N-ary expansions (#113)

This commit is contained in:
Patrick Stevens
2020-04-12 12:16:20 +01:00
committed by GitHub
parent 380548134d
commit 269f2aa14f
11 changed files with 156 additions and 217 deletions

View File

@@ -1,6 +1,7 @@
{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Numbers.Naturals.Definition
open import Numbers.Naturals.Naturals
open import Numbers.Integers.Integers
open import Groups.Groups
@@ -22,6 +23,7 @@ open import Fields.FieldOfFractions.Addition IntDom
open import Fields.FieldOfFractions.Multiplication IntDom
open import Fields.FieldOfFractions.Ring IntDom
open import Fields.FieldOfFractions.Field IntDom
open import Fields.FieldOfFractions.Lemmas IntDom
open import Fields.FieldOfFractions.Order IntDom OrderedRing
: Set
@@ -43,7 +45,10 @@ a *Q b = fieldOfFractionsTimes a b
0Q = Ring.0R Ring
injectionQ :
injectionQ z = z ,, (nonneg 1 , λ ())
injectionQ = embedIntoFieldOfFractions
injectionNQ :
injectionNQ n = injectionQ (nonneg n)
injectionQInjective : Injection injectionQ
injectionQInjective pr = equalityLeft pr
@@ -78,6 +83,9 @@ a-A a = Group.invRight (Ring.additiveGroup Ring) {a}
TotalOrder : SetoidTotalOrder fieldOfFractionsOrder
TotalOrder = fieldOfFractionsTotalOrder
OrderInherited : (a b : ) a <Z b injectionQ a <Q injectionQ b
OrderInherited a b a<b = fieldOfFractionsOrderInherited a<b
open SetoidTotalOrder fieldOfFractionsTotalOrder
open SetoidPartialOrder partial
open Setoid fieldOfFractionsSetoid