1)

(a)Our Mishnah declares Kasher a Sukah ha'Meduvleles and one which has more shade than sun (which will be explained in the Sugya). Likewise, the Tana declares Kasher a Sukah ... .

1. ... with very thick Sechach ...

2. ... even if it is so thick that one is unable to see the stars through it.

2)

(a)Rav defines 'Sukah ha'Meduvleles'- (a sparsely covered Sukah, but without any spaces of three Tefachim or more) as a Sukah Aniyah (like the word 'Meduldeles' - poor).

(b)Shmuel interprets 'ha'Meduvleles' like 'ha'Mevulbeles' - meaning 'mixed up' (with some of the beams higher than others).

(c)The Halachah which follows 've'she'Tzilasah Merubah me'Chamasah' is a continuation according to Rav (i.e. provided the Sukah ha'Meduvleles casts more shade than sun), but a new Halachah according to Shmuel (in whose opinion it comes to add Rav's Din [of Sukah Aniyah] to that of Sukah ha'Meduvleles).

3)

(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 ...

(b)... because then we apply the principle of 'Chavot Rami', which joins them by creating walls from the top plank to the bottom one.

(c)'Chavot Rami' itself is - part of the principle of 'Gud Achis Mechitzasah'.

4)

(a)Rava proves his point from a Mishnah in Ohalos, which discusses uncemented beams of a house with an attic on top, and Tum'ah (a piece of Mes) lying underneath it. If there are two rows of planks, one on top of the other, with gaps between each plank, if the Tum'ah is lying...

1. ... underneath one of the planks - the vessel will have to be underneath the same plank, in order to become Tamei.

2. ... on top of the lower plank - it will have to be in between the two planks.

3. ... on top of the top plank - it will have to be above it, anywhere up to the sky.

(b)Whereas if the top planks, instead of being directly above the lower planks, are exactly above the spaces in between the lower ones, then, if the Tum'ah is ...

1. ... underneath any one of the planks - the vessel will 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 will have to be anywhere directly above that plank, anywhere up to the sky.

(c)The Beraisa establishes the former case (d 1.) when the spaces and consequently the top planks, are at least one Tefach wide. If they are not, then only vessels that are underneath the same plank as the Tum'ah will become Tamei ...

(d)... proving Rava's point, that 'Chavot Rami' applies exclusively to an Ohel that is at least one Tefach wide.

5)

(a)We already quoted the Beraisa (on 18a), which extends (through the Din of 'Lavud') a Korah 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, 'Lavud' goes up to four Tefachim.

(b)The minimum combined width of two beams placed side by side to serve the Mavoy as a Korah - 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.

6)

(a)If the two beams were of a different height, Rebbi Yosi 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 'Lavud' that we apply to combine them, not 'Chavot Rami'.

7)

(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 Sechach), and our Mishnah, at the Sechach (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'.

8)

(a)The Tana of our Mishnah validates a Sukah even if the Sechach is so thick that the stars cannot be seen through it. If however, if it is so thick that even the sun's rays cannot penetrate it - then according to Beis Shamai, it is Pasul ...

(b)... but Kasher, according to Beis Hillel.

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 fulfilled the Mitzvah of Sukah.

10)

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

1. ... if two walls of the Sukah are supported by trees whilst the third wall extends all the way down to the ground, or ...

2. ... if the two adjacent walls are completely man-made, and the third one was supported by the tree.

(b)One is however, permitted to enter a Sukah which is partially supported by trees - if three of the walls are man-made, and only the fourth wall is supported by a tree (or if the two parallel walls are man-made and the third wall is supported by a tree).

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