Proof using.
induction l1; intros; simpl in *; intuition.
- subst. break_if; do_bool; try omega.
eexists; repeat (simpl in *; intuition).
- specialize (H1 e); intuition. conclude H1 ltac:(apply in_app_iff; intuition).
break_if; do_bool; try omega. eexists; intuition; eauto.
simpl in *. intuition.
eapply_prop_hyp sorted sorted; eauto. break_exists; intuition.
find_rewrite. eauto.
Qed.

(* Specifications: *)
Lemma sorted_app_in_1 :
forall l1 l2 e,
sorted (l1 ++ l2) ->
eIndex e > 0 ->
In e l1 ->
eIndex e > maxIndex l2.
Lemma sorted_app_in_1 :
forall l1 l2 e,
sorted (l1 ++ l2) ->
eIndex e > 0 ->
In e l1 ->
eIndex e > maxIndex l2.