elim H; auto with arith.
intros.
apply le_trans with (m0 - p).
assumption.
apply le_minus_n_Sn.
Qed.
Hint Resolve le_reg_minus.

Lemma lt_transp_r : forall n m p : nat, 0 < n -> p < n + m -> p - m < n.
simple induction m; simple induction p.