GEMARA

7b - Abaye: The following require (or allow) a Sukah to be Diras Keva - Rebbi, R. Yoshiyah, R. Yehudah, R. Shimon, R. Gamliel, Beis Shamai, R. Eliezer and Others:

R. Eliezer disqualifies a Sukah shaped like a Tzerif (the walls slope and meet in the middle), or if a wall of the Sukah is inclined against a vertical wall, for it lacks a roof. Chachamim are Machshir.

19b - Mishnah: If a Sukah is shaped like a Tzerif, or if one wall leans against a vertical wall, R. Eliezer disqualifies and Chachamim Machshir.

Beraisa: R. Eliezer agrees that if the wall(s) are a Tefach above the ground before they begin to slope, or if a Tefach separates the leaning wall from the vertical wall, it is Kosher.

Chachamim consider a slanted roof to be a roof.

Rav Yosef slept in a canopy with a slanted roof inside a Sukah.

Abaye: Why do you abandon Chachamim and follow R. Eliezer? (Chachamim consider a slanted roof to be a roof, so you are under a roof other than the Sechach!)

Rav Yosef: A Beraisa teaches oppositely, that R. Eliezer is Machshir (a Tzerif) and Chachamim disqualify.

Abaye: Why do you rely on a Beraisa that opposes our Mishnah?

Rav Yosef: Our Mishnah is an individual's opinion:

Beraisa - R. Noson: If a Sukah is shaped like a Tzerif, or if one wall leans against a vertical wall, R. Eliezer disqualifies and Chachamim are Machshir.

RISHONIM

Rif (3a) and Rosh (1:10): The following require Diras Keva - Rebbi, R. Yoshiyah, R. Yehudah, R. Shimon, R. Gamliel, Beis Shamai, R. Eliezer and Others. Normally, when we list Tana'im that hold similarly, the Halachah does not follow any of them. However, here the Halachah follows two of them, but not because we require Diras Keva. A Beraisa teaches that the opinions of R. Eliezer and Chachamim must be switched, and Chachamim disqualify a Sukah with sloping walls because this is not considered a roof. (Also, the Halachah follows Beis Shamai.)

Rebuttal (Ba'al ha'Ma'or): Chachamim do not consider sloping walls like a roof because they require Diras Keva!

Defense (Milchamos Hash-m): On Shabbos and even Yom Tov it is forbidden to make even Ohel Arai, even to spread a cloth for straining wine. Nevertheless, one may spread a canopy with a slanted roof because it is not considered an Ohel at all.

Ran (DH k'Min): R. Eliezer disqualifies because it has no roof and it is not nice to live in.

Rif (9b) and Rosh (1:37): If a Sukah is shaped like a Tzerif, or if the beams rest on the ground and lean against a vertical wall, it is Pasul because it lacks a roof. If the wall(s) are a Tefach above the ground before they begin to slope, or if a Tefach separates the leaning wall from the vertical wall, it is Kosher, for it has a roof that is a Tefach. One may sleep in a canopy in a Sukah unless it has a roof, for then it is a Sukah inside a Sukah.

Rambam (Hilchos Sukah 4:7): A Sukah without a roof is Pasul, i.e. if the walls slope and meet in the middle or if a wall of the Sukah leans against a wall. If it has a roof even a Tefach, or if the wall leaning against the wall was lifted a Tefach off the ground it is Kosher.

Magid Mishnah: The wall(s) are vertical for a Tefach before they begin to slope. Kosher Sechach was put in the Tefach between the leaning wall and the vertical wall. Some require the walls to be Kosher for Sechach, and to be 16 Tefachim. This does not seem correct; nevertheless, one should be stringent for this opinion.

Rosh (1:37): The Ri requires that the Tefach which the Sukah is raised or separates the leaning wall from the vertical wall must be solid. Rashi does not require anything solid; we rely on Lavud. The Yerushalmi supports Rashi. Also regarding Tum'as Ohel we require room for a square Tefach under a slanted roof.

