Gemara

(Mishnah): If two of four brothers were married to sisters, and the two died, the sisters do Chalitzah, not Yibum.

R. Yochanan: I do not know who taught this Mishnah (it is not a valid Mishnah).

Suggestion: Perhaps they fell simultaneously, like R. Yosi ha'Galili, who says that this is possible!

Rejection: We do not have a Stam Mishnah like R. Yosi ha'Gelili.

Bechoros 17b (Mishnah - R. Yosi ha'Galili): If Reuven's sheep gave birth for the first time to twins, and their heads left the womb at the same time, both are (Kadosh and are) given to Kohanim - "ha'Zecharim la'Shem."

Chachamim say, Iy Efshar Letzamtzem.

(Gemara - d'Vei R. Yanai): R. Yosi ha'Galili holds that Efshar Letzamtzem b'Yedei Shomayim, all the more so b'Yedei Adam.

Question: Chachamim say Iy Efshar Letzamtzem in our Mishnah, which discusses b'Yedei Shomayim. What do they say about b'Yedei Adam?

Answer (R. Chiya bar Avin - Beraisa - R. Eliezer): If a murdered corpse was found equidistant from two cities, each of them brings an Eglah Arufah;

Chachamim say, one Eglah is brought on condition (that it is for the closer city).

Question: What is Chachamim's reason?

Answer #1: They hold that Efshar Letzamtzem, and expound "ha'Kerovah" - even ha'Kerovos.

Rejection: If so, two Eglos should be brought!

Answer #2: They hold that Efshar Letzamtzem, and expound "ha'Kerovah" - but not ha'Kerovos.

Rejection: If so, no Eglah should be brought!

Conclusion: They must hold that Iy Efshar Letzamtzem, even b'Yedei Adam.

Sukah 15a (Mishnah): If one roofed his Sukah with spits (Pasul Sechach), it is Kosher only if the spaces between them are as wide as them (and are covered with Kosher Sechach).

Suggestion: This refutes Rav Huna brei d'Rav Yehoshua!

(Rav Papa): Parutz k'Omed (the sum width of the gaps in a wall equals the sum width of what stands) permits;

(Rav Huna brei d'Rav Yehoshua): It does not permit.

Rejection: The case is, there is room between spits to insert and remove spits with leeway (i.e., the spaces are slightly bigger).

Objection: It is possible to be exact (and make the spaces equal the spits. Surely they are equal, like the Mishnah says!)

Answer #1 (R. Ami): He (intentionally) left room between spits to insert and remove spits with leeway.

Answer #2 (Rava): The Kosher Sechach is placed perpendicular to (and on top of) the Pasul Sechach (it must overlap it in order to stay up, so it is the majority).

Rishonim

Rambam (Hilchos Sukah 5:16): If exactly half the Sechach is Pasul the Sukah is Pasul, because the Pasul Sechach is like Parutz.

Rebuttal (Ra'avad): The Gemara disqualifies because Iy Efshar Letzamtzem.

Question: The Rambam is like Rav Huna brei d'Rav Yehoshua. The Halachah was fixed like Rav Papa (Eruvin 15b), who permits Parutz k'Omed! The Rambam himself rules like Rav Papa in Shabbos (16:16)!

Answer #1 (Magid Mishneh): The Gemara (22b) says that if there are equal amounts of Sechach and air above, there is more sun below, and it is Pasul. It is as if the Pasul Sechach is not there, therefore we need a majority of Kosher Sechach. The Gemara could have said that even Rav Papa must agree.

Answer #2 (Kesef Mishneh): The Rambam's text of the Gemara was like Tosfos'. The question 'it is impossible (to totally fill the spaces)' was even against Rav Papa. R. Ami answered also for Rav Papa that he puts a majority of Sechach.

Rosh (Sukah 1:29): Rashi's text says that the spaces are bigger. It asks 'Efshar Letzamtzem' (we could make the spaces equal)! The Rif had this text, so he did not need to explain the Mishnah. (The spaces are as wide as the spits, like the simple reading.) This text is difficult, for the Gemara asked (Efshar Letzamtzem) unlike the Halachah! R. Tam's text is better. The Gemara asks against everyone 'Iy Efshar Letzamtzem'; it is not normal to totally fill the spaces. We answer that he puts a majority of Kosher Sechach.

Rambam (Hilchos Rotze'ach 9:8): If a corpse was found equidistant from two cities, they bring one Eglah Arufah together and stipulate that it is for whichever city is really closer. One must be closer, for Iy Efshar Letzamtzem, even b'Yedei Adam.

Rosh (Bechoros 2:4): The Ri rules like R. Yosi ha'Gelili, who says that Efshar Letzamtzem. This is because Amora'im argue about Parutz k'Omed, and Shechitah of half the Siman. If Iy Efshar Letzamtzem, perhaps it is the minority (how can one opinion be lenient? Shechitah is a Safek mid'Oraisa!) However, R. Yochanan showed that the Mishnah in Shevu'os (32a) need not be like R. Yosi; in Yevamos, he could not explain a Stam Mishnah because he refused to establish it like R. Yosi! Regarding a Get, the Gemara (Gitin 78a) says that Iy Efshar Letzamtzem (that two people came exactly at the same time). It seems that the Halachah follows R. Yosi b'Yedei Adam, but not b'Yedei Shomayim.

