Why should the invalid Sechach of the tree combine with the valid Sechach of
the Sukah and invalidate it? If the Sukah's Sechach is valid and there is
more shade than sunlight, in what way can the branches of the tree join the
Sechach to invalidate it? If the Gemara means that the valid Sechach on the
Sukah is considered as if it is not there because it is under the tree, then
the Gemara should not have said that the branches of the tree are
"Mitztaref" (combine) with the kosher Sechach, but that the branches of the
tree are "Mevatel" (annul) the kosher Sechach!
(a) RASHI (DH v'Ha Ka Mitztaref, and 10a, DH Mahu d'Teima) seems to learn
that the Sukah underneath the tree indeed has more shade than sunlight and
is kosher by itself, and the Gemara is asking that the Sechach beneath the
tree should be discounted. Why, then, does the Gemara say that the tree is
"Mitztaref" with the kosher Sechach, and not that the tree is "Mevatel" it?
Rashi understands that it is obvious that the Sechach beneath the tree is
Batel -- that goes without saying. Once the Sechach underneath the tree is
annulled, the branches of the tree (i.e. invalid Sechach) now replace the
original kosher Sechach; as such, the tree is being Mitztaref to make the
Sechach of the Sukah, and the majority of shade comes only from the
combination of the invalid Sechach with the kosher Sechach. (PNEI YEHOSHUA,
KORBAN NESANEL #100; see also HAGAHOS MAIMONINIYOS, Hilchos Sukah 5:70, for
a different understanding of Rashi.)
This is also the opinion of the RIVA, cited by the ROSH (1:14) and the TUR
(626), the RA'AVAD (2a), the RITVA and others.
(b) TOSFOS (DH Ha) says that the Mishnah is talking about a case where the
Sukah's Sechach lets in more sunlight than shade, and only when combined
with the branches of the tree above it is there more shade than sunlight.
That is why the Gemara says that the Sukah is not valid if the shade comes
only from a combination of the invalid Sechach with the kosher Sechach.
How did the Gemara know that the Mishnah is discussing a case of a Sukah in
which the sunlight is more than the shade? The Gemara reasoned that if the
shade is more than the sunlight, then it is obvious that a tree -- the
branches of which let through more sunlight than they make shade -- cannot
ruin the Sukah. Only if the object on top of the Sukah makes more shade can
it ruin a Sukah (the Sechach of which also makes more shade), and then it
will be considered a Sukah beneath another Sukah or a Sukah beneath a tree.
(c) The BA'AL HA'ME'OR suggests that we always look at which Sechach was
placed there first. Normally, the tree was there before one built the Sukah.
Since the tree was there before the Sukah, and the tree lets through more
sunlight than shade, when one adds more Sechach to make the shade more than
the sunlight, the Sukah is invalid, since part of the shade of the Sechach
is created by a tree. It will remain an invalid Sukah no matter how much
kosher Sechach is added afterwards, since the tree was part of the Sechach
(which made a majority of shade) when the Sukah was originally built. If, on
the other hand, one built a Sukah which had more shade than sunlight, and
only afterward a tree was placed there (and the branches let through more
sunlight than shade), the tree will have no effect, because the Sukah was
already kosher. It may be assumed, though, that our Mishnah is discussing
the more normal case when the tree preceded the Sukah. This is why the
Gemara says that the tree should invalidate the Sukah, even if the Sukah now
has more shade than sunlight.
According to the Ba'al ha'Me'or, what is the Gemara's answer to its question
when it says that the Sukah beneath the tree is kosher "b'she'Chavtan" (when
he lowered the branches down to the Sechach)? How does that help? If the
Sechach above the Sukah was originally Pasul, then the Sukah should remain
Pasul forever, as the Ba'al ha'Me'or posited!
The Ba'al ha'Me'or suggests a new interpretation for "b'she'Chavtan." He
explains that it means that one shook the tree until all of its leaves fell
off the branches. The only reason a Sukah underneath a tree is Pasul is
because the tree becomes part of the Sukah. When one shakes the branches, he
shows that it *was not his intention* for the tree to be part of the shading
Sechach of the Sukah, and thus it does not become part of the Sukah. Since
there is enough kosher Sechach to create more shade than the sunlight that
penetrates it, the Sukah is valid.
(For a summary of the Halachah rulings regarding this matter, see Insights
to 10b.)