Explanation #1 (Rashi 34b): It is a three-way argument.

Rebuttal: Rashi was not precise. Our Mishnah discusses Yom Tov, and they (R. Eliezer and Chachamim) argue about whether or not one may destroy [the tower]. The Beraisa discusses when it was found on Shabbos, and they argue about R. Shimon's law (whether roofs, Chatzeros and Karfifos are like one Reshus for Kelim that were Shoves in them).

Implied question: A Tosefta (2:15) says that Chachamim agree to R. Eliezer about people of the Chatzer or balcony who collected their Eruv and put it in a house - even if they know that the key is not in its place, the Eruv is valid!

Answer: That is because [Chachamim] were lenient about Eruvei Chatzeros.

Observation: However, it seems that [the Tosefta] discusses when it was found on Shabbos, since it says "and Chachamim agree to R. Eliezer", and on Yom Tov, when the key is not found, just the contrary, Chachamim are more lenient! It should have said oppositely, "R. Eliezer agrees to Chachamim"!

Explanation: [The Eruv is valid] when it was found on Shabbos, even if it was lost Bein ha'Shemashos.

Implied question: Why couldn't [Abaye] infer from this Seifa itself?

Answer: We could say that they argue about [when it moves] due to vibrations. There is a distinction between an Ohel and a Kli. However, regarding Heset (if the Zav moved it), also an Ohel becomes Tamei.

Therefore, [Abaye] brings the Beraisa that also regarding vibrations, there is no distinction between an Ohel and a Kli;

The Beraisa itself would not suffice, for one might have thought that it is not like R. Nechemyah, and not like R. Shimon. Therefore, [Abaye] brought the Seifa of their words.

Implied question: Why don't we establish that they argue like the argument about whether Binyan does not apply to Kelim?

Answer: Beis Shamai and Beis Hillel argue about this in Beitzah (22a).

Note: Tosfos does not mean that we do not want to establish either Tana like Beis Shamai. R. Eliezer was from Beis Shamai, and he forbids, like they do! Rather, the Mishnah would not teach the same argument twice in different ways!

Explanation #1 (Rashi): If [he could break it] by hand, even R. Eliezer would permit, for this is Mekalkel (destructive);

Source (Beitzah 31b - Beraisa): Seals on Kelim - he unties, untwines [the rope] or cuts.

Implied question: Here it is an Ohel, and it says there that it is forbidden [to break seals] on land!

Answer: That is a decree mid'Rabanan, for it looks like he destroys. He does not destroy a proper Binyan, for he merely opens a door. Since it is Shevus, he does not decree Bein ha'Shemashos.

Rebuttal: Even if R. Eliezer holds like R. Nechemyah, one may move a knife. It is forbidden only mid'Rabanan! (Rashi said that R. Eliezer permits Shevus Bein ha'Shemashos.)

Explanation #2: Here it is a Kli. If he could break it by hand, it would be permitted. With a knife is forbidden, like R. Nechemyah. He does not hold like Rebbi.

Inference (Ri): Seals on Kelim, one may untie, unravel or cut - this refers only to something like a knot of ropes, but one may not break a lock of wood or metal, for Binyan and Stirah apply also to a Kli, like I explained above (34b DH v'Amai).

Explanation: This is even if Techumim are mid'Rabanan, and even according to Rebbi, who holds that everything [forbidden due to] Shevus, [Chachamim] did not decree about it Bein ha'Shemashos...

Even so, it is not an Eruv, even though Bein ha'Shemashos he could take it and bring it...

Since if he acquired Shevisah in the place to where the Eruv rolled, he would be outside the Techum, and he would have only four Amos, therefore Rabanan enacted that it is an Eruv only when it is inside the Techum.

Explanation #1: It mentioned this Sefek-Sefeka due to a Chidush in the Seifa. Even though (there are two possible reasons why he did not have a Kosher Tevilah), regarding a light Tum'ah, he is Tahor.

Explanation #2 (Ritzva): The Mishnah teaches separate cases - "even if he immersed" means "or if he immersed";

Source: We ask afterwards "just the contrary - establish the Mikveh on its Chazakah, and say that it was not deficient!" One cannot ask this if it is a Safek whether or not he immersed!

Rather, the Mishnah teaches separate cases, and we ask about the Safek of whether he immersed in 40 Sa'im, or he did not immerse [in 40 Sa'im].

