Pesak (Ri): The Halachah follows Rav Huna, that once Shabbos was permitted, it is permitted, for a Beraisa (below, 70b) teaches that whatever was permitted for part of Shabbos [is permitted for all of Shabbos].

Suggestion: R. Yitzchak can establish the Beraisa like R. Yehudah (and R. Yitzchak himself holds like R. Yosi, like our Gemara initially suggested)!

Rejection: He establishes himself even like R. Yehudah in our Sugya.

Note: The Gemara connotes that it said on behalf of Rav Huna and R. Yitzchak "he can say..."! And even if R. Yitzchak himself said so, and he is refuted about this, he can still hold like R. Yosi! Sefas Emes - Tosfos holds that the questions whether we say "once Shabbos was permitted..." when we lose residents, or when Mechitzos fall, do not depend on each other. There is no source to say that Tana'im argue about this.)

Support #1: Also Abaye holds like [Rav Huna] below (93b).

Distinction: When there are no walls, it is forbidden, like we conclude here "I said even like R. Yosi. We find that R. Yosi said that [the Heter ceases] only because there are no Mechitzos."

Support: Also Rav rules like R. Yosi (below, 93b), and also Shmuel does, when it is breached to Reshus ha'Rabim.

Implied question: Rav rules like R. Yosi even when there are Mechitzos, like is proven [there] regarding two Chatzeros, and the wall between them fell!

There, the Mechitzos are properly intact, for there are still the outer Mechitzos, through which the Chatzer became Reshus ha'Yachid;

Support: This is why we bring the case of a big Chatzer that was breached [to a narrow Chatzer] regarding R. Hoshaya's question (93b, of dwellers who came on Shabbos).

Answer: In any case (even though Rav argues), it seems that regarding this the Halachah follows Rav Huna, like I explained.

Pesak (Ri): If they were Me'arev for the sake of both of them from one house to another, and the opening became sealed on Shabbos, it is permitted, like Rav Huna;

Even if it became sealed in the middle of the week, and after it was opened on Shabbos, it is permitted, for the Eruv returns to its place (validity).

Proof #1: It says in Shabbos (101b) that boats tied to each other may be Me'arev and carry from one to another. If they became untied, they are forbidden. If they became tied again, they return to their initial Heter.

Proof #2: At the conclusion of our Sugya, R. Yitzchak establishes himself [even] like R. Yehudah, and permits even if the Korah was removed from a Mavuy. All the more so he permits when they were Me'arev via the opening! (Maharsha - initially, the Gemara was unsure which of Rav Huna and R. Yitzchak permits, and who forbids. It resolved this from Rav Huna's Heter when they were Me'arev through an opening, and it was sealed. Now that Tosfos proves that also R. Yitzchak permits, this refutes the resolution! However, according to the Ritzva below, the resolution remains.)

Source: Below (70b), it says "whatever was permitted for part of Shabbos [is permitted for all of Shabbos]", to include if they were Me'arev via the opening. "This is the general rule" includes if the Korah was removed from a Mavuy;

Inference: Had it not taught "this is the general rule", we would not permit when the Korah was removed from a Mavuy, even though we would permit if they were Me'arev via the opening, and it was sealed.

Support #2 (for Pesak (a) - Ritzva): Also from there we can prove that the Halachah follows Rav Huna [when residents were diminished], for that Sugya is like Rav Huna, who is adamant about Mechitzah more [than about residents], like it says here "we find that R. Yosi said [that the Heter ceases only because there are no Mechitzos]";

Therefore, if not for "this is the general rule", we would not permit if the Korah was removed from a Mavuy, even though we would permit if they were Me'arev via the opening, and it was sealed.

[This is unlike] R. Yitzchak, who is adamant about residents more [than about Mechitzos].

Correction: In Rashi's Perush in his own handwriting, the text says Koraso Oh Lechiyo (singular). He is correct.

Implied question: We discuss according to R. Yehudah, and we find that he holds that a Mavuy is permitted through two Koros or two Lechayayim, e.g. when it is Mefulash!

Answer: Even so, why should [the Mishnah] mention Korosav (plural), since [removal of] even one Korah or Lechi forbids the Mavuy?!

Observation: Also according to this answer, we discuss prickly shrubs and bushes. Yehoshua stipulated only about attached prickly shrubs and bushes, like it says explicitly in Bava Kama (81a).

Remark: Nowadays our custom is not to wash Mayim Acharonim, became Sodom salt is not found among us;

Alternatively, it is because we do not normally dip our fingers in salt after eating.

Explanation #1 (Rashi): This refers to Yisrael guests.

Explanation #2: The Yerushalmi says that [Chachamim] argue about this. Some establish it to discuss Nochrim;

Even so, it needed to teach that we may feed them Demai (Safek Tevel, even though Nochrim may eat even Tevel Vadai), because one may not benefit from Tevel. [Chachamim] were lenient about Demai.

Implied question: We could ask here "does he come to teach Beis Shamai's opinion?!"

Answer: He teaches that if you find a Tana who says that one may feed, do not be concerned for him, for he holds like Beis Shamai.

Support: We say like this in Yevamos (122a).

Question: Indeed, he should not be lashed, for it is a Lav without an action!

