If one makes his succah under a tree, it is as if he would have made it in his house [and it is pasul]. (If one built) a succah atop a succah, the upper is kasher and the lower pasul, [for it has two schachs, and Scripture invalidates a succah under a succah.] R. Yehudah says: If there is no "dwelling" in the upper, [i.e., if the upper cannot be used as a dwelling, as when the roof of the lower cannot support the mattresses and covers of the upper], the lower is kasher. The first tanna and R. Yehudah do not differ where it cannot support them at all, all agreeing in such an instance that the lower is kasher with the schach of the upper, its own roof not being considered a roof, so that it is not a succah under a succah. And if it were strong enough to support the mattresses and covers of the upper, all agree that it is pasul. Where do they disagree? When it can support them only with difficulty, as when the lower roof sways and buckles from the (weight of) the mattresses and covers of the upper. The first tanna holds that this is called "a succah under a succah," and is pasul; and R. Yehudah holds that since it supports them only with difficulty, it is not considered a roof and it is not called "a succah under a succah." The halachah is not in accordance with R. Yehudah.]
Bartenura on Mishnah Sukkah
כאילו עשאה בתוך הבית – and it is invalid.
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English Explanation of Mishnah Sukkah
Introduction
This mishnah deals with a person who makes a valid sukkah (we will learn more about what a valid sukkah is later) but then something is placed on top of his sukkah that does not count as valid skhakh. This causes the otherwise valid sukkah to be invalid.
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Bartenura on Mishnah Sukkah
תחתונה פסולה – for it has two [sets of] S’khakh/coverings of the festive booth, and the Biblical verse invalidates a Sukkah that is underneath [another] Sukkah.
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English Explanation of Mishnah Sukkah
One who makes his sukkah under a tree, it is as if he made it within the house. A tree while still attached to the ground cannot be used for skhakh, the roofing of the sukkah. Skhakh must come from a natural source, but it must be detached from the ground. Therefore, if one puts his sukkah underneath a tree it is invalid, just as it would be invalid if one built a sukkah inside a house with the ceiling as his roof.
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Bartenura on Mishnah Sukkah
אם אין דיורין בעליונה – which is not appropriate for dwelling, such as [if] the lower roof is unable to endure/sustain pillows and cushions of the upper [Sukkah]. But the First Tanna/teacher and Rabbi Yehuda did not disagree if it cannot endure it all, and in that, the entire world admits that the lower [Sukkah] is valid with the S’khakh/coverings of the festive booth of the upper [Sukkah], for its roof is not considered a roof, and it is not a Sukkah that is underneath a Sukkah. But if it is healthy and cable of receiving the pillows and cushions of the upper [Sukkah], the entire world does not argue that it is invalid. But they disagree when it can receive it in an emergency/when needed, such as the case where the roof of the lower [Sukkah] shakes and vibrates from the pillows and cushions of the upper [Sukkah], where the first Tanna holds that in this case it is called a Sukkah that is underneath a Sukkah and is invalid, and Rabbi Yehuda holds that since it other than in the case of an emergency cannot accept the pillows and cushions of the upper [Sukkah], it is not considered a roof, and this is not a Sukkah that is underneath a Sukkah. But the Halakha is not according to Rabbi Yehuda.
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English Explanation of Mishnah Sukkah
One [who makes] a sukkah on top of another sukkah, the upper one is valid but the lower is invalid. Rabbi Judah says: if there are no occupants in the upper one, the lower one is valid. If a person builds one sukkah on top of another, it turns out that the skhakh of the bottom sukkah is the floor of the top sukkah. Even if the skhakh meets all other halakhic requirements it is still invalid because the fact that someone is living above makes it again similar to a person who builds his sukkah inside a house. Rabbi Judah holds that if there is no one who is living in the upper one, than the bottom one is valid. The upper sukkah is not considered to be living quarters unless someone is actually living there.