Lemma dualelement_sn_stn_nge_0 {n : nat} (i : stn n) : forall lt : (0 < S n), i >= (dualelement (0,, lt)) -> empty. Proof. intros lt gt. rewrite dualelement_defs_eq in gt; unfold dualelement' in gt. simpl in gt. do 2 rewrite natminuseqn in gt. contradiction (natgthtonegnatleh _ _ (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.