Gemara

(Beraisa - R. Meir): If the lock on a door is above 10, one puts the key in the lock before Shabbos. On Shabbos, he opens or locks and returns it to its place [over the lock];

Chachamim say, one puts it on the threshold before Shabbos. On Shabbos, he opens or locks and returns it to its place;

(Abaye): The lock is less than four by four, but there is room in the door to carve out and complete the Shi'ur. R. Meir says Chokekim Lehashlim (it is Reshus ha'Yachid, as if it was carved out), and Chachamim do not (it is Makom Patur).

33a (Beraisa - Rebbi): If an Eruv was in a tree [above three Tefachim and] below 10, it is valid, but one may not take it;

Chachamim say, if one may not take it, it is invalid.

(Ravina): The tree is less than four by four wide, and the basket completes the Shi'ur of four. Rebbi holds like R. Meir, who says Chokekim Lehashlim.

Rebbi also holds like R. Yehudah who requires the Eruv to be on a place that is four by four.

46a (R. Yehoshua ben Levi): The Halachah follows R. Yochanan ben Nuri. (One who was asleep at the start of Shabbos gets 2000 Amos in every direction.)

R. Yehoshua ben Levi also taught that the Halachah follows the lenient opinion in Eruvin.

(R. Zeira): Had he taught only that the Halachah follows R. Yochanan ben Nuri, one might have thought that this is whether this is a leniency or stringency. Therefore, he taught that the Halachah follows the lenient opinion in Eruvin.

He also needed to teach that the Halachah follows R. Yochanan ben Nuri. One might have thought that we do not follow an individual to be lenient against a Rabim.

Question (Rava): Eruvin is mid'Rabanan. Why would we distinguish whether an individual argues with an individual, or with a Rabim?

Avodah Zarah 7a (Beraisa): If two Chachamim give different rulings, if one is greater than the other in Chachmah and number (of Talmidim), we follow his ruling.

R. Yehoshua ben Korchah says, if neither is greater, for a Torah law, we follow the stringent ruling. For a mid'Rabanan law, we follow the lenient ruling.

(Rav Yosef): The Halachah follows R. Yehoshua ben Korchah.

Rishonim

Rosh (5:3): Maharam says that the Halachah follows R. Meir, since R. Yehoshua ben Levi said that the Halachah follows the lenient opinion in Eruvin, even when an individual argues with a Rabim.

Tosfos (46a DH d'Amar): Shmuel taught that that the Halachah follows the lenient opinion in Avelus, even when an individual argues with a Rabim. The Klal is even for the first day of Avelus, which is mid'Oraisa, just like regarding Eruvin. It seems that we rule like the lenient opinion in Eruvin even if it is mid'Oraisa. The Gemara said 'Eruvin is mid'Rabanan. Why does it matter if an individual argues with a Rabim?' This implies that if it were mid'Oraisa, [we would still be lenient, just] it would be a Chidush.

Ramban (46a DH v'Nir'eh): It seems that R. Yakov bar Idi holds that the Halachah follows the lenient opinion in Eruvin, even when an individual argues with a Rabim. This is why R. Yehoshua ben Levi rules like R. Yochanan ben Nuri against Chachamim. Rava thought that this is obvious! Do not say that in the conclusion, R. Yehoshua ben Levi ruled like R. Yochanan ben Nuri because his reasoning was proper, but there is no Klal to be lenient against a Rabim. If so, why did we ask why two teachings are needed, and what was the answer?!

Ramban: R. Shimon allows 15 Amos past the Techum, and R. Eliezer holds that overlap of Techumim is significant (52b). R. Meir gives a Karfef even to one city (57a). R. Yosi holds that any remnant of an Eruv suffices (80b). R. Shimon does not require an Eruv for a joint house, and latter Rabanan hold that people forbidden in their place do not forbid elsewhere (71a). Why does the Rif rule unlike all of these lenient opinions? Not all agree with R. Yehoshua ben Levi. In several places, Rav explicitly rules like an individual. Here, the Gemara asked why Rav did not rule like R. Yochanan's laws [of which Tana we follow against which]. If the Halachah follows the lenient opinion, this is no question!

Note: Some say that "the Halachah follows the lenient opinion in Eruvin" does not override other Klalim. Based on this, also the coming question about R. Yehudah is not difficult. However, if so, surely we do not rule like an individual against a Rabim!

