Lemma not_EOlt_le : ∏ x y : X, (¬ (x < y)) <-> (y <= x). Proof. exact (pr1 (pr2 (pr2 (pr2 (pr2 X))))). Qed.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.Sets. Require Import UniMath.MoreFoundations.Orders. Require Import UniMath.Algebra.BinaryOperations