Gemara

22b (Mishnah): If a Chatas was lost and a replacement was offered, and then the Chatas was found, it must die.

23a (Rav Huna citing Rav): All agree that if the owner took one of the animals and offered it, the other must die. They argue about one who asks Beis Din what to do:

Chachamim enact to offer the lost Chatas, lest the other need to die;

Rebbi does not enact regarding Kodshim. Rather, we offer the replacement, and the lost Chatas must die.

Question (Rav Mesharshiya): (All agree that) we make enactments about Kodshim!

(Beraisa): "Yochlu" teaches that if Kohanim receive a small amount of Menachos to eat, they eat Chulin and Terumah first, in order to eat Kodshim when they are satiated.

(Beraisa): "Yochluha" teaches that if they have much Menachos to eat, they do not eat Chulin and Terumah with them, lest they gorge themselves to eat Kodshim when they are stuffed.

Suggestion: Even Rebbi agrees with this enactment!

Answer: No, only Chachamim enact about Kodshim.

(Rav): (On Yom Kipur, if a lottery determines which of two goats is a Chatas (offered to Hash-m) and which is Mishtale'ach (sent to Azazel). If the Mishtale'ach died, we take two other goats and do another lottery.) The goat from the first pair is offered.

This is as Rav holds elsewhere, that the Mitzvah is to offer the first one. (See below.)

Yoma 64a (Rava): Rav holds like R. Yosi, who says that the Mitzvah is with the first one.

Suggestion: He refers to R. Yosi's opinion about boxes.

(Mishnah): There were three boxes for taking Shekalim for Terumas ha'Lishkah. They are labeled Aleph, Beis, Gimel.

R. Yosi: They are labeled so we will know which is first, for the Mitzvah is to buy Korbanos Tzibur from the first box.

Rejection: Perhaps there is different, for when the first was proper (for the Mitzvah), the second was not.

Rather, Rava refers to R. Yosi's opinion about Pesach;

(Beraisa - Chachamim): If one was Makdish a Korban Pesach, and it was lost, and he was Makdish a replacement, and then the first was found, he offers whichever he wants;

R. Yosi says, the Mitzvah is to offer the first;

If the second was nicer, he offers it.

Rishonim

Tosfos (23a DH d'Rebbi): Since we can fix the Korban (offer the lost one, and the replacement will graze), why do we overtly (offer the latter, and) cause it (the lost one) to die! My Rebbi answered that this is when we gain through this, e.g. the lost animal is lean and the replacement is fat. Then we say that he should atone through the fat animal, and the lean animal will die.

Rambam (Hilchos Korban Pesach 4:6): If one lost his Korban Pesach and was Makdish a replacement, and later found the original, he may offer either one.

Lechem Mishneh (Hilchos Avodas Yom Kipur 5:16): Ri Korkus asked why this is unlike one who lost a Chatas and was Makdish a replacement. I answer that the Rambam holds that a Chatas comes for atonement, so it is more stringent, and Rabanan agree that the Mitzvah is to offer the first one. Rabanan argue about, which is not for Kaparah. The Gemara (Yoma 64a) means that just like R. Yosi holds that regarding Pesach the Mitzvah is to offer the first, Rav holds that here that it comes for Kaparah, all agree that the Mitzvah is to offer the first.

Sha'ar ha'Melech (Hilchos Korban Pesach 4:6): This is difficult, for in Temurah we say that if he offered one, all agree that the other must die. They argue about one who asks Beis Din what to do. Rebbi holds that we do not enact regarding Kodshim. We offer the replacement, and the lost Chatas must die. Rabanan hold that we enact regarding Kodshim. According to the Lechem Mishneh, since Chatas is for atonement, Rav holds that all agree that the Mitzvah is to offer the first. The Rambam holds that there was no enactment. He should obligate offering the first! Also, why did we say that Rabanan enact to offer the first so that neither animal must die? The Mitzvah is to offer the first! Granted, if we would say that R. Yosi and Rabanan argue about Chatas just like they argue about Pesach, we could say that Rebbi and Rabanan hold like Rabanan of R. Yosi. Rather, we can answer like Tosfos. When the latter is nicer, all agree that there is no Mitzvah to offer the first. However, the continuation is difficult for Tosfos. Why did the Gemara say that the enactment about eating Chulin before Kodshim is only like Rabanan? It is even like Rebbi! Rebbi enacts when there is no benefit! Rather, also there there is a benefit, in order that Kodshim be eaten when satiated, the way kings eat.

Rosh (Teshuvah 2:9, brought in Beis Yosef OC 13 DH v'Chasav ha'Rosh): The custom is to fix Tzitzis (when some of the ends snapped) even before they are Pasul.

Mordechai (Menachos 948): Only the same Min (type) (of string) can exempt a garment. Rashi explains that one must put red strings on a red garment. This is difficult, for the Gemara said that the color does not matter! Rather, it teaches that the same material must be used, e.g. silk strings for a silk garment. Alternatively, mid'Rabanan we require the same color, due to Zeh Keli v'Anvehu.

Sefer Chasidim (879): If one wrote a Sefer Torah, and one of the Dapim (parchments) is not as nice as the others, even if there is no mistake in it, he may remove it and bury it and write a nicer Daf. This is not Bal Tashchis (being wasteful), for it says "Zeh Keli v'Anvehu."

Poskim

Shulchan Aruch (OC 15:1): One may remove Tzitzis from a Talis to put them on another Talis, but not if he will not put them on another Talis.

