Lemma EOlt_le : ∏ x y : X, x < y -> x <= y. Proof. intros x y Hxy. apply not_EOlt_le. intros H. refine (isirrefl_EOlt _ _). refine (istrans_EOlt _ _ _ _ _). exact Hxy. exact H. Qed.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.Algebra.BinaryOperations