Proof. Note, that the numbers
and
are symmetrically located around the number
(see the figure (
Reflection principle
picture
)):
Suppose that
crosses the level
at some point
and returns down to
at time
Such path may be inverted symmetrically around the level
on the time interval
The resulting path has the same likelihood of occurrence as the original.
Hence,
Note, that
,
hence the condition
is redundant. We
conclude
as claimed.
