134:6 Sometimes a succah is built so that its boards project inside on its walls and the poles on which the schach rests is placed on these. This is okay so long as the board is not more than four cubits (about six feet) because we have a tradition received from Moses at Sinai that up to four cubits it is considered like a bent wall. This means that it is considered part of the wall, as if the wall continues up at a slanted angle. We do not, however, sit or sleep under such a board because it is not considered a part of the succah – even if it is only four handbreadths wide (about a foot) – but the rest of the schach is still valid. However, if boards that are four cubits or wider are resting on the walls, this is considered unfit schach and it invalidates the entire succah. On the other hand, if it is only the case on one side that the wall formed a little bit of a ceiling, it does not invalidate the succah. This is because it is only on one side and there are still three other walls on which the schach is properly resting. A succah made from three walls is valid so long as it meets the minimum dimensions of a succah, i.e., seven handbreadths by seven handbreadths. One may not sit under the ceiling that is formed by the board.
134:7 A succah built under the branches of a tree is invalid. (Here we are speaking of a tree whose branches are literally on top of the succah, as schach – Bi’ur Halacha 626:1 s.v. tachas.) Even if the branches allow more light than shade and one put additional schach on it to complete the succah, it is nevertheless invalid. If one built the succah this way and later cut the branches off the tree, the succah remains invalid. This is because, regarding Succos, the Torah says “make for yourself,” in the active, not in the passive. Therefore, after cutting the branches, one must lift each one up from the schach and then replace them for the specific purpose of building the succah. It is similarly prohibited to put on the schach before one has set up the walls because it is the act of putting on the schach that validates a succah.