Lemma 9.
Assuming that:
B
⊂
Q
n
is
i
-binary compressed
for all
i
B
not an initial segment of binary
Then
B
=
P
(
n
−
1
)
−
{
1
,
2
,
3
,
…
,
n
−
1
}
∪
{
n
}
(“downstairs minus the last point, plus the first upstairs point”).