Explanation #1 (Rashbam): R. Avahu holds like R. Shimon, who obligates Mekalkel b'Chaburah, and R. Yochanan holds like R. Yehudah, who exempts Mekalkel b'Chaburah and b'Hav'arah;

If one needs [blood from the wound] for his dog, or he needs [to burn for the sake of] the ashes, he is liable even according to R. Yehudah. Also Rashi connotes like this below.

Question: If so, why did [R. Yochanan] tell [R. Avahu] "go outside"? Because he holds like R. Yehudah, do we silence one who teaches like R. Shimon?! The Gemara asks like this in Chulin (15a).

Explanation #2: R. Avahu and R. Yochanan argue according to R. Shimon. R. Avahu holds that wounding and burning, even if he does not need for his dog or for the ashes, is liable according to R. Shimon, for he learns from Bris Milah and burning a Bas Kohen;

R. Yochanan holds that also R. Shimon obligates only if there is some Tikun, e.g. he needs for his dog or for the ashes, for also Milah and burning [a Bas Kohen] has some Tikun. It is needed for a Mitzvah;

However, according to R. Yehudah, even if he needs it for the ashes or for his dog, he is exempt, for this is not an important Tikun. It is not normal to wound another person in order to give to his [own] dog, or to burn a stack for the sake of ashes.

Implied question: Every case of Shechitah is Mekalkel, like it says in Chulin (8a) that one may slaughter with a knife of idolatry! (Why does R. Yehudah obligate for Shechitah?)

Answer #1: R. Yehudah agrees that regarding Shabbos, he is liable. Only regarding idolatry he considers it Mekalkel, for it says "Lo Yidbak b'Yadcha Me'umah Min ha'Cherem", and this is not considered Hana'ah, since the ruin is more than the Tikun.

Answer #2 (R. Tam): R. Yehudah considers it Mekalkel when he needs for his dog or for the ashes, because the Tikun does not come at that time, only afterwards. The blood comes after the wound was made, and the ashes come after the burning finished;

However, regarding Shechitah, at the time of the ruin comes the Tikun. It removes [the animal] from the status of Ever Min ha'Chai.

Tearing in order to instill fear on his household, R. Yehudah considers also this to be Tikun, for at the time of the ruin comes the Tikun.

Similarly, killing damagers (below, 121b), R. Yehudah obligates for this, since the Tikun comes at the time of the ruin. R. Shimon exempts, for it is Melachah she'Einah Tzerichah l'Gufah.

Implied question: Tearing in order to sew, and erasing in order to write, all agree that one is liable, even though at the time of the ruin the Tikun does not come!

Answer: This is because the ruin causes more Tikun at the end. It is full Tikun, for he can do the Tikun only through the ruin.

Question: R. Avahu obligates even when he does not need for his dog. Since he does not need it at all, it is Melachah she'Einah Tzerichah l'Gufah;

Even though R. Shimon obligates Mekalkel b'Chaburah, still he requires Tzerichah l'Gufah, like we say in Sanhedrin (84b) "whom do we know that he obligates Mekalkel b'Chaburah? It is R. Shimon. He exempts Melachah she'Einah Tzerichah l'Gufah (below, 121b) and Kerisus (20b)!

Answer: We find that even total ruin is Tzerichah l'Gufah, e.g. wounding and burning Isur Hana'ah. He thought that he may give [the blood] to his dog, and to cook a pot [from the fire. Tosfos did not discuss benefit from the ashes, for Isur Hana'ah for which it is a Mitzvah to burn them, the ashes are permitted - Maharsha];

R. Avahu holds that even though need for a Mitzvah is not considered Tikun, it is considered Tzerichah l'Gufah.

Question: When he needs for his dog or for the ashes, how is this considered Tzerichah l'Gufah? Why is this unlike one who digs a ditch and needs only the earth?

Answer: That is different. Here, he needs Netilas Neshamah in order to give to his dog, for the blood is the soul (taking the blood is Netilas Neshamah);

Also burning, the burning is needed to make ashes, just like one who burns in order to cook a pot;

However, one who digs [for the earth], the crater is made automatically, and he does not benefit from it at all.

Question: Why do we need to learn from Milah? We should learn the entire matter from burning a Bas Kohen, which does not override Shabbos, for there is Netilas Neshamah in this burning. Also wounding is liable only due to Netilas Neshamah!