Magen Avraham (2): Tosfos says that it is because one may not be Mevatel the Mitzvah from this Talis. I say that if he wants to convert the Talis into a garment without four corners, it is permitted. Menachos 43a forbids selling a Talis with Tzitzis to a Nochri. This connotes that one may remove the Tzitzis, for when he buys it, it is not obligated. The She'altos forbids removing Tzitzis if he will sell it to a Yisrael, unless he will put them on another garment. Likewise, he permits removing a Mezuzah in order to put it on another opening. Tosfos forbids regarding a Mezuzah. The Levush permits removing Tzitzis in order to put on nicer Tzitzis, even though the first ones are Kosher. I say that the same applies if the first ones were cut, even though they are still Kosher. Teshuvas ha'Rosh permits.

Birkei Yosef (4): R. David Shriro says that the Isur to remove Tzitzis is due to disgrace to the Talis. Even so, it is permitted if he will put them on another Talis. If so, why does Shirei Keneses ha'Gedolah bring that the Levush permits if one will put nicer Tzitzis on the Talis, due to Zeh Keli v'Anvehu. Why is this only if the latter are nicer? It should be permitted because he does not leave the garment without Tzitzis! Perhaps the Levush's Chidush is lest one err and think that the Shulchan Aruch means that one must put them elsewhere (on another garment), but one may not discard them, and along with this he taught that he will make nicer ones. We do not discuss fools who would replace them with others that are the same or worse. If he will replace them, one may even cut the old ones.

Birkei Yosef: R. David assumes that we are concerned only for disgrace to the Talis, but not for disgrace to the Tzitzis. This is unreasonable. The Tzitzis are the Mitzvah. The Talis is the person's garment. How can it be more stringent?! Really, the Levush said 'it is forbidden only if he removes them without intent to put on another garment, and he will not put other Tzitzis on this garment, for this disgraces the Tzitzis or the garment.' He mentioned disgrace to the Tzitzis before disgrace to the garment.' Therefore, one may remove Tzitzis and discard them only if he will put nice Tzitzis in place of them. This is permitted to beautify Mitzvos. If they are no better, it is forbidden.

Mili d'Avos (5 OC 8, cited in Yabi'a Omer 3 YD 18:5): Yad Yitzchak (3:277,339) forbids removing a Mezuzah in order to put up a more beautiful one. The Magen Avraham did not see the Levush inside, for the Levush permits putting on nicer Tzitzis even if he will discard the old Tzitzis. Surely one may not do so regarding a Mezuzah, for this disgraces the Mitzvah. I say that if he will put up a nicer Mezuzah and bury the old one, it is permitted, due to Zeh Keli v'Anvehu.

Yabi'a Omer (ibid.): Also Heshiv Moshe and Misgeres Zahav on Kitzur Shulchan Aruch say so. Sefer Chasidim supports them.

Shulchan Aruch (OC 649:1): If a Nochri tied a Lulav, it is Kosher, just like the Sukah of a Nochri.

Magen Avraham (8): This implies that l'Chatchilah, a Nochri should not tie it. This is difficult, for we hold that one need not tie it. This is not part of the Mitzvah! We must say that since it beautifies Mitzvos, it is considered like the Mitzvah itself.

Chacham Tzvi (45): If one was sticking wax candles to the wall to light them for Ner Chanukah, and they brought to him olive oil, should he abandon the candles and light the olive oil, which is the ideal Mitzvah? Shevus Yakov ruled that he lights the candles. I disagree. He bring a proof from Yoma 6b, in which Rav Sheshes says that if one was offering the Omer and it became Tamei, he brings another, for Tum'ah is Hudcheh (permitted b'Di'eved. It is not totally permitted) b'Tzibur. If we cease a Mitzvah to do it in a nicer way, what is the proof that Tum'ah is Hudchah? Even if Tum'ah were Hutrah, and a Tamei Mishmar (division of Kohanim) may offer it if it is their turn, even if other Mishmaros were Tehorim, we would seek to do the Mitzvah b'Taharah! This is no proof, for there they already started the Mitzvah. Here, he merely prepared candles. Also, what is his source that it is a greater Mitzvah to seek a Tahor Minchah than Tahor Kohanim? Just the contrary! There is a greater punishment for Tum'ah of people (Kares) than for Tum'ah of Korbanos (a Lav)! Also, Rav Nachman said that we bring another only if Kohanim will eat the remainder. Here, if he lights candles, he is Mevatel Hidur Mitzvah and transgressed Zeh Keli v'Anvehu. In Yoma 64a, we suggested that Rav learns from R. Yosi's opinion about boxes. Even if one is holding the third box, he puts it down and takes from the first box. Here also, he puts down the wax and lights the olive oil, which is the choice Mitzvah. Do not learn oppositely from there, that the first box has precedence because it was ready for the Mitzvah before the latter boxes were, and here the wax was ready before the olive oil. I.e. the first overrides what came later, even though the person is holding the latter, so wax overrides olive oil, which came later. This is wrong. Regarding the boxes, the only advantage of the first is that it preceded the other. R. Yosi explicitly says that of the second was superior, we offer it.

Birkei Yosef (OC 272:1): If one blessed on wine that was exposed, and in front of him was Kosher wine (that was not exposed), must be he say Kidush again on the Kosher wine? Even if you will say that b'Di'eved Kidush on exposed wine is valid, he must say Kidush again, just like if one slaughtered a lean Chatas, we tell him to slaughter the fat one. Because one who brings an inferior animal transgresses "Hakrivehu Na..." (do not offer inferior animals to Hash-m), he offers another and does several Avos Melachos on Shabbos. Also here, one who made Kidush on exposed wine transgressed "Hakrivehu Na". Even though it is not like "Hakrivehu Na" of Korbanos, and some say that Kidush on wine is mid'Rabanan, there we do Avos Melachos, and here we make an unnecessary Berachah, which some say is mid'Rabanan. This requires investigation.