Rejection: Really, it discusses returning - the Mishnah is abbreviated, it means as follows:

One may return a Tavshil to a Kirah heated with straw or stubble, if Gefes or wood was used, it is forbidden unless it was Garuf v'Katum;

Shehiyah is permitted even if it was not Garuf v'Katum;

Beis Shamai permit Shehiyah of hot water and forbid a Tavshil, Beis Hillel permit even a Tavshil;

The Heter to return [if it was heated with straw or stubble, or if it was Garuf v'Katum] is not unanimous - Beis Shamai permit removing and forbid returning, Beis Hillel permit both.

Answer #2: R. Chelbo said that the Mishnah permits putting food on a Kirah, but it is forbidden to put inside it.

If the Reisha discusses returning [like we just explained], we understand the difference (Ramban - returning inside looks like cooking);

But if the Reisha discusses Shehiyah, it permits only if it is Garuf v'Katum - if so, this should be permitted even inside!

Rejection: R. Chelbo does not discuss the Reisha, rather, the Seifa:

(Mishnah - Beis Hillel): Even returning is permitted.

(R. Chelbo): One may return on top, but not inside.

Answer #3 (Beraisa - R. Meir): If two Kiros are connected, and only one of them is Garuf v'Katum, Shehiyah is permitted on it, not on the other.

Beis Shamai forbid any Shehiyah, Beis Hillel permit only hot water.

If one removed the water, all forbid returning it.

R. Yehudah says, Beis Shamai permit Shehiyah of hot water, Beis Hillel permit even a Tavshil;

Beis Shamai permit removing but not returning, Beis Hillel permit even returning.

If the Reisha of our Mishnah discusses Shehiyah, the Mishnah is like R. Yehudah;

But if the Reisha discusses returning, the Mishnah is unlike either Tana:

Regarding Beis Shamai, it is unlike R. Meir in one respect (the Mishnah distinguishes whether or not it was Garuf v'Katum, R. Meir does not, he forbids all Shehiyah);

Regarding Beis Hillel, it is unlike R. Meir in two respects (the Mishnah permits all Shehiyah, R. Meir permits only water and only if it was Garuf v'Katum; the Mishnah permits returning if it was Garuf v'Katum, R. Meir forbids even then)!

It is unlike R. Yehudah - he says that all forbid Shehiyah if it was not Garuf v'Katum, in the Mishnah Beis Hillel and Beis Shamai argue about what is permitted in this case!

Rejection: Really, the Reisha discusses returning; the Tana of our Mishnah holds like R. Yehudah regarding the distinctions between hot water and Tavshil, and between Shehiyah and returning (in both cases, Beis Shamai permit only the former, Beis Hillel permit both);

He argues with R. Yehudah regarding Shehiyah - he permits in any case, R. Yehudah permits only if it was Garuf v'Katum. (Rashba - the Gemara prefers to establish out Mishnah like R. Meir or R. Yehudah, who distinguish between water and Tavshil, and whether or not it was swept or covered, and not like Chananyah, who did not.)

Question: May one Somech [put a pot near a Kirah]? (Rif proves from here that the Halachah does not follow Chananyah - he permits Shehiyah in or on a Kirah, all the more so one may leave pots near a Kirah! Tosfos - if the Reisha discusses returning, here we ask whether or not one may return near a Kirah; really, the Halachah follows Chananyah.)

Perhaps it is forbidden to put in or on a Kirah, but Semichah is permitted;

Or, perhaps there is no distinction!

Answer #1 (Beraisa): If two Kiros are connected, and only one of them is Garuf v'Katum, Shehiyah is permitted on it, not on the other.

One leaves the food near a (i.e. the other) Kirah in which Shehiyah is forbidden, even though it is warmed by it!

Rejection: Since the pot is above, the heat from the 'forbidden' Kirah dissipates in the air - we cannot learn to Semichah next to a Kirah.

Answer #2: Rav Safra taught that if one put ashes on coals and they flared up, Semichah and Shehiyah are permitted, one may remove and return.

Inference: Semichah is permitted because the coals were covered - otherwise, it is forbidden!

Objection: If so, you should likewise permit removing only if the coals were covered (surely, this is not true, one may remove in any case)!

Rather, you must say that one may remove in any case - removing was taught only on account of returning;

Likewise, Semichah is always permitted, it was taught only on account of Shehiyah!

Answer: No - one returns to the same place he removed from, to teach returning one must first mention removing;

But Semichah and Shehiyah are in different places, there is no need to teach Semichah on account of Shehiyah!

Question: What was the conclusion?

