intros; cut ({n <= m /\ m < p} + {p <= m /\ m < t}).
intro; elim H0; intro y.
left; apply (inser_trans n m p q y).
right; auto with core arith.
apply (inser_trans n m t p H).
Qed.

(**********)
Lemma inser2_trans_lt :
forall n m p q t : nat,
n < m /\ m < t -> {n < m /\ m < q} + {q <= m /\ m < p} + {p <= m /\ m < t}.