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Some graphs stuff (#98)

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Patrick Stevens
2020-02-15 13:41:51 +00:00
committed by GitHub
parent 9de323c5e8
commit f41f5226b9
18 changed files with 275 additions and 39 deletions
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12
Modules/DirectSum.agda
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@@ -11,11 +11,11 @@ open import Modules.Definition
module Modules.DirectSum {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+R_ : A → A → A} {_*R_ : A → A → A} (R : Ring S _+R_ _*R_) {m n o p : _} {M : Set m} {T : Setoid {m} {n} M} {_+_ : M → M → M} {G' : Group T _+_} {G : AbelianGroup G'} {_·1_ : A → M → M} {N : Set o} {U : Setoid {o} {p} N} {_+'_ : N → N → N} {H' : Group U _+'_} {H : AbelianGroup H'} {_·2_ : A → N → N} (M1 : Module R G _·1_) (M2 : Module R H _·2_) where
open import Groups.Abelian.DirectSum G H
open import Setoids.DirectSum T U
open import Setoids.Product T U
directSumModule : Module R directSumAbGroup λ r mn → ((r ·1 (_&&_.fst mn)) ,, (r ·2 (_&&_.snd mn)))
Module.dotWellDefined directSumModule r=s t=u = directSumLift (Module.dotWellDefined M1 r=s (_&&_.fst t=u)) (Module.dotWellDefined M2 r=s (_&&_.snd t=u))
Module.dotDistributesLeft directSumModule = directSumLift (Module.dotDistributesLeft M1) (Module.dotDistributesLeft M2)
Module.dotDistributesRight directSumModule = directSumLift (Module.dotDistributesRight M1) (Module.dotDistributesRight M2)
Module.dotAssociative directSumModule = directSumLift (Module.dotAssociative M1) (Module.dotAssociative M2)
Module.dotIdentity directSumModule = directSumLift (Module.dotIdentity M1) (Module.dotIdentity M2)
Module.dotWellDefined directSumModule r=s t=u = productLift (Module.dotWellDefined M1 r=s (_&&_.fst t=u)) (Module.dotWellDefined M2 r=s (_&&_.snd t=u))
Module.dotDistributesLeft directSumModule = productLift (Module.dotDistributesLeft M1) (Module.dotDistributesLeft M2)
Module.dotDistributesRight directSumModule = productLift (Module.dotDistributesRight M1) (Module.dotDistributesRight M2)
Module.dotAssociative directSumModule = productLift (Module.dotAssociative M1) (Module.dotAssociative M2)
Module.dotIdentity directSumModule = productLift (Module.dotIdentity M1) (Module.dotIdentity M2)