cut (n = 0 \/ n = 1).
intros H_Cut.
apply no_or_r with (n = 0); try trivial with arith.
apply pred_n_O; try trivial with arith.
Qed.

Lemma lt_le_pred : forall n m : nat, n < m -> n <= pred m.
simple induction n; simple induction m; auto with arith.