path_fin_to_finnat_fsucc@{} {n : nat} (k : Fin n) : fin_to_finnat (fsucc k) = succ_finnat (fin_to_finnat k). Proof. apply path_sigma_hprop. apply path_nat_fsucc. Defined.
Require Import Basics.Overture Basics.Tactics Basics.Trunc Basics.PathGroupoids Require Import Types.Empty Types.Sigma Types.Sum Types.Prod Types.Equiv. Require Import Spaces.Nat.Core. Require Import Finite.Fin.