Proof with eauto.
intros E e1 T Typ.
remember (exp_inr e1) as e. generalize dependent e1.
induction Typ; intros e' EQ U1 U2 Sub; inversion EQ; subst.
Case "typing_sub".
eauto using (sub_transitivity T).
Case "typing_inr".
inversion Sub; subst...
Qed.
(* ********************************************************************** *)
(** ** Preservation (20) *)

Lemma preservation : forall E e e' T,
typing E e T ->
red e e' ->
typing E e' T.