Explanation: R. Meir discusses in Reshus ha'Rabim, like the Tosefta in Taharos (6:8). It says that R. Meir is Metaher, for Safek Tum'ah in Reshus ha'Rabim is Tahor.

Note: The Tosefta discusses one who touched someone at night. This is why the Dibur ha'Maschil must be changed, for "Sefeko Tahor" refers to the case of Safek Tevilah.

Question #1 - Citation (Nidah 2a - Mishnah - Shamai): All women are Dayan Shaitan (when they see menstrual blood, they are not Tamei retroactively);

Even Hillel and Chachamim are Metamei [retroactively] me'Es la'Es (to 24 hours ago) or to the last time she checked herself, i.e. only for Terumah and Kodshim, or according to one version there, only for Kodshim, but all agree that it is Tahor for Chulin!

Why don't we say that all Tum'os are like at the time they are found, like here? We should not establish a woman on her Chazakah [that she was Tehorah until now]!

Question #2: There, we are Metaher her even in Reshus ha'Yachid, like is proven there in the first Sugya. Here we are Metamei even in Reshus ha'Rabim, like is proven in the Tosefta I brought (in the previous Tosfos)!

Suggestion: Here we do not establish [the man who died] on his Chazakah [that he was alive when Ploni touched him] because he was not checked the day before (i.e. shortly before he was touched) if he is alive, like the Seifa teaches "and Chachamim agree to R. Meir if they saw him alive the night before..."

Rejection: Also a woman, since it is common for her to see blood, it is as if she was not checked, like we say in Nidah (4a)!

Answer (Ri): "All Tum'os are like at the time they are found" is only for Terumah and Kodshim, just like me'Es la'Es of Nidah.

Implied question: According to this, we must resolve the Sugya in Nidah. And there, I explained 92a DH me'Es) that also Shamai holds that all Tum'os are like at the time they are found. Why is he Metaher me'Es la'Es even for Kodshim?

Answer #1: He considers a woman as if she were checked. (Had the blood left her Makor earlier, it would have left her body earlier.)

Answer #2: It is due to [concern for] Bitul of Peru u'Rvu, like it says there. (If we will be Metamei her retroactively, her husband will think that he was Bo'el Nidah, and in the future he will refrain from relations.)

Question: According to R. Meir, who is Metaher [here] in Reshus ha'Rabim, why is me'Es la'Es different? He is Metamei even in Reshus ha'Rabim, like it says in the Yerushalmi!

Answer: A woman has a Re'usa from her body (she is prone to see blood, so her Chazakah is weak), so Chachamim were more stringent.

Question #1: What was the question from R. Meir [in that Mishnah] to R. Meir in our Mishnah? He does not establish Terumah in its Chazakah (Tahor), not because it is Tamei now, rather, because there is another Chazakah against it. We leave a person in his Chazakah that he was not Me'arev!

Question #2: Also below (36a, Rava) says that R. Yosi's reason is because he establishes a Tamei [person] in its Chazakah, and I say that he did not immerse. Also in our Mishnah, we should establish a person in the Chazakah of the Techum of his house, and say that he was not Me'arev!

Answer #1 (to both questions): If we would say that the Gemara does not consider "Chazakah that he was not Me'arev" be a Chazakah, this would be fine.

Disclaimer: Rashi below (36a) explained [unlike this. He says that R. Yosi says] "establish a Tamei [person] in its Chazakah", for there is a Chazakah to be stringent, but there is not [a Chazakah there] to be lenient;

However, in our Mishnah, there is a Chazakah to be lenient - establish Terumah in its Chazakah, and there is also a Chazakah to be stringent, establish a person in the Chazakah of the Techum of his house, and say that he was not Me'arev. For mid'Rabanan laws, we are lenient.

Answer #2: [The Tartzan] wants to answer even if R. Meir holds that that Eruvei Techumim are mid'Rabanan. Now, he cannot answer that [he is stringent] in our Mishnah because the Chazakah is to be stringent, since there is also a Chazakah to be lenient. He can say that Eruv is a Safek mid'Rabanan, and we are lenient;

Therefore, he established our Mishnah to discuss two sets of witnesses. It is not appropriate to say so (he follows Chazakah), since there is a set that removes it from the Chazakah;

Rabah and Rav Yosef come to explain R. Yirmeyah's words.

Implied question: we could have asked "in such a case, would R. Meir and R. Yehudah say that this is Chamar Gamal?!"

Answer: [The Makshan] asked a better question.