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Cauchy-completion, first parts (#52)

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Patrick Stevens
2019-10-22 07:51:09 +01:00
committed by GitHub
parent 959071214e
commit 6eaa181104
15 changed files with 567 additions and 518 deletions
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5
Fields/Fields.agda
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@@ -4,6 +4,7 @@ open import LogicalFormulae
open import Groups.Groups
open import Groups.Definition
open import Rings.Definition
open import Rings.Order
open import Rings.Lemmas
open import Setoids.Setoids
open import Setoids.Orders
@@ -31,7 +32,7 @@ module Fields.Fields where
open Equivalence eq
open Ring R
a!=0 : (a ∼ Group.0G additiveGroup) → False
a!=0 pr = SetoidPartialOrder.irreflexive pOrder (SetoidPartialOrder.wellDefined pOrder (symmetric pr) reflexive x)
a!=0 pr = SetoidPartialOrder.irreflexive pOrder (SetoidPartialOrder.<WellDefined pOrder (symmetric pr) reflexive x)
invA : A
invA = underlying (Field.allInvertible F a a!=0)
q : 1R ∼ (invA * a)
@@ -47,7 +48,7 @@ module Fields.Fields where
open Equivalence eq
open Ring R
a!=0 : (a ∼ Group.0G additiveGroup) → False
a!=0 pr = SetoidPartialOrder.irreflexive pOrder (SetoidPartialOrder.wellDefined pOrder reflexive (symmetric pr) x)
a!=0 pr = SetoidPartialOrder.irreflexive pOrder (SetoidPartialOrder.<WellDefined pOrder reflexive (symmetric pr) x)
invA : A
invA = underlying (Field.allInvertible F a a!=0)
q : 1R ∼ (invA * a)