Answer #1: Regarding Mekalkel b'Chaburah, we cannot learn from burning, for there the Tikun comes at the time of the ruin. However, regarding Mekalkel b'Hav'arah, we learn properly, for the Tikun comes after the burning, like I explained.

Answer #2: If we would not learn from Milah that Mekalkel b'Chaburah is liable, one might have thought that execution overrides Shabbos, for it is not a Melachah, and the Torah excluded only burning, because Mekalkel b'Hav'arah is liable.

Explanation: He does not say so because he holds like R. Yehudah. Rather, he explains according to R. Yehudah.

Implied suggestion: Just like cooking ingredients fixes them to be more important, so lead is more important through cooking.

Rejection #1: If this were R. Yehudah's reason, what is the source that other Misos Beis Din do not override Shabbos, since there is no Tikun? The Torah forbade burning only due to Tikun of the lead!

Rejection #2: What is the source that burning a Bas Kohen does not override Shabbos when the lead was prepared (melted) from before Shabbos?

Explanation (Ri): It means as follows. What is the difference between cooking lead for the sake of burning a Bas Kohen, or cooking ingredients for the sake of dying a garment? Just like cooking ingredients for the sake of dye is considered Tikun, also cooking lead for the sake of [execution through] burning;

From here we properly learn that all other Misos Beis Din are considered Tikun, due to the Mitzvah. If not that burning itself were considered Tikun, it would not be forbidden due to cooking the lead;

Even though [the lead] is fixed through [cooking], since it is [fixed] only due to burning, [if burning itself were not considered Tikun, cooking] would not be considered Tikun.

Support: Also taking out a shovel to bury a Mes according to R. Shimon is [exempt,] like taking out a pouch to collect emissions of Zivah (12a. Since collecting Zivah is Einah Tzerichah l'Gufah, R. Shimon exempts also Hotza'ah for the sake of collecting. Likewise, since he exempts for Hotza'ah of a Mes for burial, he exempts for Hotza'ah of a shovel for the sake of burial.)

Question: Granted, according to R. Yehudah we properly hear that burning [was written explicitly] to teach that it is only a Lav, or it separates (one is liable for every Melachah by itself), since the Torah did not write "Lo Sa'asu Melachah b'Chol Moshvoseichem', rather, it wrote "Lo Seva'aru." This shows that it was written to teach that it is only a Lav, or to separate, like I explained above (70a);

However, according to R. Shimon, the Torah needed to write burning to obligate Mekalkel b'Hav'arah. What is his source to teach that it is only a Lav, or to separate?

Suggestion: He learns to separate from "Achas me'Henah", like R. Yosi.

Rebuttal: Above (103b), R. Shimon explicitly argues with R. Yosi, and expounds [that verse] differently!

Answer: He learns to separate like Shmuel does above (70a).

Support: This resolves what was difficult for Shmuel. Like which Tana does he hold? He is unlike R. Nasan, and unlike R. Yosi! Now, we can say that he holds like R. Shimon.

Citation (Yevamos 6b): We need the verse to forbid burning a Bas Kohen, for one might have thought to permit based on a Kal v'Chomer from Avodah, which overrides Shabbos.

Explanation: That is according to R. Yehudah, who considers it Tikun. According to R. Shimon, we need the verse "Lo Seva'aru" to obligate every Mekalkel b'Hav'arah.

Explanation #1 (Rashi): The argument about Mekalkel b'Chaburah, we learn from the argument of Melachah she'Einah Tzerichah l'Gufah. (R. Yehudah obligates even if Einah Tzerichah l'Gufah, as long as there is some Tikun, even if the Melachah itself ruins. The same applies to burning and wounding. R. Shimon obligates only for Tzerichah l'Gufah, i.e. Tikun in the Melachah itself. This never occurs in burning and wounding. Since the Torah forbids them regarding Milah and execution, for them, even Mekalkel without Tikun is liable.) This implies that R. Shimon does not require that he needs for his dog or for the ashes. (Chasam Sofer - for burning and wounding, the Torah obligates Einah Tzerichah l'Gufah. R. Yehudah learns from Shnei Kesuvim ha'Ba'im k'Echad to everywhere else, and R. Shimon does not.)

