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Kilayim 4:3-4 teaches various halachos about walls, as a wall could divide between fields to allow planting on either side. Among those halachos taught are:

  1. A wall must be 10 tefachim tall.
  2. A ditch must be 10 tefachim deep and 4 tefachim wide.
  3. Reeds forming a wall must be within 3 tefachim of each other.
  4. A gap of 10 amos is an entrance and does not ruin a wall; more than that is a breach and ruins the wall.
  5. There must be more wall than gaps.

These are all rules taught in other places: 1. Sukkah 1:1 2. Later in Kilayim, 5:3 2. Sukkah 1:9 is explained by the Gemara there as operating under the same principle, a Halacha L'Moshe MiSinai (which means this Mishnah is still unnecessary). This principle is called Lavud. See further Sukkah 4b and 5b. 3. Eiruvin 1:1 4. This is a general principle in Lavud, discussed in the sources above, in #2.

In fact, the masechta itself repeats itself when it says in 4:7 that a wall less than 10 tefachim allows for two fields to combine, but taller than 10 tefachim does not.

Now, you might say the chiddush is that these rules apply to Kilayim as well. Well, the Mishnah makes clear the issue is that it's a מחיצה - a word used to split between domains. The Kehati emphasizes this point, that the Mishnah is trying to make each field a separate domain, and the Mishnah cited in 4:7 would seem to make that point as well by talking about "combining" fields.

Principle #1 would seem to also be working behind the Halacha in Kilayim 5:4, that a house in a vineyard counts as a separation.

So, then, why are these principles taught in so many places? Isn't just one enough?

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    You could broaden this question to be about the repetition of mishnayot in general. Some mishnayot are repeated verbatim in other masekhtes, while some contain dinim that can be explicitly learnt out from other mishnayot. Is there anything about your question that needs it to concern the halakhot of kilayim specifically? – Shimon bM Jul 17 '17 at 6:46
  • @Shimon First of all, perhaps there's a specific reason for these Mishnayos to be repeated. Second, what are the odds that asking for every Mishnah would get closed as too broad? Maybe there's a different reason in each case. As noted elsewhere, many times a Mishnah is repeated just because it's relevant, or to lead in to the next discussion. But as I noted there, that doesn't seem to always apply - hence the down-arrow on that answer. – DonielF Jul 17 '17 at 18:41

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