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https://github.com/Smaug123/agdaproofs
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30 lines
1.1 KiB
Agda
30 lines
1.1 KiB
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 Orders
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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 Sets.FinSet
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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 Groups.QuotientGroup.Definition
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Groups.Subgroups.Normal.Definition where
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record NormalSubgroup {a} {b} {c} {d} {A : Set a} {B : Set c} {S : Setoid {a} {b} A} {T : Setoid {c} {d} B} {_·A_ : A → A → A} {_·B_ : B → B → B} (G : Group S _·A_) (H : Group T _·B_) {f : B → A} (hom : GroupHom H G f) : Set (a ⊔ b ⊔ c ⊔ d) where
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open Setoid S
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field
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subgroup : Subgroup G H hom
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normal : {g : A} {h : B} → Sg B (λ fromH → (g ·A (f h)) ·A (Group.inverse G g) ∼ f fromH)
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