mirror of
https://github.com/Smaug123/agdaproofs
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21 lines
714 B
Agda
21 lines
714 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import Groups.Definition
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open import Setoids.Setoids
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open import Sets.EquivalenceRelations
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open import Groups.Subgroups.Normal.Definition
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module Groups.Subgroups.Normal.Examples {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} (G : Group S _+_) where
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open import Groups.Subgroups.Examples G
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open Setoid S
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open Equivalence eq
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open Group G
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trivialSubgroupIsNormal : normalSubgroup G trivialSubgroup
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trivialSubgroupIsNormal {g} k=0 = transitive (+WellDefined reflexive (transitive (+WellDefined k=0 reflexive) identLeft)) (invRight {g})
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improperSubgroupIsNormal : normalSubgroup G improperSubgroup
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improperSubgroupIsNormal _ = record {}
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