mirror of
https://github.com/Smaug123/agdaproofs
synced 2025-10-11 22:58:40 +00:00
20 lines
867 B
Agda
20 lines
867 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
|
|
|
|
open import LogicalFormulae
|
|
open import Setoids.Setoids
|
|
open import Functions
|
|
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
|
|
open import Numbers.Naturals.Naturals
|
|
open import Sets.FinSet
|
|
open import Groups.Definition
|
|
open import Sets.EquivalenceRelations
|
|
open import Groups.Abelian.Definition
|
|
|
|
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
|
|
|
|
open import Groups.DirectSum.Definition G1' G2'
|
|
open import Setoids.DirectSum S T
|
|
|
|
directSumAbGroup : AbelianGroup directSumGroup
|
|
AbelianGroup.commutative directSumAbGroup = directSumLift (AbelianGroup.commutative G1) (AbelianGroup.commutative G2)
|