Proof using.
induction l; intros; simpl in *; intuition.
break_if; do_bool; auto.
- f_equal. eauto.
- exfalso.
destruct l'; simpl in *; intuition.
specialize (H1 e); conclude_using intuition; intuition.
Qed.

(* Specifications: *)
Lemma thing3 :
forall l l' e,
sorted (l ++ l') ->
(forall e', In e' (l ++ l') -> eIndex e' > 0) ->
In e (l ++ l') ->
eIndex e <= maxIndex l' ->
In e l'.