Gemara

(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 three days before Yom Tov, Yom Tov cancels Shivah (the restrictions of the first seven days of mourning). If burial was eight days before Yom Tov, Yom Tov cancels Sheloshim (the restrictions of the first 30 days), and he may shave on Erev Yom Tov. If he did not, he may not shave after Yom Tov;

Aba Sha'ul says, in either case he may shave after Yom Tov. Just like fulfilling three days of Aveilus (before Yom Tov) nullifies the rest of Shivah, also seven days nullifies the rest of the 30.

Aba Sha'ul holds that the seventh day counts towards Shivah, and also towards Sheloshim.

Objection: Perhaps Aba Sha'ul said this only about the seven days of Aveilus, which are mid'Rabanan, but he would not say this about Nezirus, which is mid'Oraisa!

Pesachim 91b (Mishnah): An Onen immerses and eats Korban Pesach at night. He may not eat other Kodshim.

The Tana holds that Aninus Laylah is only mid'Rabanan. Chachamim did not apply this stringency to Pesach, for which there is Kares (for not bringing it). They apply their stringency to (eating other) Kodshim,

Berachos 16b (Mishnah): R. Gamliel bathed on the night after his wife died.

His Talmidim: You taught that a mourner is forbidden to bathe (for seven days)!

R. Gamliel: I am an exception, I am an Istenis (not bathing causes pain to me).

(Gemara) R. Gamliel holds that Aveilus on the night after death is only mid'Rabanan - "va'Acharisah k'Yom Mar" (mid'Oraisa, it is only during the day). Chachamim did not decree to forbid an Istenis.

Kesuvos 3b (Beraisa): If the food was prepared for a Nisu'in, and then the Chasan's father or bride's mother died, we put the deceased in a room until after the Chupah... All 14 days he sleeps among men, and she sleeps among women.

4a: This supports R. Yochanan, who says that even though we do not show signs of Aveilus during the Mo'ed (the seven days of nuptial festivities are like a Mo'ed), private matters (relations) are forbidden.

Rishonim

Rif (Berachos 9b): Some say that the seven days of Avelus are mid'Oraisa. They learn from "Va'Ya'as l'Aviv Evel Shiv'as Yomim". This is wrong. The Gemaros in Zevachim and Pesachim say that it is only mid'Rabanan. Only R. Yehudah holds that Aveilus of the first night is mid'Oraisa. The Halachah follows the other Tana'im. The Asmachta for seven days of Avelus is "V'Hofachti Chageichem l'Evel". Just like the Chag is seven days, also Aveilus.

Rosh (3:3): The Rif and some Ge'onim say that Aveilus of the first day is mid'Oraisa. The Ri says that it is mid'Rabanan. Only Aninus, i.e. the Isur to eat Kodshim or Ma'aser Sheni, is mid'Oraisa on the first day. Chachamim added other Isurim to Onenim before burial (Berachos Reish Perek 3). If it was mid'Oraisa, the seven days of Mishteh of a Chasan (whose father died) would not override Aveilus (Kesuvos 4a)!

Rosh: This does not refute the Rif. The Rif holds that Aveilus is mid'Oraisa only when the burial was on the day of death. He learns from Aharon and "va'Acharisah k'Yom Mar". When the Chasan's father died, we bury him the next day, so the Aveilus is not mid'Oraisa. The Ri brings another proof from Bechoros (49a). If a baby died on day 30, it is a Safek Nefel. We are stringent about Pidyon ha'Ben, but lenient about Aveilus. We would not be lenient about Aveilus if the first day were mid'Oraisa! Even though it is mid'Rabanan, the Gemara calls it an Aseh because there is an Asmachta. R. Gamliel holds that Aveilus on the night after death is only mid'Rabanan, therefore he was lenient (Berachos 16b). We may not infer that Aveilus of the day is mid'Oraisa. Rather, Aninus Yom is mid'Oraisa, therefore he was not lenient about Aveilus Yom. He was lenient only at night, when even Aninus is only mid'Rabanan.

Rambam (Hilchos Evel 1:1): Aveilus is mid'Oraisa only on the first day when it is the day of burial. The rest of Shivah is only mid'Rabanan. Moshe enacted that Yisrael observe seven days of Aveilus and seven days of Mishteh (for a Chasan).

Poskim

Shulchan Aruch (YD 398:1 and OC 696:7): Aveilus of the first day is mid'Oraisa if it is the day of death and burial. The rest of the days are mid'Rabanan. This refers to the seven relatives for whom a Kohen becomes Tamei. The other relatives are mid'Rabanan even on the first day. Some say that Aveilus of even the first day of death and burial is mid'Rabanan for all relatives.

Beis Yosef (DH u'Mah she'Chosav sheha'Ra'avad): The Ra'avad says that the Isurim of laundering and cutting hair for 30 days are mid'Oraisa. The Ramban disagrees.

Beis Yosef (DH u'Mah she'Chosav b'Shem): Perhaps the Rambam holds that it is mid'Oraisa, but he calls not explicit in the Torah 'mi'Divrei Sofrim'.