Definition replace_dni_first (n : nat) : dni (@firstelement n) = dni_firstelement. Proof. intros. apply funextfun; intros i. apply subtypePath_prop. exact (compute_pr1_dni_first n i). Defined.
Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.MoreFoundations.DecidablePropositions. Require Import UniMath.MoreFoundations.NegativePropositions.