intros. inversion H0. auto with arith.
simpl in |- *. elim plus_n_Sm. elim plus_n_Sm.
apply le_n_S. apply le_n_S. apply H. apply le_Sn_le. exact H1.
Qed. Hint Resolve le_plus_n_m.

Theorem lt_plus_n_m : forall n m : nat, n < m -> S (n + n) < m + m.
simple induction n.