proposition: Lemma Lgt_Lge : ∏ x y : X, Lgt lat x y → Lge lat x y.
proof: Proof. intros x y H. apply notLgt_Lle. intro H0. eapply isasymm_Lgt. exact H. exact H0. Qed.
imports: UniMath.MoreFoundations.All UniMath.Algebra.Monoids UniMath.Algebra.Groups