In this appendix we prove the lemma required by the proof of Theorem 3.3:
![]() |
Let
and
. Then
![]() |
![]() |
![]() |
|
![]() |
![]() |
||
![]() |
![]() |
||
![]() |
![]() |
||
![]() |
![]() |
||
![]() |
![]() |
Thus, we have that
. Now
define
. Since
,
. Consequently, if
, then
holds for all
, as well. From
now on, we will assume that
.
Let
. Since
, the
process
![]() |
![]() |
![]() |
|
![]() |
![]() |
![]() |
Since
,
and
. So there exists an index
for which
. Then inequality (15)
can be satisfied by setting
so that
holds and letting
.