Beit Midrash
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- Chemdat Yamim
- Bemare Habazak - Rabbis Questions
Answer: The Rambam (Shabbat 23:7) says that washing dishes is forbidden (based on Shabbat 118a) because it is "like fixing" the dishes, but since it is forbidden only if done for use after Shabbat, it must be based on hachana, which tells us about how the Rambam defines it. The Ra’avad (ad loc.) argues that it is forbidden because he is toiling on Shabbat for a weekday.
The halachot of hachana are elusive, because several gemarot and accepted rulings of Rishonim seem to ignore it. There are opinions that only "transformative" actions (seemingly following the Rambam’s approach) or more taxing activities (seemingly following the Ra’avad’s) (see the development of Eliya Rabba’s (308:8) thesis in Pri Eliezer III, p. 616) or actions that finish a process (see Chayei Adam II, 153:6) are included. While in cases with lenient characteristics and/or need, poskim entertain leniencies (see ibid.; Mishna Berura 667:5), in general we apply hachana expansively, following the Magen Avraham (667:3), who forbade even bringing wine for Havdala on Shabbat.
If changing mantels had halachic rules, it might impact your question. For example, if it needed to be done by the next laining, we could compare it to rolling a sefer Torah on Shabbat to the right place for the upcoming Yom Tov’s laining, which most poskim forbid (Mishna Berura 667:5). However, we have not found such halachot and don’t believe they exist. Rather, people (some more than others) like to be "on the right page" chronologically. The shul looks unprofessional if the chagim and/or Yamim Noraim adornments are still around much thereafter and for some gabbaim and/or shuls, doing it promptly is significant as a matter of pride.
We can now compare it to a different case. Although it is forbidden to make a bed on Shabbat to sleep in it on Motzaei Shabbat (Shabbat 113a), it is permitted to straighten it out so that it is aesthetically appropriate according to the household’s Shabbat standards (Magen Avraham 302:6; Mishna Berura 302:19). Poskim presume the same is true even if it is more significant for him as preparation for sleep that night. On the other hand, there seems to be a proof, from the halacha (see above) not to wash dishes on Shabbat after one finished his last meal that to permit potential hachana based on Shabbat, that benefit must be quite significant (at least in comparison to the weekday benefit). One can ask: Besides having utensils for the next meal, don’t people prefer not having dirty dishes around their kitchen?! Apparently, in comparison to the positive benefit of having clean dishes, not having dirty dishes around is not halachically significant.

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It is difficult to claim the action of switching the mantels does not fall under the realm of hachana. It is not trivial in terms of time/effort, there was no special need, and it was clearly for after Shabbat. While the switching might be less transformative for the sifrei Torah than washing is for dishes, at least the great majority of poskim would forbid it.

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