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https://github.com/Smaug123/agdaproofs
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23 lines
794 B
Agda
23 lines
794 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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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 Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Rings.Units.Lemmas {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} (R : Ring S _+_ _*_) where
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open import Rings.Units.Definition R
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open import Rings.Ideals.Definition R
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open Ring R
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open Setoid S
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open Equivalence eq
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unitImpliesGeneratedIdealEverything : {x : A} → Unit x → {y : A} → generatedIdealPred x y
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unitImpliesGeneratedIdealEverything {x} (a , xa=1) {y} = (a * y) , transitive *Associative (transitive (*WellDefined xa=1 reflexive) identIsIdent)
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