Rashi: He did not lay the canes flat one beside the other, only one going up and one going down, as a result of which there is more sun than shade.

Rashi (cont.): And the Mishnah teaches us that 'We view it in such a way that, if they were lying flat the shade would be more than the sun, it is Kasher (Rashi).

Inference (Reason #1): From his explanation it appears that, when there is three Tefachim space between them, it is Pasul according to Abaye - because 'the sun is in excess to the shade'.

Refutation: This is not correct however because, since if the sun would be directly above people's heads, there would be more shade than sun, one cannot invalidate it simply because the sun that comes in from the side at an angle creates more sun?

Explanation #2: The reason must therefore be - because, in such a case, when there is a space of three Tefachim, it is not considered S'chach to combine ...

Explanation #2 (cont.): But when the space is less than three Tefachim, it is considered joined, and it is all one entity.

Clarification: this is a Mishnah in Maseches Ohalos (Perek 12, Mishnah 5), and the 'Tani Alah' is a Beraisa ...

Beraisa: This is how the Tosefta in Ohalos reads: 'When is that? When there is a Tefach space between them (the beams), but when there is not and there is Tum'ah underneath them, them underneath them is Tamei, but above them and in between them, is Tahor ...

Beraisa (cont.): And if the Tum'ah is in between them or on top of them, then corresponding to them (and upwards) up to the sky is Tamei, but underneath them is Tahor.

Beraisa (concl.): And when is that? When they are a Tefach wide; But if they are not, then the Tum'ah goes up (to the sky) and down (to the ground).

Clarification: It now emerges that the Beraisa refers to the Seifa of the Mishnah - where 'The top ones are the same as the space between the bottom ones' - so that where the space between the bottom ones is less than a Tefach, then the top ones (too) are less than a Tefach wide (equivalent to the space between the bottom ones),

Clarification (cont.): Therefore when there is Tum'ah underneath the bottom ones, underneath them is Tamei ...

Reason: Since each one transmits Tum'ah across all of it, seeing as it is a Tefach wide ...

Clarification (cont.): 'Between them is Tahor' - since the top one is not a Tefach wide, we do not say "Chavot Rami" to consider the air between the bottom ones as if it was closed up ...

Clarification (cont.): And on top of it is also Tahor, because, since it is a Tefach wide, it serves as a partition before the Tum'ah.

Conclusion: And finally it says 'When does that speak?' - that it either transmits Tum'ah or divides before it 'When the bottom one is a Tefach wide' ...

Conclusion (cont.): 'But if it is not', then whether the Tum'ah is underneath or whether it is on top, corresponding to the Tum'ah, it is Tamei; on the side, it is Tahor.

Question: What is the problem? Instead of asking from Rebbi Yossi b'Rebbi Yehuah, why not bring a support from the Rabanan who do not hold 'Ro'in'?

Proof: Since the Rabanan argue with him, as is evident in the first Perek of Eruvin (Daf 14a & 14b), where Abaye says 'Rebbi Yossi holds like his father in one point and disagrees with him in another (See Maharam); he holds like him in the one - that he holds 'Ro'in'?

Answer: The reason of the Rabanan is not because they do not hold 'Chavot Rami' by less than a Tefach, but because they declare Pasul a beam that is lying in such a way that it cannot hold a small brick, since it needs to be wide and strong ...

Answer (cont.): And they do not say 'Ro'in', and therefore they declare Pasul a beam that can be blown away by the wind and two parallel beams even if they are less than three Tefachim apart, because they require it to be 'fit to hold a small brick'.

Answer (concl.): But if they would have said 'Ro'in', they would say 'Ro'in' even with beams that are less than a Tefach wide. Therefore, we can learn from Rebbi Yossi b'Rebbi Yehudah that we do say 'Ro'in' when the beams are more than three Tefachim apart.

Proof: Seeing as they only argue inasmuch as what they do not hold 'Ro'in' for the reason that Tosfos mentioned.

