(P : forall n : nat, Fin n -> Type) (z : forall n : nat, P n.+1 fin_zero) (s : forall (n : nat) (k : Fin n), P n k -> P n.+1 (fsucc k)) (n : nat) : fin_ind P z s fin_zero = z n. Proof. unfold fin_ind. generalize (path_fin_to_finnat_to_fin (@fin_zero n)). induction (path_fin_to_finnat_fin_zero n)^. intro p. destruct (hset_path2 1 p). lhs nrapply transport_1. nrapply finnat_ind_beta_zero. Defined.
Require Import