Tosefta for Chullin 1:3

הַשּׁוֹחֵט מִתּוֹךְ הַטַּבַּעַת וְשִׁיֵּר בָּהּ מְלֹא הַחוּט עַל פְּנֵי כֻלָּהּ, שְׁחִיטָתוֹ כְשֵׁרָה. רַבִּי יוֹסֵי בַּר יְהוּדָה אוֹמֵר, מְלֹא הַחוּט עַל פְּנֵי רֻבָּהּ:

Should a person have to cut through the great or top ring of the trachea or windpipe, that but the width of a thread of the whole circumference of the ring remained [on the upper part], the animal so killed is Cashér. R. José bar Jehudah saith, "It is Cashér when the greatest part of this breadth remained."

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