Inference: The Gemara now concludes that, if it is a Tefach, then, we say 'Chavot Rami', even even if it is three Tefachim (away)

Introduction to Question (cont.): In the first Perek of Eruvin (Daf 9a & 9b) the Gemara says, in connection with a beam that is drawn (from the wall) or that is suspended ...

Introduction to Question (cont.): Where one stuck two bent pegs atop the two walls of the Mavoy, which are less than three Tefachim from the wall both vertically and horizontally ...

Introduction to Question (concl.): And it teaches us that we say 'L'vud' and 'Chavot ... '.

Question: Why does it need to be less than three Tefachim high - since, seeing as the beam is a Tefach wide, we say 'Chavot Rami' even if it is three Tefachim high?

Answer: It is not comparable, seeing as one can anyway ask there that without 'Chavot Rami' the Mavoy ought to be Kasher, bearing in mind that the beam is less than twenty Amos high?

Answer (cont.): The answer is that the beam needs to be on top of the Mavoy, as the Gemara explains there, and that, even if we hold that 'The beam serves as a Mechitzah' (Ibid. 8b), one nevertheless requires a minimal 'Heker' (recognition ) ...

Answer (concl.): And unless it is within three Tefachim, there is no Heker at all ...

Precedent: As in thre case there where one places it outside the wall', (where it is invalid) even if it is close to the wall.

Clarification: When it says that 'When they are equal it is Pasul' it refers to the top - when there the same space between one cane and the other as the width of the actual cane; and it is Pasul even if it is exactly the same ...

Reason : Because the sun in the spaces appears on the ground wider than the shade of the S'chach.

Clarification (cont.): And when the Gemara extrapolates that 'If they are equal it is Kasher, it refers to below ...

Reason: Because when the sun and the shade are the same, then we know that the canes above are wider than the spaces.

Explanation #1: When the hole above is the size of a Zuz, then the sun below is the size of a Sela (double that of a Zuz [Rashi]).

Question #1: Rabeinu Tam queries this however, in that Rav Papa himself, in the first Perek of Eruvin (Daf 15b), permits 'Parutz ke'Omeid', and there too, the Gemara Paskens like that?

Question #2: Furthermore, he asks from the Gemara in the first Perek of Kidushin (Daf 11b), which cites the custom to call half a Zuz an 'Astira' - from which we see that it is smaller than a Zuz?

Explanation #2: Rabeinu Tam therefore explains 'Ka'an mi'Lema'alah' - Someone who measures the air from the top to be equal, it is Kasher, seeing as it is then 'Omeid ke'Parutz' ...

Explanation #2 (cont.): Whereas if when one stands on the ground and looks upwards it appears equal, it is Pasul, because air that is a Zuz wide looks as if it is only an Astira, since it is far from him.

Proof: And proof of this lies in the Pasuk (in connection with the Spies) "And we were in our eyes like grasshoppers" (Bamidbar, 13).

Conclusion: And a large star in the sky appears to us to be small, as is evident in Perek ha'Mocher es ha'Sefinah (Bava Basra, 73a).

Explanation #1: 'He supported most of the floor of the Sukah on a tree and made two walls around it on top of the tree. He then made a wall from the ground up; he supported the floor of the Sukah half way up it and raised it (the wall) another ten Tefachim above the floor.

Explanation #1 (cont.): Or two man-made (adjacent) walls and one on the tree', because, seeing that, if the tree would be taken away, the floor of the Sukah would collapse, since it cannot stand with the support of only the two walls that are on the ground, one may not go up into it on Yom-Tov, since he will be making use of the tree' (Rashi).

Refutation: This is not how the Gemara in 'Mi she'Hichshich' (Shabbos, Daf 154b & 155a) seems to explain it however. The Gemara there extrapolates from here that the sides (of a tree) are forbidden and says - 'Does it not speak when he carved a niche in the tree into which he placed canes - which is the side?' ...

Explanation #2: This implies that it speaks where the trees serve as the walls of the Sukah and the canes of the Sukah are supported by the (side of the) tree. Consequently, if he enters the Sukah on Yom-Tov, they decreed out of concern that he may place his personal items on the S'chach. And that is how Rashi explains it there.