a stolen meal on the first night of sukkos -- mitzvah haba'ah b'aveira?

My son mentioned the following chakira posed by R’ Baruch Ber: if one steals bread for one’s meal on the first night of sukkos, is the kiyum mitzvah of eating that meal in the sukkah invalidated because of mitzvah ha’ba’ah b’aveira?

As we shall hopefully see, it seems that this chakira gets to the heart of how we define the mitzvah of eating in sukkah on the first night.

In contrast to R’ Eliezer’s view that one is obligated to eat meals in the sukkah every day of the chag, the Chachamim (Sukkah 27) hold that it is only on the first night that one must eat in the sukkah. Why is the first night different? The gemara explains that the Torah connects Pesach and Sukkos by using the same term of “15th of the month” to describe both; just as there is an obligation to eat a k’zayis of matzah on the first night of Pesach, so too, there is an obligation to eat in the sukkah on the first night of Sukkos.

The Rishonim are puzzled by the gemara’s need for a special din to teach us this obligation to eat in sukkah on the first night. The gemara elsewhere (Brachos 49) writes that if one omits ya’aleh v’yavo from bentching on Yom Tov, one must repeat birchas hamazon because eating a bread-based meal is obligatory on Yom Tov. If one must eat bread, then obviously one must eat in the sukkah!

Tosfos resolves the question by denying its premise. According to Tos there is no obligation to eat bread on Yom Tov. The requirement to repeat bentching applies only on the first night of Pesach and Sukkos where there is an obligation to eat because of the mitzvah of matzah or sukkah.

However, most Rishonim accept that there is an obligation to eat a bread-based meal on Yom Tov and offer other solutions. The Ran suggests two other answers:
1) Normally only an amount of bread equal to more than a k’beitza is required to be eaten in the sukkah. The special derivation from Pesach teaches that just as the shiur of matzah is a k’zayis, on the first night of Sukkos even a k’zayis must be eaten in the sukkah.
2) One can fulfill the obligation of eating a Yom Tov meal by consuming exactly a k’beitza of bread. However, on the first night of Sukkos we are required to consume slightly more than a k’beitza to obligate ourselves in the mitzvah of sukkah.

The question of whether one must eat a k'zayis or more than a k'beitza perhaps hinges on how one understands this special chiyuv on the first night. Is the chiyuv one of eating, just like the chiyuv of eating matzah, or is the chiyuv one of sitting in sukkah, and the meal is just a means of establishing residence, so to speak?

If the chiyuv is one of eating, then it can be fulfilled by consuming a k’zayis, the usual shiur used to define an act as eating. But if the chiyuv is one of dwelling in the sukkah, one must eat a shiur that normally calls for sitting in sukkah, namely more than a k’beitza.

It is interesting that the Rambam requires eating a k’zayis in the sukkah on the first night, but makes no mention of a prohibition of eating less than a k’beitza outside the sukkah even on the first night. The Tur, however, does. The Rambam apparently learned that this chiyuv of eating a k’zayis has nothing to do with the mitzvah of yeshivas sukkah, but is simply a separate chiyuv achila that takes place in the context of sukkah. The Tur, however, seems to have understood that the Torah redefines the mitzvah of yeshivas sukkah on the first night so that it is inclusive of meals even less than a k’zayis in size.

Returning to the chakira of R’ Baruch Ber, if the special chiyuv of the first night is one of eating a k’zayis, then it stands to reason that the food itself is a cheftza shel mitzvah and becomes disqualified because of mitzvah ha’ba’ah b’aveira. However, if the chiyuv is one of yeshivas sukkah, and the food is just a means to that end, then one could argue that it is the sukkah, not the food, which is the cheftza shel mitzvah, and therefore a stolen meal is not disqualified because of mitzvah haba’ah b’aveira.

There are other nafka minos to this issue...