Answer #1: [Rav Acha] asks according to the opinion that one is lashed for a Lav without an action.

Answer #2: Bending the lips is an action.

Note: In Kerisus 3b, Reish Lakish says that the Tana taught Ov, but not Yid'oni, because he holds that one is lashed only for a Lav with at least a small action. A Ba'al Ov knocks his arms. Why did Tosfos answer differently? Perhaps he answers also for Yid'oni, for Rav Acha asked also about it, and Reish Lakish's answer does not apply to it. Rav Acha argues with Reish Lakish, and holds that even bending the lips is an action. Alternatively, Tosfos holds that Al Tifnu forbids asking the witch, like the Havah Amina of Tosfos Sanhedrin 65a DH veha'Nish'al.

Explanation #1 (Rashi): [We read it] like "Al Yotzi." We learn from it Hotza'ah from Reshus to Reshus. Rav Ashi answered that it is written "Al Yetzei." This is not an expression of taking out loads.

Question #1: What need was there to mention that the Lav is a warning for [an Aveirah of] Misas Beis Din, since the Makshan asked because he wanted to say that the verse discusses Hotza'ah, and not Techumim?

Question #2: What was R. Yonason's question? R. Akiva holds that Techumim is mid'Oraisa, and he learns (below, 51a) from "Al Yetzei";

Suggestion: R. Yonason comes to say that presumably, [the Halachah follows] the one who says [that Techumim is] mid'Rabanan.

Rejection: Rav Ashi would not argue with this, for everywhere it is obvious to the Gemara that Techumim is mid'Rabanan;

Source #1: It says below (37b) that Rava said to Rav Nachman "who is the Tana who holds that Ein Bereirah even for mid'Rabanan laws?"

Source #2: Below (46a), Rava said to Abaye Eruvei Techumim is mid'Rabanan [therefore, the Halachah follows the lenient opinion]. What is the difference whether an individual argues with a Rabim...?

Question #3: It connotes everywhere that Hotza'ah is written regarding Shabbos, for in Pesachim (85b) we say that one who is Motzi meat of Pesach from one group (eating it together) to another group is not liable until he puts it down, for Hotza'ah is written [regarding Besar Pesach] like regarding Shabbos;

The only place where an expression of Hotza'ah is written regarding Shabbos is this verse "Al Yetzei"!

In Horiyos (4a), in some Seforim the text explicitly says 'Hotza'ah is written - "Al Yetzei Ish mi'Mekomo"!'

Explanation #2: Both R. Yonason and Rav Ashi learn Hotza'ah from "Al Yetzei", like it connotes elsewhere. The simple meaning of the verse connotes like this, that one may not go out on Shabbos with his Kelim to collect the manna, like they do during the week;

R. Yonason holds that even according to the opinion that Techumim is mid'Oraisa, one is not lashed [for it], since from this verse we learn also the Isur of Hotza'ah, which has Misas Beis Din;

Rav Ashi answered "is it written 'Al Yotzi'", that the verse primarily discusses Hotza'ah? Then, one would not be lashed for it, even though it comes also to teach about Techumim;

It is written "Al Yetzei." Since primarily it is an expression of leaving, one is lashed for it, even though it comes also for the Isur of Hotza'ah.

Implied question: In Shabbos (96b) we learn Hotza'ah from "va'Yikalei ha'Am me'Havi"!

Answer: We need two verses. One teaches about Hotza'ah of an Oni (standing outside the house, with a basket to receive Peros), and one teaches about Hotza'ah of the Ba'al ha'Bayis. Because Hotza'ah is an inferior Melachah, two verses are needed, like I explained in Shabbos (2a).

Inference: It connotes here that if the verse primarily discussed Hotza'ah just like Techumim, according to everyone one would not be lashed, even though there is no Misah for Techumim.

Implied question: In Bava Kama (74b), regarding witnesses who were contradicted in a capital case, and later they were Huzmu (other witnesses testified that they were not present to see the testimony at the time and place they testified about), it connotes that they are lashed according to the opinion that they are not killed, because it is not considered a Lav that warns for [an Aveirah of] Misas Beis Din!

Answer: There it is explained. (Tosfos DH Havah says that the Torah revealed that one is lashed for "Lo Sa'aneh", even though it is a warning for Misas Beis Din.)

Implied question: It says above (15b) that Hash-m taught Moshe "the majority should not be open!" (How can Pasei Bira'os permit carrying in Reshus ha'Rabim? The majority is open!)

Answer: That is when there are not four Mechitzos, like there are here, and on each side there is an Amah on each end. [The area in between] is considered a Pesach.

Implied question: We should say that the air on each side [of the corner-posts] is Mevatel it!

Answer: For Olei Regalim (people coming to Yerushalayim for the festival, Chachamim) established Torah law [and did not decree that air is Mevatel].

Comment (Tosfos Yeshanim): Perhaps only regarding a plank an Amah wide, we do not say mid'Oraisa that the air is Mevatel it;

Source: Regarding pillars of a Chatzer, [Tosfos] explained above (2b DH Bein) that air is Mevatel them mid'Oraisa.

Observation (Tosfos Yeshanim): The argument here was not sufficient. We needed [also] the argument above that simple planks (i.e. not in the corner) help according to R. Meir, and we do not say that the air comes and is Mevatel them.