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Split partial and total order of rings (#61)

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Patrick Stevens
2019-11-02 18:42:37 +00:00
committed by GitHub
parent 55995ea801
commit 763ddb8dbb
26 changed files with 768 additions and 618 deletions
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Fields/Orders/Partial/Definition.agda Normal file
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Groups
open import Groups.Definition
open import Rings.Definition
open import Rings.Orders.Partial.Definition
open import Rings.Lemmas
open import Setoids.Setoids
open import Setoids.Orders
open import Orders
open import Rings.IntegralDomains
open import Functions
open import Sets.EquivalenceRelations
open import Fields.Fields
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Fields.Orders.Partial.Definition {m n : _} {A : Set m} {S : Setoid {m} {n} A} {_+_ : A → A → A} {_*_ : A → A → A} {R : Ring S _+_ _*_} (F : Field R) where
open Ring R
open import Fields.Lemmas F
record PartiallyOrderedField {p} {_<_ : Rel {_} {p} A} (pOrder : SetoidPartialOrder S _<_) : Set (lsuc (m ⊔ n ⊔ p)) where
field
oRing : PartiallyOrderedRing R pOrder