Lemma dualelement_eq {n : nat} (i j : ⟦ n ⟧%stn) : dualelement i = j -> i = dualelement j. Proof. do 2 rewrite dualelement_defs_eq; unfold dualelement'. intros H; apply subtypePath_prop; revert H; simpl. intros eq; rewrite <- eq; simpl. rewrite minusminusmmn; try reflexivity. apply natlthsntoleh. apply natgthtogehm1, (pr2 i). 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.