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The Gemara discusses whether a fence made with just Shesi (horizontal component) or just Eirev (vertical component) is a wall. Some opinions say that its not.

Then there is another Gemara which discusses whether a tree with branches sticking up is considered a diomed, or whether sticks with breaks under 3 tefachim can be called a diomed.

I don't understand. In all of these cases we should say Lavud.

When do we say Lavud and when when do we not?

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We do say lovud as long as they are less than 3 tefochim. These gemoros you mention are talking about where the distance between them is more.

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sources would greatly improve your answer – user2110 Apr 19 '13 at 12:40
It's not always. See hebrewbooks.org/… re. the Diomed – Shmuel Brin May 31 '13 at 5:04

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