Implied Question: This is despite the fact that regarding similar cases, namely the case of an opening wider than ten cubits and the case regarding the leather straps on a toilet seat, the Gemara in Eruvin (10b) says that the air on each side nullifies what is in the middle. (Why isn't the Tefach nullified with the larger amount of space on both sides of it?)

Answer: Here that there is a Tefach that is considered a wall according to Torah law due to a Halachah l'Moshe mi'Sinai, the air (on both sides) does not nullify it.

Explanation: A pole that is less than three Tefachim from the wall is not enough to be considered a Tefach due to Lavud, as this is why a Tefach Sochek is necessary, in order that the wall should be four Tefachim wide.

Explanation (cont.): This is as Rashi explains that the purpose is that it should take up most of the wall which is a little more than seven Tefachim. Additionally, the pole which is less than a Tefach would be nullified by the larger amount of airspace on both sides.

Explanation: This means that it is only permitted if that Tefach is turned into part of a Tzuras ha'Pesach that runs along the entire wall. How is this done? A half Tefach pole is put by the area where one goes out and a half Tefach pole is placed at the opposite corner, and a beam is placed on top of both of them (that connects them and forms a Tzuras ha'Pesach). This makes it as if the entire wall is closed.

Implied Question: This is despite the fact that in Eruvin (11b) no amount of width is required for the poles of a Tzuras ha'Pesach. Rather, even the slightest pole on each side with a beam on top of them constitutes a Tzuras ha'Pesach. This is as long as the poles on either side are strong enough that they could serve as doorposts for a door, which could even be a door made of straw. (Why, then, do we require each pole to be a half Tefach thick when it comes to the laws of Sukah?)

Answer: We are stringent regarding the laws of Sukah, as we require recognizable walls.

Observation: This is unlike Rebbi Yoshiyah's opinion later, as he requires walls that are like Sechach in that their shade is more than their sun.

Observation: This implies that if the closed space and open space are exactly the same, it is forbidden.

Implied Question: The Gemara could have asked a question from our Gemara on Rav Papa who says in Eruvin (15b) that if the open space is the same amount of closed space that it is permitted. (Why wasn't this question asked?)

Answer: Even without asking this question Rav Papa's opinion is heavily questioned (and therefore this question does not need to be asked).

Implied Question: This is despite the fact that we do end up ruling like his opinion, as we say there, since the Mishnah implies that his opinion is correct. (If so, it would seem this question is necessary!)

Answer: If our text here is that Shabbos is not permitted when there is more open space than closed space, this is understandable (this would imply that if they were the same, it would be permitted).

Question: Both according to the opinion in Eruvin (12b) that an upright Eruv pole is for people to recognize the border between the private and public domain, and according to the opinion that it in fact acts as a wall, our Gemara is difficult. What does Sukah, which requires walls according to Torah law, have to do with making an Eruv in an alleyway which only requires walls according to Rabbinic law? It is permitted to carry in an alleyway without an upright pole according to Torah law!

Answer: It is possible that this is referring to a Lechi that is a Tefach. This is as we said earlier that it is placed less than three Tefachim from the wall, which is a Rabbinic law. On Shabbos it is permitted based on a Migu, even if it is close to the wall.

Implied Question: However, one should not answer that we only require a Tefach regarding Sukah according to Rabbinic law, but according to Torah law any width qualifies. (Why not?)

Answer: This is because the Gemara in Nidah (26a) considers the wall of a Sukah as one of five things that must be one Tefach. The Gemara there says that the thickness of the beam on top of an alleyway is not mentioned as one of these five things since it is only a Rabbinic law. The Gemara only mentions laws that are written and their amounts are not stated.

Question: Why shouldn't this alleyway be a valid Sukah since it has three valid walls, even if it does not have an upright pole at the entrance? We hold like the Rabbanan that two actual walls are required but the third one can even be a pole of a Tefach!

Answer: Rashi therefore explains that it must be that this alleyway is open on both sides (and therefore there are only two walls).

Question #1: This is not possible. If so, this alleyway would only be permitted with an upright pole or a crossbeam according to Rebbi Yehudah. The Amoraim generally hold like the Rabbanan, as is stated in Eruvin (12b).

Question #2: Additionally, we say in Eruvin (81b, 95a) that we do not rule like Rebbi Yehudah regarding walls.

