Proof using.
induction l; intros; simpl in *.
- find_inversion. simpl in *. intuition.
- break_match. find_inversion. simpl in *. intuition.
+ subst. simpl. omega.
+ eauto using le_gt_trans, le_plus_l.
Qed.

Lemma processPackets_num_monotonic :
forall n l n' l',
processPackets n l = (n', l') ->
n' >= n.