Proof using.
induction ys; intros; simpl in *.
- break_match; intuition.
- break_match; intuition.
subst. apply sorted_cons; eauto.
intros. eauto using subseq_In.
Qed.

Theorem maxTerm_is_max :
forall l e,
sorted l ->
In e l ->
maxTerm l >= eTerm e.