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