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https://github.com/Smaug123/agdaproofs
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20 lines
758 B
Agda
20 lines
758 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import Numbers.Naturals.Definition
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open import LogicalFormulae
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open import Groups.Definition
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open import Groups.Orders.Partial.Definition
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open import Setoids.Orders.Partial.Definition
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open import Setoids.Setoids
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Groups.Orders.Archimedean {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ : A → A → A} {G : Group S _+_} {c : _} {_<_ : A → A → Set c} {pOrder : SetoidPartialOrder S _<_} (p : PartiallyOrderedGroup G pOrder) where
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open Setoid S
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open import Groups.Cyclic.Definition G
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open Group G
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Archimedean : Set (a ⊔ c)
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Archimedean = (x y : A) → (0G < x) → (0G < y) → Sg ℕ (λ n → y < (positiveEltPower x n))
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