Gemara

15a (Mishnah): If one said 'I will be a Nazir when I have a son. I am a Nazir for 100 days', and he had a son within 70 days, he does not lose any days counted.

(Rav): The 70th day counts for both Neziruyos.

Suggestion: Rav holds like Aba Sha'ul.

(Beraisa): If burial was eight days before Yom Tov, Yom Tov cancels Sheloshim (the restrictions of the first 30 days of mourning).

Aba Sha'ul says, seven days of Aveilus before Yom Tov nullify the rest of Sheloshim.

He holds that day seven counts towards Shivah and towards Sheloshim.

Objection: Perhaps Aba Sha'ul says so only about Aveilus, which is mid'Rabanan, but he would not say so about Nezirus, which is mid'Oraisa!

Answer #2: Rav holds like R. Yosi:

(Mishnah - R. Yosi): If the Korban Pesach was offered for a Shomeres Yom k'Neged Yom (a woman on the morrow of seeing non-menstrual blood), and later that day she saw blood, she is exempt from Pesach Sheni.

R. Yosi holds that Miktzas ha'Yom k'Kulo. (Since she did not see blood at the very start of the day after her first sighting, it is like a full clean day. Therefore her next sighting does not join with the first to make her a Zavah Ketanah retroactively. Therefore, she was Tehorah at the time of Shechitah.)

Question: According to R. Yosi, how can a woman bring a Korban for Zivah (for seeing blood three consecutive days)? The first part of the second (or third) day, before she saw, should be considered an intervening clean day!

Answer #1: Blood flowed continuously from the first day until the third day.

Answer #2: On three consecutive nights, she saw at the start of the evening, so there was no time to count like a day.

Mo'ed Katan 19b (Abaye): The Halachah follows Aba Sha'ul regarding day seven. Chachamim agree that Miktzas ha'Yom k'Kulo on day 30.

(Rava): The Halachah follows Aba Sha'ul for day 30, but not for day seven.

Neharda'a: The Halachah follows him regarding both, for Shmuel taught that the Halachah follows the lenient opinion in Aveilus.

Megilah 20a: A Shomeres Yom cannot immerse the next night. This is because she must count (a clean day), and counting must be by day.

Rishonim

Rif and Rosh (Mo'ed Katan 11a and 3:26): If the seventh day of Aveilus is Erev Yom Tov, he may shave, for Miktzas ha'Yom k'Kulo, and the seventh day also counts like day eight, i.e. part of Sheloshim. Chachamim agree that Miktzas ha'Yom k'Kulo on day 30. Rava says that the Halachah follows Aba Sha'ul regarding day 30, but not regarding day seven. Neharda'a say that the Halachah follows him regarding both, for we follow the lenient opinion in Aveilus.

Rambam (Hilchos Evel 7:1,2): If one heard about the death of a relative more than 30 days ago, he observes only one day of Aveilus. Miktzas ha'Yom k'Kulo. I.e. since he observed Aveilus for a short time, it is as if he observed the entire day. He may wear shoes, bathe, etc. the rest of the day.

Rosh (30): The Rivam's Rebbi was unsure whether or not Miktzas ha'Yom k'Kulo applies also to part of the night. If one heard a Shmu'ah Rechokah (that a relative died more than 30 days ago) at night and sat (observed laws of Aveilus) part of the night, may he bathe at night? The Rivam concluded that Miktzas Laylah does not help. It is not evident that he observed Aveilus, for people often remove their shoes at night. The Rashbam says 'the custom is to sit part of the day on day seven. Miktzas Laylah does not help. I do not know why.' Rabbeinu Meir (me'Rotenburg) says that if one heard a Shmu'ah Rechokah at night and sat part of the night (Bach's text), it is like Kulo. We do not say so about day seven of Aveilus. Shiv'ah ends when the consolers leave, during the day. It seems that part of the night does not help for Sheloshim, for counting must always be during the day, like it says in Megilah (20a). He must wait until sunrise. Miktzas Laylah helps for Shmu'ah Rechokah, for it does not require counting.

Rosh (37): The Rif (13a) permits an Avel to wear Tefilin on day two. This is like R. Yehoshua ben Levi, who forbids two days, but Miktzas ha'Yom k'Kulo. Is he permitted right after sunrise, or not until the consolers leave, i.e. after Shacharis? It seems that only Shiv'ah depends on when the consolers leave, for they console him all seven days.

Hagahos Ashri (Chulin 3:31): If the consolers left on day seven, Aveilus ends, for Miktzas ha'Yom k'Kulo. However, Miktzas Laylah is not like the entire day.

Poskim

Shulchan Aruch (YD 395:1): Once the consolers leave on day seven, everything forbidden during Shivah is permitted. The same applies to Sheloshim. After sunrise on day 30, the laws of Sheloshim do not apply.

Rema: In our lands, we do not normally console on day seven. He must wait until consolers normally come on other days, i.e. after people leave the Beis ha'Keneses. Some wait an hour. This is wrong.

Shulchan Aruch (2): If one heard a Shemu'ah Rechokah at night, since any time (of Aveilus) suffices, he fulfills this even at night.

Beis Yosef (DH u'Mah she'Chosav Yesh and DH veha'Ramban): The Mordechai brought only Rabbeinu Meir's opinion (that Miktzas Lalylah helps only for Shemu'ah Rechokah). The Ramban says that it is always like a full day. We follow Rabbeinu Meir (text of Chidushei Hagahos), for he is Basra and his reasoning is sound.

Ramban (Toras ha'Adam, Sha'ar ha'Evel, cited in Gra 1): We learn from R. Yosi that Miktzas Laylah is like a full day. Chachamim disagree only because if she sees later in the day, it nullifies the day. We extend Aveilus until the consolers leave on day seven because it is the custom for them to come. The Gemara obligates inverting the bed on Motza'ei Shabbos when it is day seven. This is a Chidush only if Miktzas Laylah is like a full day! In pressed circumstances, R. Tam permitted an Avel to bathe on the seventh night.

Taz (402:4): If one heard a Shmu'ah Rechokah on Shabbos, since he cannot observe proper Aveilus on Shabbos, we cannot apply Miktzas ha'Yom k'Kulo until the next day.

Shulchan Aruch (399:3): If one buried his relative seven days before the festival and observed Shivah, the festival nullifies Sheloshim. Even if day seven is Erev Yom Tov, Miktzas ha'Yom k'Kulo, and the seventh day also counts for Sheloshim.