------------------------------------------------------------------------ -- Properties satisfied by total orders ------------------------------------------------------------------------ open import Relation.Binary module Relation.Binary.Props.TotalOrder (t : TotalOrder) where open Relation.Binary.TotalOrder t open import Relation.Binary.Consequences decTotalOrder : Decidable _≈_ → DecTotalOrder decTotalOrder ≟ = record { isDecTotalOrder = record { isTotalOrder = isTotalOrder ; _≟_ = ≟ ; _≤?_ = total+dec⟶dec reflexive antisym total ≟ } }