------------------------------------------------------------------------
-- The Agda standard library
--
-- Properties satisfied by strict partial orders
------------------------------------------------------------------------
{-# OPTIONS --cubical-compatible --safe #-}
open import Relation.Binary.Bundles using (StrictTotalOrder; DecTotalOrder)
module Relation.Binary.Properties.StrictTotalOrder
{s₁ s₂ s₃} (STO : StrictTotalOrder s₁ s₂ s₃)
where
open StrictTotalOrder STO
open import Relation.Binary.Construct.StrictToNonStrict _≈_ _<_
import Relation.Binary.Properties.StrictPartialOrder as SPO
------------------------------------------------------------------------
-- _<_ - the strict version is a decidable total order
decTotalOrder : DecTotalOrder _ _ _
decTotalOrder = record
{ isDecTotalOrder = isDecTotalOrder isStrictTotalOrder
}
open DecTotalOrder decTotalOrder public
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