Rif Succah 9b {Succah 19b - 20b}

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9b

{Succah 19b}
Mishna:
If one makes his succah in the form of a cone {tzrif} or leans it {=the roof of it} against a wall: Rabbi Eliezer invalidates, because it has no roof {=its roof cannot be distinguished from its walls}.
And the Sages declare it valid.

A large reed mat made for sleeping on is subject to defilement, and one may not use it for schach. If made for schach, one may use it for schach and it is not subject to defilement.

Rabbi Eleazar says: Whether a large one or a small one {reed mat}, made for sleeping on is subject to defilement, and one may not use it for schach. If made for schach, one may use it for schach and it is not subject to defilement.

Gemara:
Abaye found Rav Yosef sleeping under a kilat chatanim {nuptial bed, which presumably because of its slanted roof does not constitute a valid succah, and thus Rav Yosef was not in a succah within another succah, but just in a bed inside a succah}
He {Abaye} said to him: Like whom are you conducting yourself? Like Rabbi Eliezer? You have abandoned the Sages and adopted the position of Rabbi Eliezer {an individual}!
He {Rav Yosef} said to him: The brayta reverses the opinions. Rabbi Eliezer invalidates and the Sages invalidate.
He {Abaye} said to him: You have abandoned a Mishna and act in accordance to a brayta?
He {Rav Yosef} said to him: The Mishna is the lone opinion {namely, Rabbi Natan}.

For we learnt in a brayta: If one makes his succah in the form of a cone {tzrif} or leans it {=the roof of it} against a wall:
Rabbi Natan says: Rabbi Eliezer invalidates, because it has no roof {=its roof cannot be distinguished from its walls}. And the Sages declare it valid.

And the halacha is like Rav Yosef.

And we derive from this that if one makes his succah in the form of a cone /\, that the Ishmaelites call it machnis, or he leans it {=the roof} against a wall -- such that he places the boards down on the ground distant from the wall and leans them against the wall /| -- such that the succah does not have a {horizontal} roof -- it is invalid.
And if he raises the succah off the ground a handsbreadth, or he distances it from the wall a handbreadth, it is valid, for it has a roof of a handbreadth.

And we derive from this that it is permitted to sleep in a succah in a nuptial bed which lacks a {horizontal} roof -- for since it lacks a roof, it is not like a succah within another succah.

And we derive from this that a nuptial bed which has a roof, it is prohibited to sleep in it -- for it is like a succah within a succah.

{Succah 20a}
"A large reed mat...":
Rav Pappa concludes that by a small one, all agree that it is by default for sleeping. When do they argue? By a large one. That the first Tanna holds that by default a large one is for schach. And Rabbi Eleazar holds that a large one is also by default for sleeping.
And the halacha is like the first Tanna.

The Sages learnt {in a brayta}: A mat of rushes and of bulrushes: large, we make schach of it; small, we do not make schach of it.

{Succah 20b}
They learnt {tanya}: Rabbi Chanina said: When I descended to the exile, I found a certain elder, and he said to me: we make schach of reed mats {budia}. And when I to my father's brother, he agreed to his words.
Rav Chisda said: And this is where it lacks a rim.
Ulla said: These reed mats of Mechoza, if not for their rim, we would be able to use them as schach.
A brayta also says so: One may use reed mats as schach , and if they have a rim one may not use them as schach.
And even though he removes the rim, one may {still} not use them as schach, just as we say by worn out vessels, which one may not use as schach.

END PEREK ONE - succah shehi gavoah
BEGIN PEREK TWO - hayashen tachat hamitta

Mishna:
He who sleeps under a bed in a succah did not fulfil his obligation.
Rabbi Yehuda said: We had the practice that we sleps under beds before the elders {zekeinim} and they said not a word to us {objecting to this}.
Rabbi Shimon said: An incident with Tavi the servant of Rabban Gamliel that he slept the bed {in the succah}. Rabban Gamliel said to the Sages: Do you see Tavi my servant, that he is a Torah scholar and knows that servants are exempt from succah, and so he sleeps under the bed.
And according to our way, we learn that one who sleeps under a succah does not fulfil his obligation.