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Restructure towards ideals

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Smaug123
2019-11-20 21:20:03 +00:00
parent f2f4e867fc
commit b03a5279bc
22 changed files with 417 additions and 296 deletions
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16
Groups/Actions/Stabiliser.agda
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@@ -12,7 +12,6 @@ open import Groups.Groups
open import Groups.Subgroups.Definition
open import Groups.Homomorphisms.Definition
open import Groups.Actions.Definition
open import Groups.Groups2
open import Sets.EquivalenceRelations
open import Groups.Actions.Definition
@@ -29,12 +28,13 @@ stabiliserWellDefined x {g} {h} g=h gx=x = transitive (actionWellDefined1 (Equiv
where
open Equivalence eq
stabiliserSubgroup : (x : B) → subgroup G (stabiliserWellDefined x)
_&_&_.one (stabiliserSubgroup x) gx=x hx=x = transitive associativeAction (transitive (actionWellDefined2 hx=x) gx=x)
open Setoid T
open Equivalence (Setoid.eq T)
stabiliserSubgroup : (x : B) → subgroup G (stabiliserPred x)
_&&_.fst (stabiliserSubgroup x) = stabiliserWellDefined x
_&_&_.one (_&&_.snd (stabiliserSubgroup x)) gx=x hx=x = transitive associativeAction (transitive (actionWellDefined2 hx=x) gx=x)
_&_&_.two (_&&_.snd (stabiliserSubgroup x)) = identityAction
_&_&_.three (_&&_.snd (stabiliserSubgroup x)) {g} gx=x = transitive (transitive (transitive (actionWellDefined2 (symmetric gx=x)) (symmetric associativeAction)) (actionWellDefined1 (invLeft {g}))) identityAction
where
open Equivalence eq
_&_&_.two (stabiliserSubgroup x) = identityAction
_&_&_.three (stabiliserSubgroup x) {g = g} gx=x = transitive (transitive (transitive (actionWellDefined2 (symmetric gx=x)) (symmetric associativeAction)) (actionWellDefined1 (invLeft {g}))) identityAction
where
open Equivalence eq
open Group G