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https://github.com/Smaug123/agdaproofs
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14 lines
652 B
Agda
14 lines
652 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import Setoids.Setoids
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open import Groups.Definition
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open import Groups.Abelian.Definition
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module Groups.Abelian.DirectSum {a b c d : _} {A : Set a} {B : Set b} {S : Setoid {a} {c} A} {T : Setoid {b} {d} B} {_+1_ : A → A → A} {_+2_ : B → B → B} {G1' : Group S _+1_} {G2' : Group T _+2_} (G1 : AbelianGroup G1') (G2 : AbelianGroup G2') where
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open import Groups.DirectSum.Definition G1' G2'
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open import Setoids.Product S T
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directSumAbGroup : AbelianGroup directSumGroup
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AbelianGroup.commutative directSumAbGroup = productLift (AbelianGroup.commutative G1) (AbelianGroup.commutative G2)
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