GEMARA

Mishnah: If one draped a vine or gourd vine or ivy over a Sukah, it is Pasul. If there was more Sechach than vines (or ivy) or if he cut them, it is Kosher.

9b - Question: If he did not do Chavatah, why it is Kosher? Pasul Sechach joins with Kosher Sechach! (Meforshim argue about whether Chavatah means separating the Pasul (attached) Sechach from the Kosher Sechach, or cutting what was attached, or lowering the vine and mixing it with the Kosher Sechach, or knocking the leaves off the vines.)

Answer: We must say that he did Chavatah.

15a - Mishnah: If one roofed his Sukah with roasting spits or bed boards (which are Pasul for Sechach):

It is Kosher only if the spaces between them are as wide as them (and are covered with Kosher Sechach).

Suggestion: This refutes Rav Huna brei d'Rav Yehoshua:

Rav Papa: Parutz k'Omed (the width of the gaps equals that of the wall) permits;

Rav Huna brei d'Rav Yehoshua: It does not permit.

Rejection: The case is, there is room between spits to insert and remove spits with leeway (i.e., the spaces are slightly bigger).

Objection: It is possible to be exact (and make the spaces equal the spits. Surely they are equal, like the Mishnah says!)

Answer #1 (R. Ami): He (intentionally) left room between spits to insert and remove spits with leeway.

Answer #2 (Rava): The Kosher Sechach is placed perpendicular to (and on top of) the Pasul Sechach (it must be bigger in order to stay up).

RISHONIM

Tosfos (15b DH v'Ha): Rashi's text is difficult. The Gemara said that the spaces are bigger. It asks 'It is possible to be exact' (surely, the spaces are equal)! R. Ami's answer (the spaces are bigger) does not answer the question! Rather, the text says 'it is impossible (to totally fill the spaces)'. The question is even against Rav Papa. R. Ami answers that he puts Kosher Sechach also over the spits, so it is the majority.

Rif: The Gemara established our Mishnah to be when he did Chavatah. If not, Pasul Sechach joins with Kosher Sechach, and it is Pasul.

Ran (DH Masnisin): The Mishnah (11a) teaches that if one spread a vine over a Sukah and put Sechach on it, it is Pasul. R. Tam infers that if the Sechach preceded the vine it would be Kosher; Pasul Sechach cannot disqualify a Sukah that is already Kosher. This forced R. Tam to say that the Pasul Sechach is needed to preserve the Kosher Sechach. Most argue with R. Tam.

Rejection #1 (Rashba, brought in Gra OC 626:1 DH Bein): The Mishnah disqualifies whether one spread a vine over a Sukah or put Sechach on it (the vine). It teaches that even if the Sechach preceded the vine it is Pasul.

Rejection #2 (Ran DH umi'Ha): Rav Ashi said that a shirt hung in the Sukah to dry should be removed when it dries, because of Mar'is ha'Ayin, lest people say that something that is Mekabel Tum'ah may be used for Sechach. This episode disproves R. Tam, who says that that Pasul Sechach cannot disqualify a Sukah that is already Kosher.

Note: Perhaps R. Tam would say that there was almost as much sun as shade, and we are concerned lest people think that the shirt is needed to comprise a majority of shade!

Rejection #3 (R. Mano'ach, Hilchos Sukah 5:17): The Gemara allows a sheet spread for Noy over a Sukah with enough Sechach. This implies that if it was for another reason, it is Pasul! When the Rambam discusses spreading a sheet over the Sechach, he does not say 'for shade'.

Rambam (Hilchos Sukah 5:13): If one combined Kosher and Pasul Sechach, even if the majority is Kosher it is Pasul. If he used each by itself it is Pasul only if there are three Tefachim of Pasul Sechach in one place, whether it is in the middle or on the side.

Ra'avad: It is difficult to say that separating (the Pasul Sechach from the Kosher) helps. The Gemara (10a) thought to disqualify a bottom Sukah underneath an upper Sukah more than 20 Amos tall because the Kosher and Pasul Sechach combine, even though they are far from each other! We have another explanation.

Magid Mishnah: Some explain that Kosher Sechach under (or over) Pasul Sechach it itself Pasul. The Gemara answers that Chavtan, i.e. he mixed them together.

