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The Shulchan Aruch writes (472:2) that before the Seder one should prepare his seat for "Heseiba," leaning in a regal manner, which is required at the Seder. The Torah tells that when Benei Yisrael left Egypt, God led them in a circuitous path through the wilderness (Shemot 13:18), and, as the Midrash notes, the Torah uses in this context the word "Vayasev," which resembles the word "Heseiba." The Midrash infers from this term that when God led Benei Yisrael from Egypt, He carried them as they reclined comfortably in their beds. We commemorate this "reclining" by leaning as we eat and drink at the Seder.
Later (472:3), the Shulchan Aruch rules that when leaning at the Seder, one leans specifically on his left side, rather than his right. One reason given for this Halacha is that most people eat with their right hand, and thus leaning on one's right side will cause considerable discomfort during eating. Others explain that leaning on one's right side while eating poses the risk of choking, God forbid, and this is generally considered the primary reason for leaning on one's right side. Hence, even those who are left-handed, and thus eat with their left hand, must lean on their left side, despite the difficulty this might entail during eating.
In the next Halacha, the Shulchan Aruch rules that women are not required to perform "Heseiba" at the Seder, with the exception of an "Isha Chashuva," a "distinguished woman," who is required to lean. Several different views exist in explaining this term. One view, cited in the name of Rabbenu Mano'ach, claims that this refers to a single woman, who is independent and not bound to a husband, and is therefore required to lean. Others claim that an "Isha Chashuva" is the daughter of a prominent and distinguished figure, while still others understand this term as referring to a woman who has servants and attendants serving her.
The Rama (Rabbi Moshe Isserles, Poland, 1525-1572), in his glosses to the Shulchan Aruch, famously writes that nowadays, all women are under the category of "Isha Chashuva" and are therefore, strictly speaking, required to lean at the Seder. Nevertheless, he adds, the common practice is for women not to lean, as they rely on the position of the Ra'aveya (Rabbi Eliezer Halevi, Germany, 1140-1225), who held that the "Heseiba" requirement does not apply at all nowadays, since today even people of royal stature don't recline as they eat. Given the uncertainty surrounding the inclusion of women in the "Heseiba" obligation, coupled with the position of the Ra'aveya that nowadays this obligation does not apply even to men, Ashkenazic women have the practice not to lean at the Seder.
Sephardic women, however, should be instructed to perform "Heseiba" at the Seder. Nevertheless, if a woman did not lean while drinking one of the cups of wine, for example, she is not required to drink the cup again.
Summary: One is required to lean on his left side while eating and drinking at the Seder. Ashkenazic women have the practice not to lean, whereas Sephardic women should preferably lean while eating and drinking at the Seder.
[Chazon Oavdaia, page 6.]