The text: This is the correct text. It does not say "to cut hair", for in Mo'ed Katan (27b) it says that 30 days are forbidden for Gihutz (superior laundering) and cutting hair.

Defense #1 (of the text "Lesaper"): The Ri of Orlins brought from Bahag that a woman may remove hair. (I.e. some may cut hair, i.e. women.)

Defense #2: Further, we could say that here is according to R. Yosi, who permits haircuts hair during Avelus;

Citation (Bahag - Beraisa - R. Yehudah): Just like one may not shave during the Mo'ed, one may not shave during Avelus. R. Yosi permits all 30 days;

Citation (cont.): Haircuts are forbidden. This applies to his beard, head, and all other hair. Just like one may not cut nails during the Mo'ed, it is forbidden during Avelus. This is R. Yehudah's opinion. R. Yosi permits;

Citation (cont.): A woman may remove hair after seven days.

Rejection (of Defense #1): Perhaps just like a woman is permitted during her Avelus, she is permitted also [regarding, i.e. in the week of] Tish'ah b'Av! (The Kal va'Chomer is based on the law that it is forbidden regarding Tish'ah b'Av.)

Rejection #1 (of Defense #2): Similarly, R. Yosi who permits haircuts during Avelus, permits also [regarding] Tish'ah b'Av!

Rejection #2 (of Defense #2): It seems that even R. Yosi forbids haircuts [during Avelus]. Presumably, he learns a Gezeirah Shavah "Para-Para" from Nazir;

The Heter is to shave the entire head, which is repulsive. However, a haircut is forbidden. Also Bahag that I brought connotes like this.

Conclusion: The text does not say "to cut hair." Shaving the entire head is not called cutting his hair.

Explanation: This refers to after seven days, within 30 days.

Implied question: Mo'ed Katan (23a) connotes that an Avel may not launder his garment in water!

Answer: That is within seven days. Only Gihutz (superior laundering) is forbidden within [the rest of the] 30 days.

Distinction: Our Gihutz (in Chutz la'Aretz) is permitted, like it says in Kesuvos (10b) "our Gihutz is like their (Eretz Yisrael's) Kivus (standard laundering).

Explanation: Based on what I explained (42b DH Rebbi) that R. Yehudah and R. Yosi argue about Avelus, this is difficult. (What was Rav Chisda's question?)

We should establish the Heter to become engaged [in the week before] Tish'ah b'Av like R. Yehudah, who permits also during Avelus!

Suggestion: In any case it is difficult that R. Yosi's opinion is opposite to R. Yehudah's. R. Yehudah is more stringent about laundering than Eirusin, and R. Yehudah holds oppositely!

Rejection: This does not bother the Gemara. Below (43b), it suggests that Tana'im argue about this. (The Tana forbids Eirusin from Rosh Chodesh Av, but permits laundering until the week of Tish'ah b'Av. The Mishnah in Ta'anis cited on 43a is more stringent about laundering than Eirusin!)

Answer: The Gemara presumes that no Tana would argue with the Mishnah that permits Eirusin [before] Tish'ah b'Av, unless a Beraisa explicitly forbids;

Below, when it found an explicit Beraisa, which says "we diminish Eirusin", it strains to establish it to discuss Seudas Eirusin, in order that it not argue with the Mishnah there.

Explanation #1: The Yerushalmi in Ta'anis establishes this to discuss building and planting of Simchah, e.g. shady trees that kings eat under them.

Explanation #2: Some say that business also discusses of Simchah, e.g. needs of Chupah.

Rejection: We forbid only the Seudah itself!

Rather, we forbid excess business, more than on other days.

Question #1: How can we learn from before the week before [Tish'ah b'Av]? One may cut hair then!

Question #2: We should forbid cutting his hair before the week before, from a Kal va'Chomer! During 30 days of Avelus, business is permitted [but cutting hair is forbidden. Before the week before, business is forbidden, so all the more so one may not cut hair!]

Alternatively, we should forbid business during 30 days of Avelus from a Kal va'Chomer from cutting his hair [which is permitted] before the week before!

Or, we should permit cutting his hair during 30 days of Avelus [from a Kal va'Chomer from business, which is forbidden before the week before]!

Explanation: The Beraisa mentioned Redufah and others [who are not pregnant] due to R. Meir [to teach that he forbids even though to marry until three months. R. Yosi permits immediately, even if they could be pregnant!]

Explanation: Now we do not want to say that they argue about Avelus, for it is unreasonable that R. Yehudah should not be concerned for Avelus regarding [permitting] Nisu'in, like Rashi explained.

Implied question: According to the conclusion, there is no Avelus for an Arusah!

Answer: In any case, according to the current Hava Amina, that there is Avelus for an Arusah, there is no reason why R. Yehudah should not be concerned regarding Nisu'in.

Explanation #1 (Rashi): The Avelus of Tish'ah b'Av is old and of the Rabim. It is lenient.

Question: We can still ask a Kal va'Chomer like before!

