Gemara

13a (Mishnah): R. Yosi admits that if Kemitzah was done with intent to eat the Shirayim tomorrow or be Maktir the Kometz tomorrow, the Minchah is Pigul, and there is Kares;

R. Yosi says, if he intended to be Maktir the Levonah tomorrow, the Minchah is Pasul, and there is no Kares;

Chachamim say, it is Pigul, and there is Kares.

Chachamim: This is no different than a Zevach! (Intent to be Maktir Eimurim makes Pigul!)

R. Yosi: That is different, for blood, meat and Chelev are all the same Min (species, i.e. all are from the animal), but Levonah is not from the Min of (the Kometz, i.e. of) the Minchah.

(Reish Lakish): R. Yosi holds that one Matir is not Mefagel another Matir;

The same applies to the two Bazichei (spoons of) Levonah that permit Lechem ha'Panim. One is not Mefagel the other.

One might have thought that R. Yosi exempts from Kares in the Mishnah because Levonah is a different Min than the Minchah, but Levonah can be Mefagel Levonah, for they are the same Min. Reish Lakish teaches that this is not true.

The Mishnah says that R. Yosi exempts because Levonah is not from the Minchah. I.e. Haktaras ha'Kometz is not Me'akev it; one may offer the Levonah before the Kometz, or vice-versa, but Shirayim may not be eaten before this;

Chachamim say that one Matir is not Mefagel another Matir when they were never in one Kli together. Kometz and Levonah were in one Kli together, so they are Hukve'u (they become like one). Either is Mefagel the other.

17a (Eifah and Avimi): Haktarah is Mefagel Haktarah.

Even Chachamim say only that intent during only part of the Matirim is not Mefagel, e.g. intent in the Kometz for the Shirayim, for there was no improper intent for the Levonah. When the intent is for the Levonah, it is as if he intended for all the Matirim, so they agree that there is Pigul.

Support (Rava - Mishnah): The general rule about Kemitzah, Nesinah, Holachah or Haktarah done with intent (Chutz) to eat something that is normally eaten, or to be Maktir something that is normally Huktar:

If he intended Chutz li'Mkomo, the Minchah is Pasul, and there is no Kares. If he intended Chutz li'Zmano, it is Pigul, and there is Kares.

Suggestion: Haktarah is like the other Avodos. It is Mefagel whether the intent was to eat or to be Maktir.

Rejection: No, the other Avodos are Mefagel whether the intent was to eat or to be Maktir, but Haktarah is Mefagel only if the intent (during the entire Haktarah) was to eat.

(Rav Menasiya bar Gada citing Rav Chisda): Haktarah is not Mefagel Haktarah;

Even R. Meir says only that intent during part of the Matirim is Mefagel when he intends for the Shirayim, for the Kometz permits them, but not when he intends for the Levonah, for the Kometz does not permit it.

(Rav Chisda citing Rav): Haktarah is not Mefagel Haktarah.

Support (Abaye - Mishnah): If he slaughtered one of the two lambs (brought with Shtei ha'Lechem) with intent to eat it tomorrow, it is Pigul, and the other lamb is Kosher. If he slaughtered it with intent to eat a k'Zayis of the other lamb tomorrow, both are Kesherim.

Suggestion: One lamb does not permit the other. This is why one does not Mefagel the other.

Rejection: One lamb does not Mefagel the other because they were not in a Kli together. Kometz and Levonah were in a Kli together, so they are like one. (Perhaps) Kometz can be Mefagel Levonah.

(Rav Hamnuna citing R. Chanina): If Haktaras Kometz was with intent to be Maktir the Levonah with intent to eat the Shirayim tomorrow, it is Pigul.

(Rav Ada bar Ahavah): Really, Haktarah is not Mefagel Haktarah, and intent for part of the Matirim is not Mefagel. This case is different, for all of the Minchah is involved in the intent Chutz li'Zmano.

Rishonim

Rambam (Hilchos Pesulei ha'Mukdashim 16:8): If during Haktarah of the Kometz he intended to be Maktir the Levonah tomorrow, it is not Pigul, for Haktarah is not Mefagel Haktarah. If during Haktarah of the Kometz or Levonah alone he intended to eat the Shirayim tomorrow, it is Pasul, but not Pigul, for Chetzi Matir does not make Pigul.

Kesef Mishneh: The Rambam rules that Haktarah is not Mefagel Haktarah because Rav and several Amora'im hold like this. The Halachah follows the first Tana, that Chetzi Matir does not make Pigul.

Chazon Ish (Menachos 22:13 DH Sham): Why did the Rambam need to say that Haktarah is not Mefagel Haktarah? It suffices that Chetzi Matir does not make Pigul! It seems that he teaches unlike Eifah and Avimi. This is not called Chetzi Matir, because the intent spread throughout the entire Matir. Do not say that he holds like them, and here the reason is because Haktarah is not Mefagel Haktarah. If so, Kemitzah with intent to be Maktir the Levonah tomorrow would make Pigul!

Likutei Halachos (9a, and Zevach Todah DH u'Muchach): The Halachah does not follow Eifah and Avimi, for many argue with them. It is clear from the Gemara that those who disagree hold that there is no Pesul at all. The Rambam connotes unlike this. This requires investigation.

