proposition: 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: Proof. intros x y z Hxz Hyz. apply (Lmax_case lat (latticedec_gt_so z)). - exact Hxz. - exact Hyz. Qed.
imports: UniMath.MoreFoundations.All UniMath.Algebra.Monoids UniMath.Algebra.Groups