We must say that at the height of 10 Tefachim tall the Sukah is at least seven by seven wide. Then, perhaps even what is below 10 is Kosher, just like Pesel that leaves a Sukah.

Ran (DH Gemara): Rashi says that the leaning wall is a Tefach away from the vertical wall. The roof is made through Lavud. Tosfos says that an actual roof is required, i.e. the Tefach is filled with Sechach. The wall must be at least 17 Tefachim with the horizontal Tefach, i.e. 10 Tefachim for the wall and seven Tefachim for the Sechach. It must be made of something Kosher for Sechach.

POSKIM

Shulchan Aruch (OC 631:10): If a Sukah has no roof, e.g. the ends of the walls meet like a Tzerif, or one wall leans against a vertical wall, it is Pasul.

Kaf ha'Chayim (44): We must say that there is a third wall in addition to the vertical and slanting walls, for a Sukah must have three walls.

Shulchan Aruch (ibid.): If it has a roof even a Tefach, or if the wall leaning against the wall was lifted a Tefach off the ground it is Kosher.

Gra (DH v'Yesh Omrim): The Beis Yosef (DH v'Chosav Od) says that the Rambam requires the Tefach to be solid, like the Ri.

Magen Avraham (9): It seems that if it is a Tefach wide within three Tefachim of the roof it is Kosher, for Lavud is mid'Oraisa. The Isur of Binyan or Stiras Ohel applies to such a canopy (OC 315:11).

Bechori Yakov (brought in Sha'ar ha'Tziyon 20): This is unlike the opinion in the Rema that requires the horizontal Tefach to be solid, for the roof cannot be from Lavud. The proof from a canopy (OC 315:11) is not a proof, for there we are stringent.

Kaf ha'Chayim (46,49): When the entire wall is sloped there is no (way to distinguish what is the) wall or roof. If the wall is lifted a Tefach off the ground, the entire sloped wall is the roof.

Rema: Some say that the horizontal Tefach must be solid. At the height of 10 Tefachim tall the Sukah must be at least seven by seven wide.

Question (Mizrachi, cited in Beis Yosef, ibid.): The incline for the roof must be more than seven Tefachim, for its horizontal width must be seven. The Rambam (5:23) does not require this, for he forbids to sleep in a Sukah under a canopy 10 tall even if its roof is only a Tefach wide, because it is like a Sukah inside a Sukah. This is difficult. Chachamim said that seven by seven is a minimal Sukah!

Answer #1 (Beis Yosef DH Li): One may not sleep under such a canopy because it looks like a Sukah, and people may come to permit a Sukah in a Sukah. Alternatively, it is considered an Ohel and it is not Batel to the Sukah, but it itself is not a Kosher Sukah. However, the Mizrachi's question applies to the Magid Mishnah, who sees no need to have seven by seven at the height of 10 Tefachim.

Answer #2 (Beis Yosef, ibid.): The Magid Mishnah must hold that it suffices to be seven wide at the bottom. Even though three Tefachim of air or Pasul Sechach disqualifies a Sukah that is seven by seven at the top, if the roof is a Tefach of Kosher Sechach it is Kosher.

Note: We need seven by seven to fit Rosho v'Rubo and a table. It is not clear why this should be enough at the bottom if it is narrower above. A Sukah in which branches of Sechach descend within seven Tefachim is Pasul (4a). There is no connotation that it suffices if there is a one Tefach in which they do not descend!

Rema: Above 10 Tefachim the walls must be made of something Kosher for Sechach, for they are the Sechach. It the entire walls are Kosher for Sechach one may sleep even under the walls.

Eshel Avraham (10): Whenever there is disagreement about a mid'Oraisa law of Sukah, we are stringent. If no other Sukah is available, one should eat there without a Berachah. When there is disagreement about a mid'Rabanan law of Sukah, it is proper to be are stringent. If no other Sukah is available, one eats there with a Berachah. Further investigation is needed.

Kaf ha'Chayim (56). Further investigation is needed why one may bless when there is a disagreement about a mid'Rabanan law. Perhaps the Berachah is l'Vatalah!