Lemma latticedec_lenotgt : ∏ (x y : X), Lle lat x y → ¬ latticedec_gt_so x y. Proof. intros x y H H0. simple refine (H0 _). exact H. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups.