Part of this Tosfos deals with Hachanah. He explains that Hachanah only happens with the creation of something new. Therefore, when cooking on Yom Tov for a weekday, you are not creating something new, as all the ingredients were available already, so you would be over on Bishul, since Bishul is only permitted for that day's needs.

However, the source for Hachanah is the pasuk that begins Vhayah B'yom Hashishi, which deals with the mun. The mun came down to earth already in an edible state. So, how can Tosefos say that Hachanah is only with the creation of something new?

I asked your question to a talmud chacham muflig (who has a grasp in the whole shas).He said the whole drasha in Rashi needs an explanation. Rashi starts by stating that this Hachana cannot be cooking since it says this in posek by itself. So this hachana has to be "hazmanah b'peh". what kind of "hazmanah b'peh" is needed for the mon?
He thinks that realy mon has the same shelftime on friday as the rest of the week, but by pronouncing it that it's for kovod shabbos gives it longevity for the shabbos. So the preperation on the day before makes the mon able to exist on shobbos

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Question: Does not the fact that a double portion given on Yom shishi "friday" prove that its purpose of existence was already for Shabbat? I believe that pronouncing that it is kovod shabbos is more of a recognition rather then a preparation , for the mun was already complted in heaven.

It could be argued that it was given on Friday was not that it will last on shabbos, rather that it was given to have the ability for it to last for Shabbos. Since it could be learned both ways in itself, but to understand Tosfos, only the second way of learning fits in. To the first way, it would seem that it was a ready made food, thus evn ready made foods would be prohibbited to prepare from Yom Tov to Shabbos, but is mutter (with an Eiruv Tavshilin Midirabanan) even if one doesn't hold of "Hoyil"

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I recall learning in the Gemara that it is prohibited to use something prepared for Yomtov for the purpose of Shabbat however if we happen to find something on Yomtov that was not prepared for the purpose of the yomtov then we are allowed to reserve it for shabbat as long as we cover it with something, unfortunately I have no access at the moment to the Gemara. Can anyone help me with this?

In tractate Beitza 3B "an egg that was laid on Shabbos or Yom Tov (that is prohibitted by Rabba on 2B because of a yom tov after shabbos or vice versa, if laid on the second day, then it was completed in the mother from the day before, hence being a preperation for a shabbos or Yom tov on a shabbos and Yomtov (which is learned from the obligation of preparing the mun on friday). A regular Shabbos or yom Tov, the egg is prohibbited rabinnicaly, lest you'll permit even if Shabbos and Y.T. are together) you may not move it..... but you may cover it with a utensil
The case of the egg laid on Y.T. or shabbos is what Tosfos (which this whole post was started by) is making a diference to cooking on Y.T. for Shabbos which is permitted.

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