Definition dni {n : nat} ( i : ⟦S n⟧ ) : ⟦n⟧ -> ⟦S n⟧. Proof. intros x. exists (di i x). unfold di. induction (natlthorgeh x i) as [lt|ge]. - apply natgthtogths. exact (pr2 x). - exact (pr2 x). Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.DecidablePropositions. Require Import UniMath.MoreFoundations.NegativePropositions.