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1. The judges of the Sanhedrin sat in a semi-circle so that they could all see each other.
2. A Yisrael who refused to be circumcised, a Kusi, and a Yisrael Mumar are eligible to perform Shechitah.
3. Acknowledging an Avodah Zarah is tantamount to denying the entire Torah.
4. The Korban of a Mumar is accepted, with the exception of a Mumar for Chilul Shabbos or for Avodah Zarah.
5. The Korban of a Nochri is accepted.
6. If a person is a Mumar for the prohibition of blood, and he ate Chelev b'Shogeg, or vice versa, there is a disagreement about whether his Korban Chatas is accepted.
7. Bar Kapara maintains that Raban Gamliel and his Beis Din enacted a decree that the Shechitah of a Kusi is forbidden.
A BIT MORE
1. It was necessary for the judges of the Sanhedrin to interact with each other during their debate of the Halachah. If they sat in straight rows, a judge on one end could not see a judge on the other end.
2. According to Rava, even a Mumar to eat Neveilos is eligible to do Shechitah if he is given a checked knife prior to Shechitah.
3. The Torah refers to the Aveirah of Avodah Zarah as "all of the Mitzvos."
4. A Korban is accepted from a Mumar in order that he will repent, but if he is a Mumar for the entire Torah his Korban is not accepted. The Korban of a Mumar for Shabbos or for Avodah Zarah is also not accepted.
5. Even if the Nochri worships Avodah Zarah, his Korban is accepted.
6. According to the Tana Kama, even though he ate the Chelev b'Shogeg and he repented the Aveirah, since he is a Mumar for blood, his Korban Chatas in not accepted. Rebbi Shimon ben Yosi disagrees.
7. Even if a Yisrael was standing over him to ensure that he slaughtered properly, his Shechitah is forbidden.
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