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Lots of speedups (#116)

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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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16
Rings/Orders/Total/Cauchy.agda
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@@ -5,10 +5,9 @@ open import Setoids.Setoids
open import Rings.Definition
open import Rings.Orders.Partial.Definition
open import Rings.Orders.Total.Definition
open import Groups.Definition
open import Sets.EquivalenceRelations
open import Sequences
open import Setoids.Orders
open import Setoids.Orders.Partial.Definition
open import Setoids.Orders.Total.Definition
open import Functions
open import LogicalFormulae
open import Numbers.Naturals.Semiring
@@ -16,15 +15,8 @@ open import Numbers.Naturals.Order
module Rings.Orders.Total.Cauchy {m n o : _} {A : Set m} {S : Setoid {m} {n} A} {_+_ : A → A → A} {_*_ : A → A → A} {_<_ : Rel {m} {o} A} {pOrder : SetoidPartialOrder S _<_} {R : Ring S _+_ _*_} {pRing : PartiallyOrderedRing R pOrder} (order : TotallyOrderedRing pRing) where
open Setoid S
open SetoidTotalOrder (TotallyOrderedRing.total order)
open SetoidPartialOrder pOrder
open Equivalence eq
open TotallyOrderedRing order
open Ring R
open Group additiveGroup
open import Rings.Orders.Total.Lemmas order
open import Rings.Orders.Total.AbsoluteValue order
cauchy : Sequence A → Set (m ⊔ o)
cauchy s = ∀ (ε : A) → (0R < ε) → Sg ℕ (λ N → ∀ {m n : ℕ} → (N <N m) → (N <N n) → abs ((index s m) -R (index s n)) < ε)
cauchy s = ∀ (ε : A) → (Ring.0R R < ε) → Sg ℕ (λ N → ∀ {m n : ℕ} → (N <N m) → (N <N n) → abs (Ring._-R_ R (index s m) (index s n)) < ε)