Gemara

(Mishnah): A rapist must marry the girl. If she is forbidden to Yisraelim, he may not keep her. "V'Lo Sihyeh l'Ishah" - she must be permitted to him.

40a - Question (Rav Kahana): The Aseh to marry her should override the Lav!

Answer (Rav Zvid of Nehardai): An Aseh overrides a Lav in cases such as cutting off Tzara'as during circumcision, since there is no other way to fulfill the Aseh. Here, if she says that she does not want to marry him, there is no longer an Aseh!

Yevamos 6b (Beraisa - Tana d'Vei R. Yishmael) Suggestion #1: Perhaps "When a man is Chayav Misah he will be killed" applies even on Shabbos, and "Mechaleleha Mos Yumas" applies to Melachos other than Misas Beis Din!

Suggestion #2: Or, perhaps "Mechaleleha Mos Yumas" applies even to Misas Beis Din, and "he will be killed" is only on a weekday!

Revival of Suggestion #1: Or, perhaps it is even on Shabbos!

Rejection of Suggestion #1: It says "Do not kindle fire in all your dwellings on Shabbos", and "... judgment... in your dwellings". Just like the latter "dwellings" refers to Beis Din, also the former, and the Torah forbids burning.

First, the Tana thought that execution overrides Shabbos just like an Aseh overrides a Lav. Later he thought otherwise (even before bringing the verse), because we find that an Aseh overrides a simple Lav, but not one that has Kares.

He later thought that an Aseh overrides a Lav even though a Lav is more severe. If so,this is even if it is much more severe (i.e. Kares)! Therefore, we need "Do not kindle..." to forbid execution on Shabbos.

Shabbos 132b (Rav Mesharshiya): "Besar" written regarding Milah on day eight permits a father who intends to cut his son's Tzara'as on the foreskin.

We must say that there is no one else (who is not concerned about the Tzara'as) who can circumcise. If not, the father would not be allowed!

(Reish Lakish): If one can fulfill an Aseh without transgressing a Lav, he must; if not, the Aseh overrides the Lav.

Bava Metzi'a 30a (Beraisa): "V'His'alamta" - sometimes you ignore an Aveidah, e.g. if a Kohen sees an Aveidah in a cemetery, or a Chacham sees an Aveidah that it is undignified for him to carry it... he ignores it.

We do not need the verse for a Kohen who sees an Aveidah in a cemetery. Returning an Aveidah is an Aseh. It does not override the Aseh ("Kedoshim Yihyu")and Lav forbidding a Kohen to become Tamei.

Also, Isurim are not overridden for (Mitzvos pertaining to) money!

Nazir 57b: Rav Huna equates "Do not round the corners of your head" and "Do not destroy the corners of your beard". Whoever is commanded about the beard is commanded about the Pe'os;

Since women are not commanded about the beard, they are not commanded about the Pe'os.

Rav Ada bar Ahavah holds that the verse equates the Makif (one who cuts Pe'os) and Nikaf (one whose Pe'os are cut). Whenever the Nikaf is liable, the Makif is liable;

The Torah does not punish children. Since a child is exempt, one who is Makif a child is exempt.

Rishonim

Rif (Kesuvos 14a): The Mitzvas Aseh to marry one's Anusah does not override the Lav. Aseh Docheh Lo Sa'aseh only in cases such as cutting off Tzara'as during circumcision, since there is no other way to fulfill the Aseh. Here, if she says that she does not want to marry him, there is no Aseh at all!

Ramban (Bava Metzi'a 30a DH v'Ika): Some texts say 'Isurim are not overridden for monetary Mitzvos.' I.e. if a Kohen himself lost an object in a cemetery, he would not be allowed to take it. Surely he may not take another's Aveidah! If the owner would say that he does not want the Aveidah there is no Mitzvah. The owner is obligated to say so to spare the Kohen from becoming Tamei. He is also commanded to honor Hash-m. The Torah commanded to return Aveidos, honor parents with one's money and not transgress Mitzvos.

Note: It would seem that this does not apply if we know that the Aveidah belongs to a child, who is exempt from Mitzvos.

Ramban (ibid.): The Gemara (Kesuvos 40a) says similarly that the Mitzvah for a rapist to marry the girl does not override a Lav such as Mamzeres, because she could uproot the Mitzvah by saying that she does not want to marry him. Even if she desires him we do not accede, for both of them must honor Hash-m. The Torah did not say Aseh Docheh Lo Sa'aseh in such cases.

Ran (DH v'Neisi): The Gemara asked why the Aseh is not Docheh. If the verse teaches that it is not, we should learn from here that an Aseh is never Docheh a Lav! It answers that a light Aseh which can be uprooted (if she does not want him) is not Docheh a Lav. Similarly, we learn from "V'His'alamta" that the Aseh of Hashavas Aveidah is not Docheh Tum'ah (Bava Metzi'a 30a). Even though we allow (wool) Techeiles on a linen garment, this is because in any case there is a Mitzvah without Techeiles. Even a wool garment is obligated.