Answer: The alleyway is indeed an alleyway that is closed on three sides. The case is where one only put Sechach on the part of the alleyway closest to the pole, but not towards the back part of the alleyway (meaning that the wall in the back of the alleyway is not part of the Sukah). Accordingly, this Sukah only has two walls (houses on the sides) and a Tefach.

Explanation: This is because it is a wall regarding Shabbos.

Implied Question: This is despite the fact that this was generally a leniency that was only for people who were Oleh Regel, and it was only given to them for their animals. However, people are supposed to climb up and down the pit to drink, as explained in Eruvin (21a).

Answer: Even so, since according to Torah law this is permitted in general, we say that since it is a wall for Shabbos etc., and we do not even forbid it according to Rabbinic law due to the Mitzvah of Sukah.

Observation: When the Gemara said that we need both the case of an alleyway with a pole and Pasin, it did not bother to say this reasoning. This is because the Gemara found it obvious that this was permitted because it is a Mitzvah.

Implied Question: Rebbi Yoshiyah does not derive his law from the fact that we derived earlier the amount of walls required for a Sukah from the word "ba'Sukos," which seemingly implies that the Torah is calling a wall Sechach. (Why?)

Answer: This is because the Gemara there is deriving this from the fact that these words are extra, not because "ba'Sukos" means walls.

Proof: This is clearly true, as everyone agrees that we do not require walls to be made out of the residue from silos of grain and grapes (from which we derive what can be used for Sechach, namely that it must be something that grows from the ground and does not become impure).

Opinion: These opinions obviously are not all the same.

Proof: Rebbi requires a Sukah to be four square cubits, whereas Beis Shamai only requires "his head, most of his body, and his table" (seven by seven Tefachim).

Observation: A similar list (where everyone holds the same basic principle, but they vary greatly in how they apply this principle) is stated in Yevamos (51b), where the Gemara says that all of these opinions hold that Ma'amar is a complete Kinyan.

Explanation: The reason why Rebbi Yehudah is on this list is not because we concluded earlier that the reason the Rabbanan say a Sukah higher than twenty cubits is invalid is because they require a temporary dwelling, as the author of this list is Abaye who asks a question (and therefore disagrees with Rava) on Rava who gives the reasoning of a temporary dwelling.

Explanation (cont.): However, it is still true that one cannot make a Sukah that is higher than twenty cubits tall unless he makes a permanent structure.

Explanation (cont.): We similarly say in Sukah (21b) that Rebbi Yehudah is basing himself on his position that a Sukah must be a temporary structure, and the Gemara's proof is the fact that he permits a Sukah to be more than twenty cubits tall. This implies that he would generally make his Sukah a permanent structure.

Text: The Mishnah later (22b) that says it is valid has the text, "on top of the wagon." However, in our Beraisa regarding the argument between Rabban Gamliel and Rebbi Akiva, Rabeinu Tam says that we do not have this text. Rabeinu Chananel also does not have this text in the Beraisa, as they do not argue regarding the case (involving a Sukah) on top of the wagon.

Proof: This is as the Gemara concludes later (23a) that the argument is in a case where the Sukah can stand in a wind that commonly blows on land, but it cannot stand in a wind that commonly blows at sea (which has nothing to do with a Sukah on top of a wagon).

Question: However, this proof can be pushed aside, as we can similarly say that they argue regarding a Sukah that can withstand a common wind on regular ground but it cannot withstand such a wind if it is on top of a wagon, since it is moving around.

Answer #1: This is not logical, as they could also argue regarding a Sukah that is on top of a wagon that since it is moving around it looks temporary.

Answer #2: There is an additionally difficulty as a Sukah on top of a boat also moves around. Why should the argument be (stated as depending on, see Bach) whether it can stand in a wind commonly found at sea (when it can just as easily be regarding whether it looks too temporary)?

Question: However, it is possible to answer as I will explain later (21b, DH "she'Ain") regarding a Sukah that is supported with the legs of a bed.

Explanation: The reason for this is that a Sukah is a permanent structure, and Acheirim is Rebbi Meir.

Observation: Rebbi Meir says later (8b) that if there are two Sukos of a potter, one inside (meaning it opens from inside) the other, the outer one is a Sukah and is exempt from a Mezuzah. He means it is exempt during the rest of the year (and not during Sukos).

Proof: If he meant this regarding Sukos, since he holds Sukah is a permanent structure he should hold it is obligated in a Mezuzah!

Proof (cont.): This is as it is apparent from Yoma (10a) that for this very reason Rebbi Yehudah says that a Sukah during Sukos must have a Mezuzah.