Keren Orah 17a (DH Af): What was the proof from Shechitah of a lamb with intent to eat the other tomorrow? Chachamim say that Kometz with intent to be Maktir the Levonah tomorrow makes Pigul, for this is unlike the lambs, which were not fixed in one Kli! We must say that that was according to the conclusion here. However, we need not say so. In any case it is not difficult for Chachamim, because Shechitah of one lamb with intent for the other is only half a Matir. Abaye thought that R. Meir agrees about this. Even though he holds that Chetzi Matir is Mefagel, this is only for its own Shirayim, but not for the other Matir. Chachamim hold that Kemitzah with intent to be Maktir the Levonah tomorrow is Mefagel because he intended for the entire Matir. The Gemara concluded that it depends on whether they were fixed in a Kli together. It seems that Abaye holds that Haktarah is not Mefagel Haktarah, and it is not even Pasul, just like one lamb does not disqualify the other. The Rambam connotes unlike this, even though there is no similar case to decree about.

Rambam (ibid.): If during Haktarah of the Kometz alone he intended to be Maktir the Levonah tomorrow, and afterwards he was Maktir the Levonah with intent to eat the Shirayim tomorrow, it is Pigul, for intent of Chutz li'Zmano spread throughout the entire Minchah.

Keren Orah 17a (DH Hiktir): Haktaras Kometz with intent to be Maktir the Levonah and eat the Shirayim tomorrow makes Pigul. Does this apply to another Avodah? If Holachah was with intent to be Maktir the Levonah and eat the Shirayim tomorrow, do we say that Chetzi Matir does not make Pigul? Even though Haktarah is not Mefagel Haktarah, it helps with intent to eat the Shirayim tomorrow, for then the intent spread throughout the entire Minchah. Or, perhaps the same applies to any Avodah! Our Sugya connotes that the only half-Matir of a Minchah is Haktarah. However, according to Reish Lakish there is Holachah. Also, this is relevant to a half-Matir of blood brought inside the Heichal, if one intended during Haza'os between the staves of the Aron to throw the rest Chutz li'Zmano and burn the Eimurim tomorrow. It seems that there is Pigul only regarding Haktarah, but not for other Avodah. However, the Rambam disagrees, since the primary intent is at the time of the half-Matir. What does it help if he intended to be Maktir and eat? Rather, the primary text is 'and Levonah to eat Shirayim', i.e. during Haktaras Kometz he intended to be Maktir the Levonah (tomorrow), and at the time of Haktaras Levonah he intended to eat the Shirayim tomorrow. Itw, there is intent for Pigul in the entire Matir. What is the Chidush? The Chidush is that eating and Haktarah join for Chutz li'Zmano. If one intended for eating during half of one (Matir), and intended for Haktarah during the other, even though the Shi'ur of intent is a k'Zayis, they do not join. In R. Chanina's case they join, for the intent spread through the entire Matir. This requires investigation.

Rashi (17a DH Hachi and DH d'Pashta): The text is 'he was Maktir the Kometz with intent to be Maktir the Levonah to eat Shirayim (tomorrow). It does not say 'and to eat.' The Perush is, 'he was Maktir the Kometz with intent to be Maktir the Levonah tomorrow and with intent to eat Shirayim tomorrow. Even though one does not make Pigul by itself, now that he intended for both, it makes Pigul.

Sefas Emes (17a v'Hinei): According to Rashi, why does it matter that he intended for the Shirayim? Surely, Pigul of the Kometz on the Shirayim is Pigul, but it is only Chetzi Matir, since intent for Haktaras ha'Levonah has no effect, since Haktarah is not Mefagel Haktarah. Rashi's Diyuk between 'to eat' and 'and to eat' is very flimsy. Also the Rambam's reasoning is difficult. Since the first Pigul is nothing, how does it affect the latter action? Also, the Gemara did not mention his intent at the time of Haktaras Levonah! I would have explained that at the time of Haktaras Kometz he intended to be Maktir the Levonah with intent to eat Shirayim tomorrow. This is like intent from one Avodah to another regarding Lo Lishmah. Shechitah with intent to do Zerikah Lo Lishmah is Pasul. The same applies to Haktaras Kometz with intent to be Maktir the Levonah with intent for Pigul. Even if you will say that this is not Pigul, if he actually had this intent when he was Maktir the Levonah, the first intent would help to be called Pigul in the entire Matir. This is why the Gemara said 'to be Maktir the Levonah', and did not mention 'tomorrow' regarding the Levonah.

Likutei Halachos (9a Zevach Todah DH Hiktir): Rashi explains that at the time he was Maktir the Kometz, he intended to be Maktir the Levonah and to eat Shirayim tomorrow. The Rambam explains that at the time he was Maktir the Kometz, he intended to be Maktir the Levonah tomorrow, and at the time he was Maktir the Levonah, he intended to eat Shirayim tomorrow. It seems that he holds that only in this way the intent spreads through the entire Matir. According to Rashi, he intended only in Chetzi Matir. It seems that the Rambam's text was like it says in old Seforim 'and Levonah to eat Shirayim tomorrow' (i.e. and he was Maktir the Levonah with intent to eat Shirayim tomorrow - PF).

Chazon Ish (Menachos 22:13 DH v'Hinei ha'Rambam): The Rambam rules that Holachah is considered Chetzi Matir, unlike R. Yosi, and he did not bring the law of Kemitzah with intent to be Maktir the Levonah (tomorrow - 13a). We hold like the Mishnah (13a) that considers Kemitzah to be Chetzi Matir, and the same applies to Holachah, and we hold that there is no Pigul due to Chetzi Matir.