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18 lines
837 B
Agda
18 lines
837 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import Setoids.Setoids
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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open import Numbers.Naturals.Semiring
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open import Sets.Cardinality.Finite.Definition
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open import Groups.Definition
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module Groups.FiniteGroups.Definition where
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record FiniteGroup {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_·_ : A → A → A} (G : Group S _·_) {c : _} (quotientSet : Set c) : Set (a ⊔ b ⊔ c) where
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field
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toSet : SetoidToSet S quotientSet
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finite : FiniteSet quotientSet
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groupOrder : {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_·_ : A → A → A} {underG : Group S _·_} {c : _} {quotientSet : Set c} (G : FiniteGroup underG quotientSet) → ℕ
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groupOrder record { toSet = toSet ; finite = record { size = size ; mapping = mapping ; bij = bij } } = size
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