Yosef Karo

“ Concerning a sukkah made underneath a tree - there are those who say that if the tree's shade is greater than the sunlit area, the sukkah is always 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 the tree, it is valid even if the branches were not lowered to mix with the schach of the sukkah. ”