proposition: Lemma dualelement_sn_stn_nge_0 {n : nat} (i : stn n) : forall lt : (0 < S n), i >= (dualelement (0,, lt)) -> empty.
proof: 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.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Combinatorics.Maybe UniMath.Combinatorics.StandardFiniteSets UniMath.Algebra.Domains_and_Fields UniMath.Algebra.RigsAndRings