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https://github.com/Smaug123/agdaproofs
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20 lines
981 B
Agda
20 lines
981 B
Agda
{-# OPTIONS --safe --warning=error --without-K #-}
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open import LogicalFormulae
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open import Orders.Total.Definition
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open import Orders.Partial.Definition
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open import Setoids.Setoids
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open import Functions
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open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
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module Setoids.Orders where
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partialOrderToSetoidPartialOrder : {a b : _} {A : Set a} (P : PartialOrder {a} A {b}) → SetoidPartialOrder (reflSetoid A) (PartialOrder._<_ P)
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SetoidPartialOrder.<WellDefined (partialOrderToSetoidPartialOrder P) a=b c=d a<c rewrite a=b | c=d = a<c
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SetoidPartialOrder.irreflexive (partialOrderToSetoidPartialOrder P) = PartialOrder.irreflexive P
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SetoidPartialOrder.<Transitive (partialOrderToSetoidPartialOrder P) = PartialOrder.<Transitive P
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totalOrderToSetoidTotalOrder : {a b : _} {A : Set a} (T : TotalOrder {a} A {b}) → SetoidTotalOrder (partialOrderToSetoidPartialOrder (TotalOrder.order T))
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SetoidTotalOrder.totality (totalOrderToSetoidTotalOrder T) = TotalOrder.totality T
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