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1. The Gemara explains why we perform a Bris to a baby on Shabbos despite the fact that he might be a Nefel.
2. There is a dispute about whether Shechitah done to an animal that was carried for only eight months is effective.
3. If an animal was carried in utero until full term, slaughtering it after its birth permits it to be eaten.
4. There is a dispute about whether a baby who died within thirty days of birth from an external cause (i.e. a fall off a roof) is a Nefel.
5. The Gemara discusses what should be done in the previous case (#4) if the woman remarried after the baby died.
A BIT MORE
1. If he is not a Nefel, the Bris overrides Shabbos. If he is a Nefel, there is no prohibition of cutting, since the act is akin to cutting a corpse (in which case there is no Torah prohibition of the Melachah of Shechitah, since the body and flesh are already dead).
2. While the Shechitah certainly does not permit the animal to be eaten, since it is either like a dead animal or like a Tereifah, the argument is about whether slaughtering it takes it out of the category of Neveilah which causes Tum'ah. The Tana Kama says that Shechitah is not effective to remove its Tum'ah, while Rebbi Yosi b'Rebbi Yehudah and others say that Shechitah does remove its Tum'ah.
3. One must wait for the eighth day to slaughter an animal only if it was not carried to full term.
4. The Halachic significance of this dispute is that if the child was born from a widow whose late husband was childless, she does not have to perform Chalitzah with his brother in order to remarry if the child is not considered a Nefel. This baby is considered his child (and Yibum or Chalitzah is necessary only when the husband had no children).
5. All agree that if the second husband is a Yisrael, then as a stringency she should perform Chalitzah with the brother of her first husband. She then becomes permitted to marry her second husband. However, there is a dispute about whether Chalitzah must be done when the second husband is a Kohen who may not marry a Chalutzah.
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