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