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1)

(a) Even if the S'chach is as thick as a house - the Sukah is nevertheless Kasher.

(b) And it is Kasher even if one is unable to see the stars through it.

(a) The Tana of our Mishnah invalidates a Sukah ha'Meduvleles, which Rav describes as a Sukah Aniyah - a sparsely covered Sukah, but without any spaces of three Tefachim or more.

(b) Shmuel interprets 'ha'Meduvleles' like 'ha'Mevulbeles' - meaning 'mixed up' (with some beams up, and some beams down).

(c) The Tana of our Mishnah follows the Din of a Sukah ha'Meduvleles with 've'she'Tzilasah Merubah me'Chamasah', a continuation ...

1. ... according to Rav (i.e. provided it casts more shade than sunshine),
2. ... bur not according to Shmuel - in whose opinioin it comes to add Rav's Din (of Sukah Aniyah) to that of Sukah ha'Meduvleles.

(a) Abaye disqualifies Shmuel's 'Sukah ha'Meduvleles', should the top plank be three Tefachim or more away from the one below. Rava declares it Kasher, provided the top plank is at least one Tefach wide - because then we apply the principle of Chavot Rami, which joins them by creating walls from the top plank to the bottom one.
(b) 'Chavot Rami' by a wall is known as 'Gud Acheis Mechitzasah'.
(c) If there are two rows of planks, one on top of the other, with gaps between each plank, then, if the Tum'ah (i.e. the piece of corpse) was ...

1. ... underneath one of the planks - the vessel would have to be underneath the same plank in order to become Tamei.
2. ... on top of the lower plank - it would have to be in between the two planks.
3. ... on top of the top plank - it would have to be above it, anywhere up to the sky.

(d) If the top planks, instead of being directly above the lower planks, were exactly above the spaces in between the lower ones, then, if the Tum'ah was ...

1. ... underneath any one of the planks - the vessel would have to be anywhere in the room, below any of the lower planks, in order to become Tamei.
2. ... lying on top of any one of them - it would have to be anywhere directly above that plank, anywhere up to the sky.

5)

(a) We already quoted the Beraisa (on 18a), which extends (through the Din of 'Levud') a Koreh that stretches across the entrance of a Mavoy to within three Tefachim of the opposite wall, or two Koros that do not quite meet in the middle of the entrance, stopping short within three Tefachim of each other. Raban Shimon ben Gamliel says that as long as they are within *four* Tefachim of each other, they are considered joined - because, in his opinion, 'Levud' applies up to *four* Tefachim.

(b) The minimum combined width of two beams placed *side by side* to serve the Mavoy as a Koreh - is one Tefach (sufficiently wide to hold a brick of one and a half Tefachim, including one Etzba of cement on either side of the beam.

(c) Raban Shimon ben Gamliel is lenient in this point too. According to him, as long as the two beams, when placed *close to each other* (even if they are not side by side), are strong enough to hold the brick *lengthwise* (i.e. three Tefachim), they form a Kasher beam.

(a) If the two beams were of a different height, Rebbi Yossi b'Rebbi Yehudah combines them, provided one of them is not higher than twenty Amos and the other one lower than ten Tefachim. We initially understand this to mean that they combine, even if one of the beams is just below twenty Amos, and the other, just above ten Tefachim - in which case, they combine through the principle of 'Chavot Rami'.

(b) But we are speaking of two beams, each of which is less than a Tefach wide - and, according to Rava, 'Chavot Rami' does not apply in such a case?

(c) So we explain the Beraisa to mean that either the one beam is just below twenty Amos or it is just above ten Tefachim - and, in each case, the second beam is placed within *three* Tefachim of the first. Consequently, it is the principle of 'Levud' that we apply to combine them, not 'Chavot Rami'.

(a) From our Mishnah, which *validates* a Sukah with more *shade than sunshine* - we can infer that if the shade and the sunshine are equal, the Sukah is Pasul; whereas the previous Mishnah, which *invalidates* a Sukah that has more *sunshine than shade*, implies that when they are equal, the Sukah is Kasher (an apparent contradiction).

(b) We reconcile the two Mishnahs by establishing the earlier Mishnah, looking at the shade and the sunshine on the *ground* (where the area of sunshine is twice that of its source in the S'chach), and *our* Mishnah, at the *S'chach* (where the area of sunshine is only half as large as it is on the ground).

(c) From here, they formulated the popular saying 'If it (the hole) is the size of a Zuz above, then it (the sunshine) is the size of a Sela (*two* Zuz) below'.

9)

(a) The Tana of our Mishnah validates a Sukah that is built on top of a wagon - despite the fact that it can be easily moved around, or of a ship - despite the fact that a strong wind may demolish it.

(b) These two cases are not only Kasher, but one may also enter them on Yom'Tov - which one is not permitted to do by a Sukah that is built on top of a tree or a camel, even though they too, are Kasher. That explains why the Tana separates them.

(c) Even though entering a tree-Sukah is forbidden on Yom-tov, the Tana nevertheless informs us that it is Kasher - because of Chol ha'Mo'ed, when one is permitted to enter it, too.

(d) Someone who *did* enter a tree Sukah (in spite of the prohibition), has fullfilled the Mitzvah of Sukah.

(a) One may *not* enter a Sukah on Yom-Tov ...

1. ... if two walls of the Sukah are supported by trees which were extended upwards by man-made walls, with the third wall man-made from the ground upwards.
2. ... if the two adjacent walls were completely man-made, and the third one was supported by the tree.

(b) One would however, be permitted to enter a Sukah which was partially supported by a tree - if *three* of the walls were man-made, with the fourth wall only supported by a tree.

(c) The binding principle in this matter is - that if the Sukah can stand without the help of the tree, then it is Kasher, but if not, then it is Pasul.