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https://github.com/Smaug123/agdaproofs
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24 lines
911 B
Agda
24 lines
911 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import Groups.Groups
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open import Groups.Definition
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open import Numbers.Integers.Integers
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open import Setoids.Setoids
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open import LogicalFormulae
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open import Functions
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open import Sets.EquivalenceRelations
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open import Numbers.Naturals.Naturals
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open import Groups.Homomorphisms.Definition
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open import Groups.Homomorphisms.Lemmas
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open import Groups.Isomorphisms.Definition
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open import Groups.Subgroups.Definition
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open import Groups.Lemmas
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open import Groups.Abelian.Definition
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Groups.Subgroups.Normal.Definition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} (G : Group S _+_) where
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normalSubgroup : {c : _} {pred : A → Set c} (sub : Subgroup G pred) → Set (a ⊔ c)
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normalSubgroup {pred = pred} sub = {g k : A} → pred k → pred (g + (k + Group.inverse G g))
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