The Mishnah (2:2) teaches that a sukkah "meduvlelet" and a sukkah whose shade is more than sunlight is valid. The Gemara includes two opinions regarding the meaning of sukkah "meduvlelet". Rav maintains that it is a sukkah aniya – a poor sukkah. Rashi explains that this means that the sukkah is only lightly covered with schach. Consequently, the Mishnah is only discussing one case. In other words, a sukkah meduvlelet is only valid if there is more shade than sunlight. Shmuel however understands that the case in the Mishnah is where that schach is not resting on the sukkah neatly, with some reeds pointing upwards and others down. Consequently, the Mishnah is teaching two separate cases.
Concerning the opinion of Shmuel, Abaye explains that the sukkah would only be valid if the space between the upper and lower reeds is less than three tephachim.1 Rashi understands that due to the layout of the schach there is currently more sunlight than shade in the sukkah. If the reeds however are (veritically) within three tephachim, then we can view it as if the schach is resting evenly - based on the principle of levud. The Ritva notes that normally levud would not help to solve the issue of having more sunlight than shade; for example, if the a sukkah was covered very sparsely and there was less than three tephachim between each piece. Nevertheless, this case is different as there is enough schach. It is however arranged badly, and levud is not being used not create extra schach, but rather to "flatten" the existing schach.
The Tosfot understands, based on the opinion of Rashi, once the gap is greater than three tephachim the pesul – the issue that invalidates the sukkah – is that the schach lets in more sunlight than shade. The Tosfot however find this difficult. They explain that if there were more shade than sunlight when the sun is above the sukkah, then the sukkah is valid even though there would be more sunlight then shade when the sun is on an angle. Consequently, if flattening the schach is all that is required, then there would be more shade than sunlight when the sun was above the sukkah and the sukkah should be valid.2
The Tosfot therefore understand that the issue is not related to sunlight and shade. Instead that once there is too much of a gap, the schach above and below no longer combine to be considered one covering in order provide the required amount of schach. This is true even if there is more shade then sunlight.
The Aruch LaNer however defends Rashi based on an earlier explanation of the Ritva. Let us return to the first Mishnah where we learnt that the maximum height of a sukkah is twenty amot. The Gemara includes several opinions regarding the limit. One opinion is that at that height, one is no longer sitting in the shade of the schach but under the shade of the walls. The Ritva asks that during the middle of the day, the sun will be above the sukkah, so why is the height an issue? He answers that the sun's elevation varies based on the season. During Tamuz the sun would rise directly above. However during Nissan that is not the case, even at noon, and certainly during the morning and evening. Consequently, the height of the walls does matter.
Based on the above, the Aruch LaNer explains that according to Rashi having more sunlight than shade is the issue, despite the fact that if the schach was flattened there would be more shade than sun. This is because since the sun's angle of elevation is during sukkot means that the sun does not pass directly above the sukkah, without levud there would always be more sunlight than shade in the sukkah.
1 Rava in the Gemara explains that if the reeds where were a tephach wide than even a space greater that three tephachim would be valid based on the principle of chavut rami.
2 The Piskei HaRid argues from a different angle that if there was less shade then sun, then the schach is too sparse to be defined as schach and cannot combine even with lavud.
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