Sukkah, Chapter Two, Mishnah 1. The Mishnah rules: "Hayashen tachas hamitah basukkah - lo yatza yedei chovaso" - one who sleeps under the bed in the sukkah has not fulfilled his obligation. Someone who sleeps beneath a bed that stands inside the sukkah has not fulfilled the mitzvah of sukkah.
The Gemara's explanation:
The Gemara explains that the case is a bed ten tefachim high, which therefore has the status of a tent in its own right. This tent interposes and forms a barrier between the person and the sukkah, so that he is not sitting under the sukkah at all but under an independent tent. Some understand this as a problem of a sukkah under a sukkah; in any event, the bed separates between him and the sechach, and therefore he does not fulfill his obligation with it.
The opinion of Rabbi Yehudah:
Rabbi Yehudah said: "Nohagin hayinu shehayinu yesheinim tachas hamitah bifnei hazekeinim" - it was our practice to sleep under the bed in the presence of the elders, and they said nothing to us, which shows that it is valid. His words fit with his opinion presented in the first chapter, that a sukkah must be a permanent dwelling, a fixed structure. The bed, by contrast, is only a temporary structure, since it is moved from place to place and has no permanence at all. Therefore a temporary tent does not nullify the sukkah and does not interpose between the person and the permanent dwelling that is the sukkah. Since the sukkah is the fixed structure, the person is considered to be sitting under it and not under the temporary structure that is the bed, and so it is valid.
The incident with Tavi, the servant of Rabban Gamliel:
Rabbi Shimon brought a different incident: Tavi, the servant of Rabban Gamliel, would sleep under the bed in the sukkah. Rabban Gamliel said to the elders: "Did you see my servant Tavi?" - although he is a servant, he is a Torah scholar, and he knows that servants are exempt from sukkah.
And why is a servant exempt from sukkah? A Canaanite servant, although he is obligated in mitzvos, is obligated only in those mitzvos in which a woman is obligated. Since a woman is not obligated to sit in a sukkah, the servant is not obligated either. For this reason Tavi knew, from his learning, that he was not required to sit in the sukkah, and therefore he slept under the bed.
It is worth noting that Rabban Gamliel was not coming to teach the laws of sukkah, but only to remark on the distinction of his beloved servant Tavi. Yet in passing we learn the halachah from his words: one who sleeps under the bed in the sukkah has not fulfilled the mitzvah of sukkah. For Rabban Gamliel's entire remark rests on the fact that Tavi was not fulfilling the mitzvah with this sleep - and had he been obligated in it, he would not have fulfilled his obligation this way.
In summary: In this Mishnah we learned that one who sleeps under the bed in the sukkah has not fulfilled his obligation, because a bed ten tefachim high is considered a tent that interposes between him and the sechach. Rabbi Yehudah validates it, consistent with his view that the sukkah is a permanent dwelling and a temporary tent does not nullify it, and he brings proof from their practice in the presence of the elders. Rabbi Shimon brings the opposite proof from the incident with Tavi, the servant of Rabban Gamliel, who was exempt from sukkah as a servant is exempt from any mitzvah from which a woman is exempt.