Definition isEffectiveOrder {X : UU} (le lt : hrel X) := dirprod ((ispreorder le) × (isStrongOrder lt)) ((∏ x y : X, (¬ lt x y) <-> (le y x)) × (∏ x y z : X, lt x y -> le y z -> lt x z) × (∏ x y z : X, le x y -> lt y z -> lt x z)).
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.Algebra.BinaryOperations