mirror of
https://github.com/Smaug123/agdaproofs
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22 lines
1.0 KiB
Agda
22 lines
1.0 KiB
Agda
{-# OPTIONS --warning=error --safe --without-K #-}
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open import Functions
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open import Sets.FinSet
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open import LogicalFormulae
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open import Groups.Definition
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open import Groups.Groups
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open import Groups.FiniteGroups.Definition
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open import Groups.Homomorphisms.Definition
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open import Groups.Abelian.Definition
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open import Setoids.Setoids
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open import Fields.FieldOfFractions.Setoid
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open import Sets.EquivalenceRelations
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open import Groups.Lemmas
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open import Groups.QuotientGroup.Definition
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module Groups.QuotientGroup.Lemmas {a b c d : _} {A : Set a} {B : Set b} {S : Setoid {a} {c} A} {T : Setoid {b} {d} B} {_+A_ : A → A → A} {_+B_ : B → B → B} (G : Group S _+A_) (H : Group T _+B_) {f : A → B} (fHom : GroupHom G H f) where
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projectionMapIsGroupHom : GroupHom G (quotientGroupByHom G fHom) id
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GroupHom.groupHom projectionMapIsGroupHom {x} {y} = quotientGroupLemma G fHom (Equivalence.reflexive (Setoid.eq T))
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GroupHom.wellDefined projectionMapIsGroupHom x=y = quotientGroupLemma G fHom (GroupHom.wellDefined fHom x=y)
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