Answer #1 (and Answer #3 to Question (3)): Beraisa #1 is Rebbi.

(Beraisa #2 - Rebbi): If one of the lambs (Shalmei Tzibur) was slaughtered with intent to eat (Chutz li'Zmano) half a k'Zayis of one loaf and the other was slaughtered with intent to eat half a k'Zayis of the other, it is Kosher.

Inference: This is because he specified, half a k'Zayis from each. Had he said, a k'Zayis from both of them, they would join!

Objection: Which Tana (in our Mishnah) does Rebbi hold like?

He does not hold like Chachamim. They say that even intent for a k'Zayis from one of them is Mefagel both of them!

If he holds like R. Yosi, we must say that Beraisa #1 is like R. Yosi, so this does not answer the question (13b, 4:e)!

Answer #2 (and defense of Answer #1 above (13b, 4:e:3)): Really, Beraisa #1 is Chachamim;

It should not say, 'unless he was Mefagel bi'Shteihem (the feminine form of 'both', it refers to Shtei ha'Lechem), rather, 'bi'Shneihem' (the masculine form of 'both', i.e. he intended during Shechitah of both lambs). It suffices if he intended to eat from one loaf.

Chachamim say this to oppose the opinion of R. Meir, who says that intent during the Avodah of part of the Matirim (in this case, one of the lambs) makes Pigul.

Objection #1: If so, why does it say 'there is never Kares unless...'? (This connotes, even though one factor suggests that there should be Kares, another factor is needed.)

Granted, if the Beraisa is R. Yosi, he opposes R. Meir and Chachamim. He teaches that even if he intended to eat from Shteihem (both loaves), there is not Kares unless he intended in Shneihem (both lambs);

However, if it is Chachamim, they say this just to oppose R. Meir. They should have said 'there is not Kares unless...'!

Objection #2: Rav Ashi proved otherwise from a Beraisa!

(Beraisa - R. Elazar citing R. Yosi): Intent to do (Chutz li'Zmano) an outer Avodah (i.e. outside the Heichal, but in the Azarah) takes effect. Such intent to do (or while doing) an inner Avodah does not take effect;

If one slaughtered (an inner Chatas) outside with intent to do Haza'ah (an inner Avodah), it is not Pigul;

If one did Haza'ah inside with intent to be Maktir Eimurim or be Zorek Shirayim (on the outer Mizbe'ach), it is not Pigul;

If he slaughtered outside with intent to be Maktir Eimurim or be Zorek Shirayim, it is Pigul; for the action and intention were both outside.

Question: When he intended to be Zorek Shirayim, what becomes Pigul?

Answer #1: The blood becomes Pigul.

Rejection (Mishnah): Pigul does not apply to the following (in most cases, because they do not have Matirim):

The Kometz, Levonah, Ketores, a Minchah of a Kohen, Minchas Nesachim, Minchas Chavitin (the daily Minchah of a Kohen Gadol), and blood.

Answer #2: The meat becomes Pigul.

Culmination of objection: R. Yosi says that Pigul without intent for meat (rather, for Shirei Dam) is Mefagel meat. All the more so, Pigul with intent for meat (i.e. for one thigh) is Mefagel meat (the other thigh)!

Objection #3: Ravina proved otherwise from the first Mishnah of our Perek!

(Mishnah): R. Yosi admits that if Kemitzah was done with intent to eat the Shirayim tomorrow or to be Maktir the Kometz tomorrow, the Minchah is Pigul, and there is Kares.

Question: When he intended to be Maktir the Kometz, what becomes Pigul?

Suggestion: The Kometz becomes Pigul.

Rejection (Mishnah): Pigul does not apply to the following - the Kometz...

Answer: Rather, the Shirayim become Pigul.

Culmination of objection: R. Yosi says that Pigul without intent for Shirayim (rather, for the Kometz) is Mefagel Shirayim. All the more so, Pigul with intent for one thigh, which is part of a Korban, is Mefagel the other thigh!

Answer #2 (to Question 4:c, 13b - R. Yochanan): R. Yosi learns from contradictory connotations in the verse of Shtei ha'Lechem:

They are considered to be one unit. If there are not two, it is Pasul. (Rashi - it says "Shtayim... Tihyenah." The root of Tihyenah is Havayah, which always teaches that something is Me'akev. Tosfos - "Tavi'u Lechem (singular) Tenufah" makes them like one.)

The verse also calls them two ("Shtayim Shnei Esronim"). Each must be kneaded and arranged by itself.

If one had a joint intent (e.g. to eat a k'Zayis (Chutz li'Zmano) from both of them together), they become Pesulim, for the Torah made them like one;

If his intent was individual (to eat only from one of them), only it becomes Pigul, for the Torah made them like two.

