Proof using.
induction l; intros; simpl in *; auto.
intuition; do_in_app; intuition; find_apply_hyp_hyp; intuition.
Qed.

Theorem sorted_index_term :
forall l e e',
eIndex e <= eIndex e' ->
sorted l ->
In e l ->
In e' l ->
eTerm e <= eTerm e'.