Lemma latticedec_gtmax : ∏ (x y z : X), latticedec_gt_so z x → latticedec_gt_so z y → latticedec_gt_so z (Lmax lat x y). Proof. intros x y z Hxz Hyz. apply (Lmax_case lat (latticedec_gt_so z)). - exact Hxz. - exact Hyz. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups.