Reference: It is a Mishnah in the first Perek of Uktzin (Mishnah 5).

Explanation #1: In Perek ha'Ba al Yevimto (Yevamos, Daf 64a) Rashi defines 'Asar' as a shovel (with a handle).

Refutation: This is not correct however, as one can turn over produce even without a handle ...

Refutation (cont.): And this is called a winnowing-shovel, with which one clears the produce of its chaff, as the Pasuk writes in Yeshayah (30) "which has been winnowed with a shovel and a fan".

Explanation #2: Whereas here he (Rashi) defines it as a pitchfork ...

Conclusion: And that is the correct translation.

Clarification: The Kashya goes specifically according to the Lashon of Rav later - that in the middle, a plank of four Tefachim renders the Sukah Pasul ...

Proof: Because according to the other Lashon, which holds that even in the middle, only a plank of four Amos renders Pasul, there is no Kashya.

Clarification: Whereas according to Rebbi Yehudah, they do not combine ...

Reason: Since the Sukah would be Kasher even if it was covered entirely with them.

Clarification: It refers even to a plank that is four Tefachim wide.

Source: As is evident later - when the Gemara queries Shmuel, who says that 'S'chach Pasul of four Tefachim in the middle renders the Sukah Pasul'.

Implied Question: In fact, the Gemara could also have stated that Rebbi Yehudah concedes ... '

Implied Question (cont.): And the reason that it mentions Rebbi Meir is ...

Answer #1: Because, as Rashi explains, it is a Chidush inasmuch as even Rebbi Meir, who is stringent, concedes in this point.

Answer #2: Moreover, because basically, 'uModeh' refers to the 'Ein bahen Arba'ah' over which they are arguing.

Implied Question: And it Davka says that 'between one plank and the other there is the space of a plank' ...

Answer: Because if it was less, even though one is permitted to sleep underneath S'chach Pasul that is less than four Tefachim, there where the Pasul area is the majority, it is worse.

Clarification: By a plank of four Tefachim however, according to how Shmuel establishes it later - by a Sukah of exactly eight Amos, that, when one places a plank and Pesel (waste from the granary ... ) up to the middle on one side and the same on the other side, placing first the plank and then the Pesel ...

Clarification (cont.): In which case, the two Pesalim end up in the middle, making what would constitute a Kasher Sukah by other Pesalim, there is no difference as to whether there is the space of a plank in between or not ...

Reason: Because if it is because there is a Hechsher Sukah, then even if the rest of the Sukah was entirely covered with planks, we would apply the principle of 'Dofen Akumah' ('a bent wall') ...

Reason (cont.): Whereas if it is order to render Kasher the remaining Pesalim between the planks, they are in the middle of the Sukah, and Shmuel said 'In the middle of the Sukah, a plank of four Tefachim renders it Pasul ...

Reason (concl): In which case, it (even Pesel that is the width of a plank) doesn't help.

Summing Up: A formation of a plank and Pesel that is the width of a plank assuming the planks are less than four Tefachim, even if the entire Sukah is made like that, it is Kasher even underneath the planks, and even according to Rebbi Meir ...

Reason: Seeing as there is no plank of four Tefachim in one location.

Rebbi Meir #1: And when does Rebi Meir declare it Pasul? There where are two planks together that make up four Tefachim.

Rebbi Meir (cont.): Alternatively, where there id no space of the width of a plank between the planks, since it is not then fiftty/fifty.

Summing Up (cont.): And there where the planks are dour Tefachim wide and the space between them equals the width of a plank ...

Opinion #1: According to Rav, who says later that both in the middle and at the side, it only renders Pasul when there is four Amos, he will establish the Beraisa where th entire Sukah is made like that, and it is Kasher underneath the Pesel but not underneath the S'chach.

Opinion#2: Whereas Shmuel establishes it where the two Pesalim are placed in the middle, and where there is less than four Amos up to the walls, in which case it is entirely Pasul - even underneath the Pesalim, except for underneath the two Pesalim in the middle, where it is Kasher.

Clarification: According to Rav, this Machlokes Amora'im can only go according to Rebbi Meir, and when the planks are four Tefachim wide ...

Clarification (cont.): And in Perek Mi she'Hotzi'uhu (Eruvin, Daf 46b), the Gemara states 'Rebbi Meir ve'Rebbi Yehudah, Halachah ke'Rebbi Yehudah'.

Clarification (concl.): But according to Shmuel, it goes according to both Tana'im.

Inference, Proof #1: Consequently, it seems that the Halachah is like Shmuel, despite the fact that generally, it is like Rav in matters of Isur.

Proof #2: Furthermore, later in Perek Lulav ha'Gazul (Daf 36b), when citing Rebbi Yehudah, who holds that 'A Sukah is only Kasher if it is made of the four species of the Lulav' ...

Proof #2 (cont.): It queries this from 'the Beraisa that supports Shmuel', which talks of a case where 'One covered the Sukah with planks of cedar wood' ...

Proof #2 (concl.): And it does not cite 'the Beraisa that supports Rav' - we have a proof that Shmuel's opinion is the correct one.