Lemma dualelement_le_comp' {n : nat} (i j : ⟦ n ⟧%stn) : (dualelement i) ≤ (dualelement j) -> j ≤ i. Proof. intros le. pose (H := @dualelement_le_comp _ (dualelement i) (dualelement j) le). now do 2 rewrite dualelement_2x in H. Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Combinatorics.Maybe. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.Algebra.RigsAndRings.