(The verse teaches this about Shtei ha'Lechem, but intent for one thigh is Mefagel the other, like Rav Ashi and Ravina taught above. R. Yochanan argues with Rav Huna (13b).)

Question (R. Yochanan): If one was Mefagel in (one kind of bread of) Lachmei Todah or Minchas Ma'afe Tanur, what is the law?

Answer (Rav Tachlifa - Beraisa): The same applies to Lachmei Todah and Minchas Ma'afe Tanur. (R. Yosi and Chachamim argue like they do about Shtei ha'Lechem and Lechem ha'Panim.)

(Beraisa): If one intended during Shechitah to eat half a k'Zayis (Chutz li'Zmano), and during Zerikah he intended for half a k'Zayis, this makes Pigul, for Shechitah and Zerikah join.

Version #1: Shechitah and Zerikah join, for both of them permit (Shechitah is Mekadesh the blood and permits Zerikah, and Zerikah permits the Eimurim to the Mizbe'ach (and in Korbanos that are eaten, it permits the meat to people). Kabalah and Holachah (do not permit, so) they do not join (with each other, or with Shechitah or Zerikah).

Version #2: Shechitah and Zerikah join, even though they are the first and last of the four Avodos. All the more so Kabalah and Holachah join (with each other or with Shechitah or Zerikah, for there is less time in between). (end of Version #2)

Question: Levi taught that the four Avodos (Shechitah, Kabalah, Holachah and Zerikah) do not join for Pigul!

Answer (Rava): The Beraisa is like Chachamim. Levi's teaching is like Rebbi:

(Beraisa - Rebbi): If one slaughtered a lamb (Shalmei Tzibur) with intent to eat half a k'Zayis of one loaf, and the other lamb with intent to eat half a k'Zayis of the other loaf, the lambs (and loaves) are Kesherim;

Rejection (Abaye): This shows that Rebbi holds that intents for partial Shi'urim during partial Matirim do not join, but perhaps he holds that such intents during (different) full Matirim join!

Question (Rava bar Rav Chanan): If Rebbi holds that intents for partial Shi'urim during full Matirim join, he should decree that such intents during partial Matirim join, lest people come to think that even the former do not join. We find that R. Yosi and Chachamim make such decrees!

(Mishnah - R. Yosi): If one intended to be Maktir the Levonah tomorrow, the Minchah is Pasul, and there is no Kares. (This is a decree, due to intent for the Shirayim or Kometz);

Chachamim say, it is Pigul, and there is Kares. (The following proves that Chachamim also decree.)

(Mishnah - R. Meir): If one was Mefagel (intended to eat the Shirayim Chutz li'Zmano during Haktarah of) the Kometz but not of the Levonah, or vice-versa, the Minchah is Pigul, and there is Kares (for eating the Shirayim);

Chachamim say, there is no Kares unless he was Mefagel in (Avodah of) the entire Matir.

(Inference: There is no Kares, but it is Pasul. This is a decree due to one who was Mefagel in both Matirim.)

Rejection (Abaye): No. In those cases, there is good reason to decree!

R. Yosi decrees about intent to be Maktir a Kometz of Levonah, due to intent to be Maktir a Kometz of a Minchah (which makes Pigul);

Chachamim decree about Haktarah of a Kometz (by itself) and Levonah (by itself) due to cases in which this is the full Matir, i.e. Minchas Chotei (which has no Levonah) and Lechem ha'Panim (which has no Kometz);

Chachamim also decree (16a, Mishnah) to disqualify a lamb due to (when he would have intent also in) the other, and one spoon (of Levonah) due to the other.

Here, there is intent in only half a Matir for only half a k'Zayis. There is no need to decree!

Support (Mishnah): Chachamim agree with R. Meir that if one was Mefagel in the Kometz of Minchas Chotei or Minchas Kena'os, it is Pigul, and there is Kares, for the Kometz is the Matir.

Question: Obviously, there is no other Matir (they do not have Levonah). Why is it necessary to say this?

Answer: This teaches that the reason Chachamim disqualify when he was Mefagel in the Kometz of Minchas Nedavah is due to the Kometz of Minchas Chotei (for then there is Kares.)

(Mishnah - R. Yehudah): If one of the loaves (of Shtei ha'Lechem) or one Seder (of Lechem ha'Panim) became Tamei, both (loaves or Sedarim) are burned in Beis ha'Sereifah (a place outside the Azarah for burning Pasul Kodshim), for a Korban Tzibur is never divided (half Kosher and half Pasul);

Chachamim say, the Tamei one is burned, and the Tahor one is eaten.

(Gemara - R. Elazar): They argue in a case when it became Tamei before Zerikah (of the blood of the Shalmei Tzibur, or before Haktarah of Bazichei Levonah of Lechem ha'Panim). If it became Tamei after Zerikah, all agree that each is treated according to its status. (The Tamei one is burned, and the Tahor one is eaten.)