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Lots of speedups (#116)

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This commit is contained in:
Patrick Stevens
2020-04-16 13:41:51 +01:00
committed by GitHub
parent 1bcb3f8537
commit 9b80058157
63 changed files with 1082 additions and 564 deletions
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6
Rings/Orders/Partial/Definition.agda
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@@ -1,8 +1,8 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import Groups.Definition
open import Setoids.Orders
open import Setoids.Setoids
open import Setoids.Orders.Partial.Definition
open import Functions
open import Rings.Definition
@@ -13,9 +13,13 @@ module Rings.Orders.Partial.Definition {n m : _} {A : Set n} {S : Setoid {n} {m}
open Ring R
open Group additiveGroup
open Setoid S
open import Groups.Orders.Partial.Definition
record PartiallyOrderedRing {p : _} {_<_ : Rel {_} {p} A} (pOrder : SetoidPartialOrder S _<_) : Set (lsuc n ⊔ m ⊔ p) where
field
orderRespectsAddition : {a b : A} → (a < b) → (c : A) → (a + c) < (b + c)
orderRespectsMultiplication : {a b : A} → (0R < a) → (0R < b) → (0R < (a * b))
open SetoidPartialOrder pOrder
toGroup : {p : _} {_<_ : Rel {_} {p} A} {pOrder : SetoidPartialOrder S _<_} → PartiallyOrderedRing pOrder → PartiallyOrderedGroup additiveGroup pOrder
PartiallyOrderedGroup.orderRespectsAddition (toGroup p) = PartiallyOrderedRing.orderRespectsAddition p