Sukkah, Chapter 3, Mishnah 1. The third chapter opens the discussion of the mitzvah of the four species - the lulav, the esrog, the hadas and the aravah - which are taken on Sukkos. The Mishnah begins with the laws of the lulav and rules: "Lulav hagazul v'hayavesh - pasul" - a stolen lulav and a dried out lulav are invalid.
A stolen lulav - two reasons for its invalidity:
"Lachem" - yours. The verse says, "And you shall take for yourselves on the first day," from which we learn that the four species must belong to the person taking them, and a stolen lulav is not his. There are, however, circumstances and opinions according to which a thief does acquire ownership of what he stole - such as after the owners have despaired of recovering it, which according to one opinion is sufficient on its own, or after time has passed - and even though he is obligated to pay its value, he becomes its owner.
A mitzvah that comes through a transgression - even if the lulav has become his property, a person cannot fulfill a mitzvah with something that came into his hands through a sin.
"V'hayavesh" - a lulav that has dried out is invalid, because the four species must be beautiful (hadar). This principle is derived from the esrog, which the Torah describes as "the fruit of a beautiful tree," and from there we learn that the other species too must retain their natural beauty. Therefore a lulav that has significantly dried out is no longer valid.
"Shel asheirah v'shel ir hanidachas - pasul" - one from an asheirah tree or from a condemned city is invalid:
Asheirah - a lulav that comes from a tree that was worshipped as idolatry, as people would worship trees.
Ir hanidachas - a city in which the majority of the residents worshipped idolatry, which the Torah commands to destroy and to burn everything in it.
The reason for the invalidity in both of these cases is the same, and it applies even when the person taking the lulav had no part in the matter and simply found it along the way: since the halachah is that there is a mitzvah to burn these items, they are considered as though they are already burned. And since a lulav requires a certain minimum size, its required measure is missing - for it is regarded as nothing more than ashes - and it is therefore invalid.
"Niktam rosho, nifretzu alav - pasul" - if its top was cut off, or its leaves were split off, it is invalid:
Three understandings are offered in explaining "nifretzu alav":
The leaves were detached from the lulav, and afterward someone tied them back on.
The leaves were not fully detached, but are still partially attached.
Each and every leaf was split in two, and although it is attached, it is split.
In all of these cases the lulav is invalid.
"Nifredu alav - kasher" - if its leaves separated, it is valid:
If the leaves of the lulav were not detached but merely separated from one another, and they are still attached and spread out in the way that palm fronds spread apart, it is valid. Rabbi Yehudah adds a qualification and rules: "Ya'agdenu milmalah" - he should bind it at the top. The leaves must be tied and pressed against the lulav itself, for the mitzvah cannot be fulfilled with spread out leaves. It is enough that they be held against the lulav by means of the binding, even though they are not attached to it naturally.
"Tzinei har barzel - kesheirim" - the palms of Har Barzel are valid:
Tzinei har barzel are a particular type of lulav whose leaves are naturally very short, and the Mishnah rules that it is valid. The Gemara qualifies this ruling and makes it conditional on the end of one leaf reaching over the beginning of the leaf that follows it. But if the leaves are so short that each leaf ends before the next one begins, it is invalid.
"Lulav sheyesh bo shloshah tefachim k'dei l'na'anei'a bo - kasher" - a lulav that has three tefachim, enough to wave with it, is valid:
The Gemara explains that the words "enough to wave with it" should be read as though it said "and enough to wave with it," meaning: in addition to the three tefachim, another tefach is required for the waving. The result is that there are three tefachim that are waved, and one tefach that a person holds and waves with - and this is the required measure of a valid lulav.
In summary: in this Mishnah we learned the disqualifications of a lulav: a stolen one, because of the requirement of "lachem" and because of a mitzvah that comes through a transgression; a dried out one, because of the requirement of hadar; and one from an asheirah or from a condemned city, which, since there is a mitzvah to burn them, are considered as already burned and lack the required measure. We also addressed a lulav whose top was cut off and one whose leaves were split off, which are invalid, as opposed to one whose leaves merely separated, which is valid - and according to Rabbi Yehudah he should bind it at the top; the validity of tzinei har barzel provided that the end of one leaf reaches over the beginning of the next; and the measure of the lulav - three tefachim plus another tefach for the waving.