Explanation #2 (R. Tam): We distinguish a new Avelus, in which they forbade to be Mekadesh, for we must be more stringent about a new Avelus than for an old Avelus. [An Isur of Kidushin] does not apply an old Avelus;

Regarding an Avelus of the Rabim, we should be more stringent about business than for an individual's Avelus;

This is because business is a public matter. If people will engage in business the entire day, people will come to say that they are not concerned to mourn over Yerushalayim.

Distinction: This is unlike Eirusin, which is a momentary action, like we establish it [to be permitted] before the week before.

However, in the week in which Tish'ah b'Av falls, one may not be Mekadesh;

If it were permitted to be Mekadesh, there would still be a Kal va'Chomer from laundering!

Question: However, a hidden scroll (initially, it was forbidden to write oral Torah, but one could write notes to remind himself) permits Eirusin even on Tish'ah b'Av, lest someone else merit to be Mekadesh her first through [prayer for] mercy. It brings a proof from the Yerushalmi.

Answer: We must say that we should be more stringent about a public Avelus also regarding laundering;

Also laundering is a public matter. It should not be that all are engaged in laundering, cutting hair and beautifying themselves, and it appears that they are not concerned to mourn at all.

Question: Here we forbid to be Mekadesh within Sheloshim;

In Mo'ed Katan (23a), it says that all 30 days are forbidden regarding Nisu'in. This implies that Eirusin is permitted!

Answer #1: That is like R. Yehoshua, who permits.

Answer #2: It mentioned Nisu'in to teach that even Nisu'in is permitted immediately after 30 days. (Really, also Eirusin is forbidden within Sheloshim.)

Implied question: Regarding one whose wife died, it was taught that one must wait three festivals before remarrying!

Answer #1 (R. Tam): Even though we forbid [an Avel due to] his father or mother to enter Beis ha'Mishteh (banquet house) until 12 months, he may marry after Sheloshim, due to the Mitzvah of Peru u'Rvu;

It was taught "all 30 days for Nisu'in" Stam, even for a father or mother. We distinguish only regarding [one who lost] his wife.

Even if he already fulfilled Peru u'Rvu, he is permitted [after Sheloshim], for the Halachah follows R. Yehoshua, who says (below 62b) "[if one married in his youth,] he should marry in his old age... "ba'Boker Zera Es Zar'echa..."

Explanation #1: If one has small children, he may marry even within seven days. Or, at least after Shivah is permitted, like the episode with Yosef ha'Kohen connotes (Mo'ed Katan 23a);

He was still in the cemetery [after burying his wife], and he said to her sister "go raise your sister's children."

The Gemara connotes that he married her immediately, for it says "even so, he did not have Bi'ah with her until a long time." It explains there that this was 30 days. It connotes that he did not have Bi'ah, but there was Nisu'in.

R. Chananel brings the Yerushalmi, which says "even though he entered her (made Nisu'in) he did not recognize her (have Bi'ah with her) until after 30 days."

An episode: A case occurred in which the brother of the betrothed died after the guests were invited, shortly before the Chupah. He (R. Tam) permitted the Nisu'in within Sheloshim, due to Peru u'Rvu of the Chasan;

This is because if he did not marry this one, he would not marry another.

Perhaps even if she was not betrothed, he would have permitted, because he desired her more than another [woman];

This is like we find regarding Yosef ha'Kohen. For the sake of nurture of his children, it was permitted, even though [also] she was an Avel due to her sister.

Rebuttal: We cannot learn from there, for it was not possible with anyone else, for she would have more mercy on her sister's children than other women.

Inference: Our Mishnah forbids Eirusin within Sheloshim, and does not distinguish. It is even if she wants to marry someone with small children, or one who has no children at all!

Explanation #1: This is because she must wait three months for Havchanah.

Explanation #2 (R. Tam): One who has no children may have Nisu'in and Bi'ah within 30 days, for one fulfills Peru u'Rvu only through Bi'ah;

However, within seven days of Avelus, Nisu'in is forbidden. This is clear from Kesuvos 4a;

We permit (Nisu'in within Shivah) only if the meat [for the wedding feast] was slaughtered and the wine was mixed (they will spoil if they are not consumed in a short time) and specifically the Chasan's father or Kalah's mother died;

We discuss there when he has no children, since we say that the Chasan's father will toil. (His father would not toil if his son was previously married.)

Implied question: R. Yosef ha'Kohen [had Nisu'in within Shivah]!

Answer #1: Even though he spoke with her in the cemetery, he did not have Nisu'in with her until after Shivah.

Answer #2: Perhaps for the sake of nurturing his children, Nisu'in was permitted even within Shivah.

Question: It says in Maseches Semachos (Perek 7) that regarding one's wife, he must wait three festivals if he has children;

If he has no children, or has small children, he may marry another after 30 days.

Answer: We must say that "he may marry" means Nisu'in and Bi'ah. Nisu'in alone is permitted even within Sheloshim, like is proven from the episode with R. Yosef.