Hagahos Ashri (Eruvin 1:21): The Or Zaru'a rules that Efshar Letzamtzem even b'Yedei Shomayim.

Tosfos (Bechoros 17b DH Efshar): Rashi says that Efshar Letzamtzem b'Yedei Shomayim means that natural events can occur simultaneously or produce identical measurements, even though Hash-m does not need this. All the more so b'Yedei Adam, people sometimes intend to make things equal! If so, why does the Gemara call a found corpse b'Yedei Adam? He fell b'Yedei Shomayim! Rather, the argument is whether or not we can know that things are exactly equal. B'Yedei Adam is when man has time to measure precisely; b'Yedei Shomayim is when he does not, e.g. when twins left the womb.

Poskim

Shulchan Aruch (EH 175:2): If two of four brothers were married to sisters, and these two died and we do not know who died first, the Yevamos do Chalitzah but not Yibum.

Shulchan Aruch (3): If the two died (at once) or one after the other but before the Yevamah did Yibum, the Yevamos do Chalitzah but not Yibum. If they did Yibum, they may remain married. Some say that they must be divorced.

Question (Beis Shmuel 4): The latter opinion is difficult because the Gemara permits the second to do Yibum may remain married, for he can say 'the first did Yibum with the second to fall. My wife fell first; she was permitted, forbidden and permitted again.' Also the first opinion is difficult. Since Iy Efshar Letzamtzem, surely one fell first, so the second one to do Yibum should be allowed to keep her!

Shulchan Aruch (OC 305:1): If (on Shabbos) an animal is excessively guarded (by ropes, chains...) it is considered a load.

Mishnah Berurah (2): This is only if it is much more than needed. It is Iy Efshar Letzamtzem to have exactly the amount needed.

Shulchan Aruch (631:8): If one roofed his Sukah with spits and left spaces between them as wide as a spit, if he put Kosher Sechach in the spaces it is Pasul, for it is impossible to fill all the spaces, hence there is a majority of Pasul Sechach.

Shulchan Aruch (648:11): If Chazazis (blisters) on an Esrog in one place cover half of the Esrog, some are Machshir and some are Posel.

(Tur): My brother is Machshir. Since it is b'Yedei Adam, Efshar Letzamtzem.

Levushei Serad (32): This is considered b'Yedei Adam because one can measure to see if it is exactly half.

Note: According to Rashi, this is b'Yedei Shomayim. The Tur's brother holds like Tosfos, who defines Efshar Letzamtzem to mean that we can know that it is exact. If we do not have time to measure something exactly, e.g. whether or not twins were born simultaneously, this is b'Yedei Shomayim.

Gra (DH Im): The lenient opinion holds that even though Chachamim say Iy Efshar Letzamtzem even b'Yedei Adam, the Halachah follows R. Yosi ha'Gelili regarding b'Yedei Adam.

Gra (DH v'Yesh): The stringent opinion holds that the Halachah follows Chachamim also b'Yedei Adam. Nevertheless, a tradition from Sinai teaches that half suffices for Shechitah or Mechitzos.

Levush (YD 55:4): If the (entire) bottom leg bone of an animal was cut off it is Tereifah, lest part of the middle bone or juncture of the sinews was cut. This is b'Yedei Adam, so Iy Efshar Letzamtzem. However, an animal born without the bottom leg bone is Kosher, for b'Yedei Shomayim Efshar Letzamtzem.

Note: We never find an opinion that Efshar Letzamtzem only b'Yedei Shomayim. The Levush does not mean that this Halachah depends on the argument of R. Yosi ha'Gelili and Chachamim. All agree that we are concerned when it was cut, and this concern does not apply when it was born this way.

Mishnah Berurah (586:79): If a Shofar is inside a Shofar and they are flush (neither extends past the other), one could be Yotzei by blowing the inner Shofar. However, it is difficult to make them exactly flush. If the outer Shofar extends further, it is Pasul. Therefore, the inner Shofar must extend further.

Birkei Yosef (586:13): Rav Achai says that the Gemara concludes that Chachamim hold that Efshar Letzamtzem, and expound "ha'Kerovah" - but not ha'Kerovos. This is unreasonable! If Iy Efshar Letzamtzem, one city is closest! It is unreasonable that the verse teaches that if they appear equidistant we need not bring one Eglah on condition, for this is uncommon. Rather, "Kerovah" is not extra; it excludes a further city. Chachamim merely say that the word connotes one city. In other places we expound the singular to exclude two, e.g. "Shofar" and not Shofaros. Tosfos (Eruvin 6a DH v'Safek) says that we conclude that Chachamim hold that Efshar Letzamtzem, and expound "ha'Kerovah", even ha'Kerovos. The verse teaches that if they appear equidistant we bring an Eglah on condition. One might have thought that both cities are exempt due to a Sefek-Sefeka. Perhaps they are equidistant (even though we cannot know this); and if one is closer, perhaps the other is closer.

Shulchan Aruch ha'Rav (OC 90:18): One should fix a place for Tefilah. It is impossible to pray in exactly the same place, so within four Amos suffices.