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על כן לא יאכלו בני ישראל את גיד הנשה אשר על כף הירך (בראשית לב:לג)י

מסכת חולין פרק ז משנה א
גיד הנשה [The prohibition against eating the] sciatic nerve (literally: the sinew on the socket)
נוהג בארץ ובחוצה לארץ is practiced both in the land [of Israel] and outside the land [of Israel],
בפני הבית ושלא בפני הבית before the Temple (i.e. while the Temple stood) and not before the Temple,
בחלין ובמקדשין by the unconsecrated and consecrated.
נוהג בבהמה ובחיה It is practiced by domestic animals and wild animals,
בירך של ימין ובירך של שמאל in the right thigh and the left thigh.
ואינו נוהג בעוף But it is not practiced by a bird
מפני שאין לו כף as it does not have a spoon [shaped socket for its thigh joint].
ונוהג בשליל And it is practiced by a fetus (that was nine-moths old, and therefore viable, though found alive in its mother's womb after she had been slaughtered);
רבי יהודה אומר Rabbi Yehuda says
אינו נוהג בשליל it is not practiced by a fetus (as he accords a fetus found in its mother's womb, even if viable, to be merely another part of the mother);
וחלבו מותר

and its fat [of the sciatic nerve] is permissible .

ואין הטבחים נאמנין Butchers are not trusted
על גיד הנשה regarding the [proper removal of] sciatic nerve,
דברי רבי מאיר these are the words of Rabbi Meir (who held that the removal of the sciatic nerve was a more painstaking process than that was required by the Sages, and so he held that butchers could not be trusted to remove it properly),
וחכמים אומרים and the Sages say
נאמנין עליו ועל החלב they are trusted regarding it and regarding [the removal of the prohibited] fats.

פרק ז משנה ב

שולח אדם ירך לנכרי A person may send a thigh with a gentile
שגיד הנשה בתוכה that has the sciatic nerve within it
מפני שמקומו נכר because its place is discernable (and so we do not fear that someone, having seen a this meat originate from a Jew, would assume that the sciatic nerve had been removed).
הנוטל גיד הנשה One who removes the sciatic nerve
צריך שיטל את כולו is required to remove its entirety,

רבי יהודה אומר

Rabbi Yehuda says,
כדי לקים בו מצות נטילה

[it suffices if he removed] enough to fulfill the commandment of removal (he refers to the portion on the surface of the animals muscle).