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FOOTNOTES:

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(1) See Insights for a summary of this Sugya.

(2) The people in the outer Chatzer cannot "cut themselves off" from the inner one, since the residents of the inner Chatzer are accustomed to trampling through the outer Chatzer; therefore the residents of both the inner and the outer Chatzer must join in the Eruv in order to permit carrying in the outer Chatzer. Since it is impossible for the person in the inner Chatzer who forgot to join the Eruv to be Mevatel his Reshus to the residents of the outer Chatzer (because of the rule that one may not be Mevatel his Reshus from one Chatzer to another), therefore carrying is prohibited in the outer Chatzer.

(3) This is because the residents of the outer Chatzer are present, by virtue of the Eruv, in the inner Chatzer, and the person in the inner Chatzer who forgot to join the Eruv cannot be Mevatel his Reshus to them, because one may not be Mevatel from one Chatzer to another. (Over here, the inner Chatzer does not have the right to "close the door" and separate themselves from the outer Chatzer, since the outer Chatzer was not at fault.)

(4) "Closing the door" to the outer Chatzer is not an option in this case, since the Eruv is in the outer Chatzer (and without it, carrying is forbidden).

(5) They may "close the door" to the outer Chatzer and consider themselves independent of it, since the people of the outer Chatzer were at fault in the prohibition of carrying in the inner Chatzer (by not having a proper Eruv amongst themselves). According to the Rabanan (75b), no Bitul is necessary in this case. However, according to Rebbi Akiva (ibid.) -- and according to Rava's interpretation of Shmuel, in our Sugya -- all the people in the outer Chatzer who joined the Eruv of the inner one must be Mevatel Reshus to the people of the inner Chatzer. Even though Shmuel does not normally allow Bitul Reshus from one Chatzer to the next, it is allowed in this case. (The reason for this appears to be that the people of the outer Chatzer are not really fully present in the inner Chatzer in any case; they are only considered to be residents there because they joined the Eruv of the inner Chatzer. To remove such a minimal presence, Bitul Reshus will suffice even from one Chatzer to the next -Rashi DH Penimis. This is why Bitul is not allowed in case 1:A.)