Rambam (16): If one put Kosher and Pasul Sechach next to each other, and there is not three Tefachim of Pasul Sechach in one place, if there is more Kosher Sechach it is Kosher. If there is exactly the same of both it is Pasul, because Pasul Sechach is like Parutz.

Question: This is like Rav Huna brei d'Rav Yehoshua. The Halachah was fixed like Rav Papa (Eruvin 15b), who permits Parutz k'Omed! The Rambam himself rules like Rav Papa in Shabbos (16:16)!

Answer #1 (Magid Mishnah): The Gemara (22b) says that if there are equal amounts of Sechach and air above, there is more sun below, and it is Pasul. It is as if the Pasul Sechach is not there, therefore we need a majority of Kosher Sechach. The Gemara could have said that even Rav Papa must agree.

Question (Igros Moshe OC 1:182): This is difficult. Four Tefachim of Pesach Sechach are needed to disqualify a Sukah, unlike air! The Magid Mishnah connotes that Pasul Sechach is like air only for this law. It is not clear why this should be.

Answer #2 (Kesef Mishneh): The Rambam's text of the Gemara was like Tosfos'. The question 'it is impossible (to totally fill the spaces)' was even against Rav Papa. R. Ami answered also for Rav Papa that he puts a majority of Sechach.

Ran (5a DH v'Nimtza) and Magid Mishnah citing Ramban: If one used Kosher Sechach next to Pasul Sechach, if half is Kosher the Sukah is Kosher (like the Mishnah 15a).

Rosh (1:29): The Rif brings the Mishnah of spits. He omits the Gemara that established it to be when there is more Kosher Sechach. This is because his text was like Rashi's, in which the question is against Rav Huna, and the Halachah was fixed like Rav Papa. This text is difficult, for the Gemara asks according to the opinion that is unlike the Halachah. Rather, the question 'it is impossible' and answer also apply to Rav Papa.

Rosh (1:14): Rashi says that 'Chavtan' means that he lowered the vine and mixed it with the Kosher Sechach. The vine is Batel in a majority of Kosher Sechach.

Question (against Rashi - Lechem Mishneh, ibid.): Rava (15b) allows to put Kosher Sechach in between Pasul Sechach, even though they are not mixed.

Answer (Rosh, ibid.): Rashi does not require mixing when the Kosher Sechach gives a majority of shade. Then we simply ignore the Pasul Sechach.

Hagahos Maimoniyos (70): Rashi (10a DH Mahu d'Seima Nigzor) retracted and is concerned even in this case.

POSKIM

Shulchan Aruch (OC 631:8): If one roofed his Sukah with spits that are Pasul for Sechach), and there is not four Tefachim of them together in one place, and left spaces between them as wide as a spit:

If he put Kosher Sechach in the spaces it is Pasul, for it is impossible to fill all the spaces, hence there is a majority of Pasul Sechach.

If he put more Kosher Sechach than Pasul, or if the Kosher Sechach is placed perpendicular to (and on top of) the Pasul Sechach (it must be bigger in order to stay up), it is Kosher.

Taz (6): If it were possible to fill all the spaces it would suffice to have an equal amount of Kosher Sechach, because the Halachah is that Parutz k'Omed permits.

Question: The Shulchan Aruch (629:7) is unsure whether or not one may put the Sechach on a ladder. The Rema says that any Keli that is Mekabel Tum'ah should not be used to hold up the Sechach or to be Ma'amid (hold it in place)!

Answer #1 (Mishbetzos Zahav 6): The decree not to use such Kelim is lest one use them for Sechach. Here we discuss metal spits. Everyone knows that they are Pasul for Sechach!

Answer #2 (Kaf ha'Chayim 32): One should put thin reeds on the spits, and the Sechach on the reeds, so the spits are merely Ma'amid the Ma'amid.

Rema: This refers to a big Sukah. In a small Sukah there cannot be three Tefachim of spits together.

Shulchan Aruch (626:1): Some say that if a tree is above a Sukah, even if the tree allows more sun and the Sechach itself is mostly shade, if the branches are over directly over the Sechach it is Pasul. This is whether the tree or Sukah was there first.

Gra (DH Bein): The Ba'al ha'Ma'or (5a) disqualifies only if the tree was there first. This is difficult, for the Gemara did not specify. Also, it should have answered that the Chidush is that we do not decree lest one use such a Sukah when the tree was there first!