Ramban: Shmuel argues, and does not rule like all of R. Gamliel's leniencies. He rules like R. Yehudah in all of Eruvin (81b), and that people forbidden in their place forbid elsewhere. R. Yochanan says that we follow a lenient individual against a stringent Rabim only in Avelus. He says that the Halachah follows R. Eliezer ben Yakov, but we do not say so to people who ask (62b), and rules unlike R. Shimon (91a). This is why the Rif and Ge'onim do not rule like an individual against a Rabim in Eruvin. Even though we do not follow a Talmid (R. Yochanan) against his Rebbi (R. Yehoshua ben Levi), also Rav and Shmuel argue with the Klal. Later Amora'im ruled about every argument of Tana'im. They did not rely on R. Yehoshua ben Levi. Why did the Ge'onim rely on it only regarding R. Yochanan ben Nuri? The Yerushalmi says that all Amora'im are lenient even like an individual against a Rabim for Eruvin, but not for Mechitzos. The Bavli disagrees.

Magid Mishneh (Hilchos Eruvin 6:17): R. Yehudah and Chachamim argue about an Eruv in a cemetery. The Rambam rules like Chachamim. The Rashba challenged this, for the Halachah follows the lenient opinion in Eruvin, even an individual against a Rabim! The Ramban says that the Ge'onim do not rule against a Rabim.

Rashba (46a DH Iy (2)): R. Yehoshua ben Levi taught that the Halachah follows the lenient opinion in Eruvin even when an individual argues with a Rabim, i.e. always, and not only regarding R. Yochanan ben Nuri. Why didn't he explicitly say that the Halachah follows the lenient opinion in Eruvin, even against a Rabim? I answer that if someone will say that the Halachah follows Rabanan, we should not say that he agrees with R. Yehoshua ben Levi's Klal, for perhaps it was said only in certain cases [and this is an exception], just like we say that R. Yochanan's Kelalim [of which Tana'im we follow when they argue] was not said in all cases.

Tashbatz (2:38): The Halachah follows the lenient opinion in Eruvin, even an individual against a Rabim. The Poskim rely on this in many places to be lenient. Nowadays there is nothing to rule about, for the Rishonim and Acharonim already fixed (ruled about) everything. Surely we are lenient about a Safek, like all mid'Rabanan matters, and all the more so for Eruvin, in which we are lenient even against a Rabim.

Ha'ara'os on Shiyurei Berachah (358:3, 1): Tashbatz says that the Klal must teach about an individual against a Rabim, for normally we are lenient about a Safek mid'Rabanan.

Poskim

Rema (OC 405:7): Even if a boat does not have Mechitzos 10 Tefachim and four wide, but there is room to carve out to 10, we say Chokekim Lehashlim.

Magen Avraham (11, according to Machatzis ha'Shekel): This is difficult. It seems that the Rema refers to a small boat next to a big boat (a Reshus ha'Yachid. The small boat becomes Reshus ha'Yachid due to Chokekim.) However, the Halachah does not follow R. Meir (345:10, 362:12)! Perhaps the walls are not 10, and the thickness of the boards (of the bottom of the boat) joins [to complete the Shi'ur of 10].

Eliyahu Rabah (405:10): Only here the Halachah follows R. Meir, who says Chokekim, for we follow the lenient opinion in Eruvin.

Gra (405:15): The Halachah does not follow R. Meir, who says Chokekim, i.e. for Torah laws. For Rabanan laws we hold like him, like Rebbi. The sea is a Karmelis. Why does the Rema say Chokekim here? The law is true [for a different reason], for here there is Gidud (the wall of a ditch joins to a wall, to complete the Shi'ur of 10 Tefachim). Perhaps he holds that Gidud helps due to Chokekim. This is wrong, for Gidud helps even for Torah laws.

Birkas Eliyahu (on Gra, Ha'arah 3): The Gra said that we follow R. Meir for mid'Rabanan laws. He did not say that we follow the lenient opinion in Eruvin, for is not clear whether we are lenient in Eruvin against a majority. Most Rishonim, including the Rashba, Ritva and Me'iri, say so. The Ramban, citing Ge'onim, holds like the Rabim, and it seems that also the Magid Mishneh does. Alternatively, the Gra was concerned for those who do not apply the Klal to Mechitzos.

Mishnah Berurah (35): Even though we do not say Chokekim, here we do, due to Gidud.

Chazon Ish (Eruvin Likutim 112:10): We follow a greater Chacham against a smaller Chacham even for mid'Rabanan laws (Avodah Zarah 7a). For equal Chachamim, we are lenient for mid'Rabanan laws. Perhaps we need to learn [about Eruvin] only for a greater Chacham against a smaller Chacham, and the same applies to a Rabim against an individual. Normally, for mid'Rabanan laws we follow the Rabim, even to be stringent. This was a special rule for Eruvin, with conditions. The Klal does not apply to Poskim. The Beis Yosef decided [even laws of Eruvin] based on the majority of Poskim.