Rambam (Hilchos Tzitzis 3:6): One would have thought that we may put linen Tzitzis on a wool garment or vice-versa, even Lavan (white threads) without Techeiles, since Sha'atnez is permitted in Tzitzis. Techeiles is wool, and we put it even on linen garments. However, we do not permit Sha'atnez for Lavan, since we can fulfill this without Sha'atnez, with threads like the garment. Whenever there is an Aseh and a Lav, if we can fulfill both this is best. If not, the Aseh is Docheh the Lav. Here it is possible to fulfill both.

Kesef Mishneh: The Rambam does not discuss when there is Techeiles on a linen garment. Then, since Techeiles is Docheh Sha'atnez, one may put also wool threads for Lavan. Tosfos says that we do not say that one can fulfill both with a wool garment, for this is not considered 'possible' (regarding this garment). It seems that this is no question at all. If we would say there is no Dichuy because one can wear wool, we could not explain the Semichus of Sha'atnez to Tzitzis!

Rosh (Kesuvos 3:6). An Aseh is Docheh a Lav only in cases such as Milah b'Tzara'as or Kil'ayim b'Tzitzis, since there is no other way to fulfill the Aseh. Here, if she says that she does not want to marry him, there is no Aseh at all! Therefore, even if she wants him it is not Docheh, for it is unlike Milah b'Tzara'as.

Question (Nimukei Yosef Bava Metzi'a 16a DH v'Al): Why did the Gemara mention the Aseh of Tum'as Kohanim? Even if it were only a Lav, the Aseh of Hashavas Aveidah would not override it because one transgresses the Lav before fulfilling the Aseh! Dichuy is only when the Aseh is b'Idna (done at the time one transgresses the Lav), like Milah b'Tzara'as!

Answer (Nimukei Yosef citing the Ran): Since one engages in the Aseh while transgressing the Lav, it is Docheh. Also Milah is not finished until Pri'ah, nevertheless cutting the foreskin overrides the Lav of cutting off Tzara'as!

Rebuttal (and Answer #2 - Nimukei Yosef): This applies when if one stopped in the middle he did part of the Mitzvah, e.g. he cut half the foreskin or put Tzitzis on two corners. The Ran holds that the Aseh of Hashavas Aveidah begins from when one sees it. However, others say that the Mitzvah is only returning it to the owner. Everything before this is only Hechsher Mitzvah, and it is not Docheh anything. Rather, the Gemara says that even if the Aseh would be b'Idna, it would not be Docheh Tum'ah.

Question: Why is Tiglachas Metzora Docheh Hakafah? The Aseh is only when he finishes, but he transgresses once he starts cutting one Pe'ah!

Answer #1 (Tosfos Gurnish, brought in Aruch l'Ner Yevamos 5a DH bi'Gmara): We must say that one Pe'ah and the rest of the hair were already cut. He fulfills the Mitzvah when he cuts the other Pe'ah.

Answer #2: Keren Orah (Nazir 41a DH v'Su): Every hair that he cuts is a Mitzvah.

Answer #3: According to the Ran and Nimukei Yosef above, it suffices that he engages in the Aseh.

Suggestion: The Aseh of Tiglachas Metzora overrides the Lav of Hakafah (Yevamos 5a). Rav Ada must agree that the Nikaf is liable even if the Makif is not, for otherwise we would require a Metzora to be shaved by a Nochri or woman and not allow Dichuy!

Rejection (Tosfos Shevuos 3a DH v'Al): The verse is needed for when no woman or Nochri is available. We do not wait for one, just like the Gemara (Chulin 141a) suggested that the Aseh of Taharas Metzora overrides Shilu'ach ha'Kan. We do not say that he should wait for another bird!

Question: Tosfos holds that since he becomes Tahor no matter who shaved him, if it could be done without Dichuy, it would not be Docheh. If so, we can learn from there! Also, even in the conclusion that Rav Ada agrees that the Nikaf is always liable, why may a man shave him? We should require someone who is not commanded, to minimize the Dichuy!

Answer (Afikei Yam 2:34 DH Ulam): Reish Lakish does not allow Dichuy when it is possible to fulfill both, i.e. the person himself can fulfill both. If not, there is Dichuy, even if someone else could fulfill both without Dichuy.

Question: In Shabbos (132b) we learn from Reish Lakish that a father who intends to cut his son's Tzara'as may not circumcise if someone else (who is not concerned about the Tzara'as) could circumcise!

Answer #2 (Afikei Yam DH veha'Nir'eh l'Aniyas): Anyone can perform the primary Mitzvah of Milah, to circumcise the baby. There is an additional Mitzvah for the father himself to circumcise. Thirteen covenants were made on the primary Mitzvah, so it overrides the Lav and Aseh of Tzara'as. The additional Mitzvah does not override them.