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https://github.com/Smaug123/agdaproofs
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36 lines
1.4 KiB
Agda
36 lines
1.4 KiB
Agda
{-# OPTIONS --safe --warning=error --without-K --guardedness #-}
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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open import Setoids.Setoids
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open import Rings.Definition
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open import Rings.Lemmas
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open import Rings.Order
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open import Groups.Definition
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open import Groups.Groups
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open import Fields.Fields
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open import Sets.EquivalenceRelations
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open import Sequences
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open import Setoids.Orders
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open import Functions
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open import LogicalFormulae
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open import Numbers.Naturals.Naturals
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module Fields.CauchyCompletion.Approximation {m n o : _} {A : Set m} {S : Setoid {m} {n} A} {_+_ : A → A → A} {_*_ : A → A → A} {_<_ : Rel {m} {o} A} {pOrder : SetoidPartialOrder S _<_} {tOrder : SetoidTotalOrder {_<_ = _<_} pOrder} {R : Ring S _+_ _*_} (order : OrderedRing R tOrder) (F : Field R) (charNot2 : Setoid._∼_ S ((Ring.1R R) + (Ring.1R R)) (Ring.0R R) → False) where
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open Setoid S
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open SetoidTotalOrder tOrder
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open SetoidPartialOrder pOrder
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open Equivalence eq
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open OrderedRing order
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open Ring R
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open Group additiveGroup
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open Field F
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open import Rings.Orders.Lemmas(order)
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open import Fields.CauchyCompletion.Definition order F
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open import Fields.CauchyCompletion.Addition order F charNot2
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open import Fields.CauchyCompletion.Setoid order F charNot2
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approximate : (a : CauchyCompletion) → (ε : A) → Sg A (λ b → a +C (-C (injection b)) < ε)
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approximate a ε = ?
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