Proof using.
intros. destruct l2; intuition.
simpl in *. right.
destruct l1; intuition.
find_copy_eapply_lem_hyp findAtIndex_None; simpl in *; eauto.
unfold contiguous_range_exact_lo in *.
simpl in *. intuition.
destruct (lt_eq_lt_dec 0 (eIndex e)); intuition; eauto.
destruct (lt_eq_lt_dec (eIndex e0) (eIndex e)); intuition.
exfalso. repeat break_if; do_bool; intuition.
match goal with
| H : forall _, _ < _ <= _ -> _ |- _ =>
specialize (H (eIndex e))
end; conclude_using omega.
simpl in *. break_exists. intuition; subst; intuition.
eapply findAtIndex_None; eauto.
Qed.

(* Specifications: *)
Lemma maxIndex_le' :
forall l1 l2 i,
sorted l1 ->
contiguous_range_exact_lo l1 0 ->
l2 <> nil ->
contiguous_range_exact_lo l2 i ->
findAtIndex l1 (maxIndex l2) = None ->
maxIndex l1 <= maxIndex l2.