Hint Rewrite swap_size_eq.
(* HIDE *)
(** ** Nominal induction *)

Lemma nominal_induction_size :
forall n, forall t, size t <= n ->
forall P : n_exp -> Type,
(forall x, P (n_var x)) ->
(forall x t, (forall y, P (swap x y t)) -> P (n_abs x t)) ->
(forall t1 t2, P t1 -> P t2 -> P (n_app t1 t2)) ->
P t.