Before us is Mishnah 2 in the first chapter of Maseches Sukkah. The Mishnah deals with two cases in which there is an additional covering or structure above the sukkah: a sukkah made under a tree, and a sukkah built on top of another sukkah.
One Who Makes a Sukkah Under a Tree:
The Mishnah opens: "Ha'oseh sukkah tachas ha'ilan - k'ilu asa'ah b'toch habayis" - one who makes a sukkah under a tree, it is as though he made it inside a house. One who makes his sukkah beneath a tree is like one who made it inside his house, and making a sukkah inside a house is not valid, as we will see further on. Here too there is an additional roof above the sukkah, and therefore it is not valid.
A Sukkah on Top of a Sukkah:
Similarly, the Mishnah continues: "Sukkah al gabei sukkah - ha'elyonah kesheirah v'hatachtonah pesulah" - a sukkah on top of a sukkah, the upper one is valid and the lower one is invalid. When one sukkah is built on top of another, the upper one is valid, since there is no additional structure above it; the lower one, however, is invalid, because it sits beneath another structure, just like one who sits inside a house.
The View of Rabbi Yehudah:
Rabbi Yehudah qualifies this halachah and says: "Im ein diurin ba'elyonah - hatachtonah kesheirah" - if there are no residents in the upper one, the lower one is valid. He does not mean that nobody actually lives in the upper sukkah, but rather that it is not fit for dwelling - it is not designed or built in a way that allows one to stay in it, such as when its floor is flimsy. In such a case the lower sukkah is valid, since we do not view the floor of the upper sukkah, which serves as the roof of the lower one, as a real floor, and we do not consider it an interruption or a barrier, but merely a flimsy object sitting in the middle of the sukkah.
It turns out, then, that the s'chach of the lower sukkah is the very same s'chach of the upper sukkah, and the whole thing is considered one sukkah - and for that reason the lower one is valid. This is provided that the s'chach of the upper sukkah is within twenty amos of the lower sukkah, for since we view the whole thing as a single sukkah, s'chach that is higher than twenty amos is invalid.
The Gemara's Explanation of the Dispute:
The Gemara explains that the dispute over whether the lower sukkah is valid does not apply in every situation, and it sets out three scenarios:
A floor that cannot bear any weight at all: If the floor of the upper sukkah, which is the roof of the lower one, is so weak that one cannot place cushions on it and seat a person there - all agree that the lower sukkah is valid by virtue of the upper s'chach, and the middle covering is of no significance.
A strong floor: If it is strong enough to support a person sitting on it with cushions and blankets - all agree that the lower one is invalid, for this is like sitting beneath a second sukkah.
A floor that barely bears weight: The dispute applies specifically in the intermediate situation, in which one can sit on the middle covering with difficulty, even though it is not comfortable sitting.
In this situation they disagree:
The first opinion in the Gemara: The lower sukkah is invalid, since one can manage to sit there, and therefore the middle covering is considered a roof that separates between the lower sukkah and the upper one.
Rami bar Chama: Since it is so flimsy that it is very difficult to sit on it, the middle covering does not count, and the s'chach of the upper sukkah serves as the s'chach of the entire structure.
In summary: In this Mishnah we learned that a sukkah made under a tree is invalid, for this is like making it inside a house; and in the case of a sukkah on top of a sukkah, the upper one is valid and the lower one is invalid. Rabbi Yehudah validates the lower one when the upper one is not fit for dwelling, in which case the whole thing is considered one sukkah and the upper s'chach renders it valid, provided that it is not higher than twenty amos. The Gemara established the dispute specifically in the case of a floor on which one can sit only with difficulty.