mirror of
https://github.com/Smaug123/agdaproofs
synced 2025-10-08 05:18:40 +00:00
38 lines
1.2 KiB
Agda
38 lines
1.2 KiB
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Groups.Groups
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open import Groups.Abelian.Definition
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open import Groups.Homomorphisms.Definition
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open import Groups.Definition
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open import Numbers.Naturals.Definition
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open import Setoids.Orders
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open import Setoids.Setoids
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open import Functions
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open import Sets.EquivalenceRelations
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open import Vectors
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open import Lists.Lists
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open import Maybe
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Groups.Polynomials.Group {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} (G : Group S _+_) where
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open import Groups.Polynomials.Definition G
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open import Groups.Polynomials.Addition G public
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open Setoid S
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open Equivalence eq
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polyGroup : Group naivePolySetoid _+P_
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Group.+WellDefined polyGroup = +PwellDefined
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Group.0G polyGroup = []
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Group.inverse polyGroup = inverse'
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Group.+Associative polyGroup {a} {b} {c} = assoc {a} {b} {c}
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Group.identRight polyGroup = PidentRight
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Group.identLeft polyGroup = PidentLeft
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Group.invLeft polyGroup {a} = invLeft' {a}
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Group.invRight polyGroup {a} = invRight' {a}
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abelian : AbelianGroup G → AbelianGroup polyGroup
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AbelianGroup.commutative (abelian ab) {x} {y} = comm ab {x} {y}
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