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https://github.com/Smaug123/agdaproofs
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26 lines
909 B
Agda
26 lines
909 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import Numbers.ClassicalReals.RealField
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open import LogicalFormulae
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open import Setoids.Subset
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open import Setoids.Setoids
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open import Setoids.Orders
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open import Sets.EquivalenceRelations
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open import Rings.Orders.Partial.Definition
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open import Rings.Definition
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open import Fields.Fields
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open import Groups.Definition
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open import Numbers.Naturals.Semiring
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open import Numbers.Naturals.Order
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open import Functions
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module Numbers.Intervals.Definition {a b c : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} {_<_ : Rel {_} {c} A} {R : Ring S _+_ _*_} {pOrder : SetoidPartialOrder S _<_} (pRing : PartiallyOrderedRing R pOrder) where
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record OpenInterval : Set a where
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field
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minBound : A
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maxBound : A
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isInInterval : A → OpenInterval → Set c
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isInInterval a record { minBound = min ; maxBound = max } = (min < a) && (a < max)
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