But the sefer, Harirai Kedem, points out that according to the explanation mentioned above that the shaking of the sechach that was originally attached to a tree must be done lishmah (according to the Rambam and the Rif), then according to Rabbeinu Tam’s view women would not be allowed to shake the sechach lishmah. Since this act of shaking is an act that is essential to the lishmah of the sukkah, women who are exempt from the mitzvah may not perform it. The Gemara that says that a sukkah erected by a woman is fit for use is referring to a sukkah that initially was made for the purpose of providing shade and therefore does not require lishmah. Hence, even though it was built by a woman, it is fit for use.
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