One who makes a Sukkah underneath a tree or under a roof, containing 3 Seifim:[No Sukkah can be made under a house or a tree]. One who makes his Sukkah underneath a tree - there are those who say that if the tree's shade is greater than the sunlit area, the Sukkah is completely invalid, even if the Sukkah is shaded more so than sunlit. However, if the tree's sunlit area is greater than its shade - if the Sukkah's shade is greater than its sunlit area without a tree, it is Kosher even if the branches were not lowered to mix with the schach of the Sukkah. However, if the Sukkah is not shaded more so than sunlit because of the tree, it is necessary to lower the branches and mix the with the Shach in such a way that they are not recognizable and the Schach is the majority and nullifies it. And there are those who say that even if the Sukkah's shade is greater than its sunlit area without the tree, and the tree's sunlit area is greater than its shaded area, if the branches of the tree are aimed or directed to the kosher Shach, it is pasul (invalid), whether the tree was there first or the Sukkah was there first, when the branches of the tree are directed toward the kosher Schach. Rema: However, if the branches were lowered down and mixed with the Schach so that it is not noticeable, it is batul and the Sukkah is Kosher (the Rosh and the R"an). Similarly, if the kosher Schach rests on the invalid Schach, it is accidentally mixed and therefore kosher (Mordechai) However, if the branches are towards the air between the Schach, it is Kosher or if the Schach is the majority such that even if it is removed from the tree it retains its measure (Tur)It is Kosher inasmuch that the valid shade is greater than the sunlit areas so that even if the tree is removed there is enough valid Schach to make it kosher. In any event it does not matter whether the tree existed first or the Sukkah existed first; there is one law for both of them.

Things That Are Invalid For S'chach, having four Seifim: 1. Invalid s'chach, makes a sukkah invalid in the middle if it is four tefachim. However, less than 4 is valid and one is permitted to sleep under it. From the side, it does not invalidate except if the invalid s'chach measures 4 amot, but less than 4 it is valid, for we say it is a curved wall; for we could say that we see it as if the wall is bent, and we consider this invalid s'chach to be from the body of the wall. This is a law given to Moshe at Sinai. Therefore, for this reason, a house which is reduced in the middle and one covers the middle area with s'chach, and there remains from the ceiling around the valid s'chach less than 4 amot between it and the walls, it is valid. However, we do not sleep underneath it whenever it measures 4 tefachim. With regard to what have these things been said? With regard to a large sukkah that has, in addition to the invalid s'chach, more than 7 x 7 tefachim. However, in a small sukkah which only has 7 x 7, whether in the middle or on the side, when there are three tefachim, it is invalid. When there are less than three tefachim, it is a valid sukkah and we may sleep underneath it and it joins together to complete the measure of the sukkah.