intros; cut ({q <= m} + {m < q}).
intro; elim H; intros.
elim H0; intro.
right; auto with core arith.
left; auto with core arith.
apply (le_lt_dec q m).
Qed.

(* Specifications: *)
(**********)
Lemma inser_trans_lt :
forall n m p q : nat, n < m /\ m < p -> {n < m /\ m < q} + {q <= m /\ m < p}.
(**********)
Lemma inser2_trans :
forall n m p q t : nat,
n <= m /\ m < t -> {n <= m /\ m < q} + {q <= m /\ m < p} + {p <= m /\ m < t}.