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Reshuffle orders (#91)

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Patrick Stevens
2019-12-29 12:11:21 +00:00
committed by GitHub
parent 876396eaaa
commit b6ef9b46f2
57 changed files with 476 additions and 462 deletions
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2
Rings/EuclideanDomains/Definition.agda
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@@ -14,7 +14,7 @@ open import Rings.Definition
open import Rings.Homomorphisms.Definition
open import Groups.Homomorphisms.Lemmas
open import Rings.IntegralDomains.Definition
open import Orders
open import Orders.Total.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)

4
Rings/Examples/Proofs.agda
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@@ -4,7 +4,6 @@ open import LogicalFormulae
open import Functions
open import Groups.Groups
open import Groups.Definition
open import Orders
open import Rings.Definition
open import Numbers.Naturals.Semiring
open import Numbers.Naturals.Naturals
@@ -14,6 +13,7 @@ open import Numbers.Primes.PrimeNumbers
open import Numbers.Modulo.Definition
open import Numbers.Modulo.Group
open import Numbers.Naturals.EuclideanAlgorithm
open import Orders.Total.Definition
module Rings.Examples.Proofs where
nToZn' : (n : ℕ) (pr : 0 <N n) (x : ℕ) → ℤn n pr
@@ -28,7 +28,7 @@ module Rings.Examples.Proofs where
mod' (succ n) pr (negSucc x) = Group.inverse (ℤnGroup (succ n) pr) (nToZn' (succ n) pr (succ x))
subtractionEquiv : (a : ℕ) → {b c : ℕ} → (c<b : c <N b) → a +N c ≡ b → a ≡ subtractionNResult.result (-N (inl c<b))
subtractionEquiv 0 {b} {c} c<b pr rewrite pr = exFalso (PartialOrder.irreflexive (TotalOrder.order ℕTotalOrder) c<b)
subtractionEquiv 0 {b} {c} c<b pr rewrite pr = exFalso (TotalOrder.irreflexive ℕTotalOrder c<b)
subtractionEquiv (succ a) {b} {c} c<b pr = equivalentSubtraction 0 b (succ a) c (succIsPositive a) c<b (equalityCommutative pr)
modNExampleSurjective' : (n : ℕ) → (pr : 0 <N n) → Surjection (mod' n pr)

1
Rings/Ideals/Prime/Definition.agda
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@@ -5,7 +5,6 @@ open import Groups.Groups
open import Groups.Lemmas
open import Groups.Definition
open import Numbers.Naturals.Naturals
open import Orders
open import Setoids.Setoids
open import Functions
open import Rings.Definition

1
Rings/IntegralDomains/Definition.agda
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@@ -5,7 +5,6 @@ open import Groups.Groups
open import Groups.Lemmas
open import Groups.Definition
open import Numbers.Naturals.Naturals
open import Orders
open import Setoids.Setoids
open import Functions
open import Rings.Definition

1
Rings/IntegralDomains/Examples.agda
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@@ -5,7 +5,6 @@ open import Groups.Groups
open import Groups.Lemmas
open import Groups.Definition
open import Numbers.Naturals.Naturals
open import Orders
open import Setoids.Setoids
open import Functions
open import Rings.Definition

1
Rings/IntegralDomains/Lemmas.agda
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@@ -5,7 +5,6 @@ open import Groups.Groups
open import Groups.Lemmas
open import Groups.Definition
open import Numbers.Naturals.Naturals
open import Orders
open import Setoids.Setoids
open import Functions
open import Rings.Definition

1
Rings/Primes/Lemmas.agda
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@@ -5,7 +5,6 @@ open import Groups.Groups
open import Groups.Lemmas
open import Groups.Definition
open import Numbers.Naturals.Naturals
open import Orders
open import Setoids.Setoids
open import Functions
open import Rings.Definition