Regarding Krisus 22 in the Machloikes Raish Lokesh and Reb Yochanan about "Dam B'Shtei Koisos" according to the Rebeinu Gershom [who explains that Resh Lakish requires a Chatas for drinking the second cup since it has mostly Dam Kilu'ach and only a little permitted, black, blood] it sounds like there was Rov DAM Kiluach in the second Kois. If so, what's the svara of the Shita that you on bring one Chatas ?? Shouldn't this be a regular sheila of Ta'aruvos of Iser and Heter.....perhaps Min B'mino...etc.?
The argument between Resh Lakish and Rebbi Yochanan, regarding whether one or two Chataos are brought for drinking the two cups that were received from one animal's blood letting, is recorded in the Gemara immediately after a major argument between the two as to which of an animal's bloodletting blood is prohibited. It would seem clear that the two arguments are related, and indeed according to Rashi they seem to be.
It is most probable that Rabbeinu Gershom also explained this argument to be a continuation of the argument between the two whether the red blood that drips after bloodletting is allowed to be eaten or not. If so, Resh Lakish holds that most of the second cup is prohibited since he prohibits the red drips and only permits black drips, making most of the second cup prohibited blood. Rebbi Yochanan, however, permits the red drips. Therefore in his view the second cup, which has half Dam Kilu'ach and the other half "dripped" blood (black and red), is not mostly prohibited and remains a Safek ha'Shakul (Min b'Mino Lach b'Lach, b'Rov). This is why he does not require a Chatas for the second cup.
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Be well, Mordecai