Lemma EOgt_noteq : ∏ x y : X, x > y -> x != y. Proof. intros x y Hgt Heq. rewrite Heq in Hgt. now apply isirrefl_EOgt in Hgt. Qed.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.Algebra.BinaryOperations