Answer #3 (Beraisa): If it was heated with Gefes or wood, Semichah is permitted, Shehiyah is forbidden unless it was Garuf v'Katum;

If the coals dimmed, or if one put thin chaff of flax on top of them, this is like covering with ashes.

(R. Yitzchak bar Nachmani): If one put ashes on coals and they flared up, one may Meshaheh fully heated water or a fully cooked Tavshil.

Inference: [Even when Shehiyah of partially cooked food is forbidden,] Mitztamek v'Yafeh Lo (fully cooked food that improves through further cooking, it dries out) is permitted!

Rejection: No, Shehiyah of such food is normally forbidden - here it is permitted because ashes were put.

Question: If so, what is the Chidush?

Answer: One might have thought that since the coals flared up, it is as if they were not covered - R. Yitzchak teaches, this is not so.

(Rabah bar bar Chanah citing R. Yochanan): If one put ashes on coals and they flared up, one may Meshaheh fully heated water or a fully cooked Tavshil, even if Rosem coals were used (they are hotter and last longer than regular coals).

Inference: Mitztamek v'Yafeh Lo is permitted!

Rejection: No - only here it is permitted, because he put ashes.

Question: If so, what is the Chidush?

Answer #1: It is a Chidush because the coals flared up.

Objection: We already learned this from R. Yitzchak!

Answer #2: Rabah bar bar Chanah permits even if Rosam coals were used.

(Rav Sheshes citing R. Yochanan): If a Kirah was heated with Gefes or wood, one may Meshaheh even water that was not fully heated and a Tavshil that was not fully cooked;

If one removed them, he may not return them until sweeping or putting ashes.

He holds that [the Reisha of] our Mishnah discusses returning, Shehiyah is permitted even if it is not Garuf v'Katum.

Objection (Rava): We already learn both laws of Rav Sheshes from Mishnayos!

(Regarding Shehiyah - Mishnah): One may not put bread in an oven just before Shabbos or a cake on top of coals unless there is time for the faces to form a crust before Shabbos;

Inference: If there is time to form a crust, it is permitted!

(Regarding returning - Mishnah - Beis Hillel): One may even return.

Beis Hillel permit only when it was Garuf v'Katum!

Answer: Indeed, Rav Sheshes teaches that we learn these laws from these Mishnayos.

(Rav Shmuel bar Yehudah citing R. Yochanan): If a Kirah was heated with Gefes or wood, one may Meshaheh water that was fully heated and a Tavshil that was fully cooked, even if it is Mitztamek v'Yafeh Lo.

A Chacham: But Rav and Shmuel forbid Mitztamek v'Yafeh Lo!

Rav Shmuel: I know that Rav Yosef says that Shmuel forbids - but R. Yochanan permits.

Rav Ukva of Meishan (to Rav Ashi): You live near the region of Rav and Shmuel, you must follow them (one may not permit something in front of people who are stringent about it); we conduct like R. Yochanan (the Halachah follows him).

Question (Abaye): [If the Kirah was not Garuf v'Katum,] is Shehiyah permitted [if the food was partially cooked, or Mitztamek v'Yafeh Lo]?

Answer #1 (Rav Yosef): People are Meshaheh on behalf of Rav Yehudah, and he eats it!

Rejection (Abaye): We cannot learn from him - if he does not eat good food, he is prone to become dangerously sick - what is the Halachah for us?

Answer #2 (Rav Yosef): In Sura, they do Shehiyah. ('D'Ha' must be deleted from the text, for Rav Nachman bar Yitzchak did not live in Sura, and Rav Yosef would not bring a proof from Rava's Talmid).

Rav Nachman bar Yitzchak was very careful about his actions; Shehiyah was done for him, and he would eat it.

Rav Ashi: I was in front of Rav Huna, they were Meshaheh Kisa d'Harsena (fish cooked with flour in their oil) for him, and he ate it;

I do not know if he permits Mitztamek v'Yafeh Lo, or if he considers it Mitztamek v'Ra Lo on account of the flour.

(Rav Nachman [bar Yakov]): Mitztamek v'Yafeh Lo is forbidden, Mitztamek v'Ra Lo is permitted;

The general rule is, anything with flour is Mitztamek v'Ra Lo, except for a Tavshil of turnips, even with flour it is Mitztamek v'Yafeh Lo;

This is only if it has meat (the fat blunts the pungency of the turnips), otherwise it is Mitztamek v'Ra Lo.

Even if it has meat, this is only if he does not need it for guests - if it is for guests, [he wants to give big pieces,] it is Mitztamek v'Ra Lo.