Definition lt_to_nleq {P : Poset} {x y : P} : x < y ⇒ ¬ (y ≤ x). Proof. intros [leq_xy neq_xy] leq_yx. apply neq_xy. apply isantisymm_posetRelation; assumption. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.OrderTheory.OrderedSets.WellOrderedSets. Require Import UniMath.OrderTheory.DCPOs.AlternativeDefinitions.Dcpo. Require Import UniMath.OrderTheory.Posets.Subposets.