.agda
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@@ -18,5 +18,8 @@ open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Rings.Ideals.Prime.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
PrimeIdeal : Set (a ⊔ c)
PrimeIdeal = {a b : A} → pred (a * b) → ((pred a) → False) → pred b
record PrimeIdeal : Set (a ⊔ c) where
field
isPrime : {a b : A} → pred (a * b) → ((pred a) → False) → pred b
notContained : A
notContainedIsNotContained : (pred notContained) → False