Lemma latticedec_gtmin : ∏ (x y z : X), latticedec_gt_so x z → latticedec_gt_so y z → latticedec_gt_so (Lmin lat x y) z. Proof. intros x y z Hxz Hyz. apply (Lmin_case lat (λ t : X, latticedec_gt_so t z)). - exact Hxz. - exact Hyz. Qed.
Require Import UniMath.MoreFoundations.All. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.Groups.