Consequence: According to this, we must say that R. Avahu [who obligates even without such a need] holds like R. Shimon, and R. Yochanan [who requires it] holds like R. Yehudah.

Rebuttal and Explanation #2: This is wrong, like I explained above (DH Chutz. Rather,) we must say that [the Amora'im] had a tradition about this argument about Mekalkel b'Chaburah.

Implied suggestion: Because fish can properly feed themselves in water, we do not toil for them. It is considered that you are not obligated to feed them.

Rejection #1: This is not always true, that food is available for fish, but not for Chayos.

Rejection #2: Below, we wanted to establish the Beraisa "one may not trap a Chayah or bird, and one may not put food in front of them" to discuss an uncovered Biver. Because there is no roof, food is available for them?!

Explanation #1 (Rashi): Since one may not trap them, they are Muktzah. Therefore, one may not put food in front of them, and we do not toil for them.

Rejection: A Mishnah below (155b) teaches that one may put water in front of geese, chickens and domestic doves, even though they are Muktzah on Shabbos!

Explanation #2 (Ri): Whenever it is considered as if they are already trapped mid'Oraisa, e.g. geese, chickens and domestic doves, even though mid'Rabanan one may not trap them...

Source: The Mishnah below (107a) teaches that if one traps a Chayah or bird in his Reshus, he is exempt. This implies that it is forbidden.

... [Even though mid'Rabanan one may not trap them, since mid'Oraisa it is as if they are already trapped, one may put food in front of them. The same applies to a Chayah or bird in a roofed Biver. They are considered more incumbent on you to feed them;

However, here mid'Oraisa they are not trapped. They are not considered incumbent on you to feed them. They are like those that are always in the field, like doves of a dovecote or of the Aliyah.

Support: According to this, it is fine that in a Mishnah in Beitzah (24a), R. Shimon ben Gamliel says that the general rule is, what is lacking trapping is forbidden...

It says in the Gemara, what is considered lacking trapping? E.g. he says "bring a trap, and we will trap it";

Abaye said to Rav Yosef "geese and chickens, one says 'bring a trap, and we will trap it", and it says that if one traps geese, chickens or domestic doves, he is exempt!"

Question: What was the question? "Exempt" implies that it is forbidden! Also in our Mishnah, R. Shimon ben Gamliel says that what is lacking trapping is forbidden!

Answer: According to what I explained here, this is fine. R. Shimon ben Gamliel refers to the Reisha, which taught "one may not trap [fish], and one may not put food in front of them", and R. Shimon ben Gamliel forbids [also for Chayos and birds] even giving food when it is lacking trapping;

If so, he considers it lacking trapping mid'Oraisa. Therefore, it is a proper question.

Implied question: R. Yehudah argues! (How could Abaye think that there is no argument?)

Answer: Even so, Abaye asked properly. If [Shmuel] came merely to teach unlike R. Yehudah, he should say "the Halachah does not follow R. Yehudah!" (Rather, he teaches also that the Halachah does not follow Chachamim, i.e. they argue.)

Observation: Here it is fine that [the Gemara] does not ask "what is considered lacking trapping?", for it already explained that when there are corners, it is a big Biver. Presumably, this is "lacking trapping" that R. Shimon ben Gamliel discusses. (Shabbos Shel Mi discusses why Tosfos mentions only the last of the three answers about what is considered big.)

Question: However, in Beitzah (24a) it is difficult. Why does it ask "what is considered lacking trapping?", since it already explained what is a big Biver and a small Biver according to Rabanan!

Answer (Rashba): There, in [Chachamim's] words, they mentioned Chayos and birds, and R. Shimon ben Gamliel refers to this. [The Gemara] asks what is considered lacking trapping for birds. It does not ask about Chayos, for it already explained this.

Support: All the [questions] brought about this [there] discuss only birds. However, here Rabanan do not discuss birds. They discuss only Chayos. (They also discuss a Tzipor, but we conclude that it is a Tzipor Dror, which is unlike a [regular] bird.)

Explanation: They had a uniform height of walls, and they knew the height.

Implied question: Why is this (he locked without knowing that there is a deer inside) more obvious than this (the second sat next to the first, who already filled the doorway)?

Answer (Riva): One might have thought that when he came and sat next to him, it is forbidden. because it looks like he comes to increase guarding of the deer.