Daf Yomi - Sukkah 19 - Nothing into Something and Vice Versa

The Chacham Tzvi (59) rules that we cannot apply the principle of lavud when there is something in between. The source for this seems to be a Tosfos on our daf that states regarding ineligible s'chach less than three tefachim, that we cannot utilize lavud to consider the ineligible s'chach as if it would be valid s'chach (this would be beneficial to sleep under this area) because there presently is ineligible s'chach there.

A question is asked on this concept from a Gemora on daf 4. It is learned that if a sukkah is less than ten tefachim high and one dug a pit seven tefachim squared in the middle of the floor so that the sukkah is completed to a depth of ten tefachim, the sukkah will be valid if there is less than three tefachim between the edge of the pit and the sukkah wall. The reason why this sukkah is valid is because there is less than three tefachim from the pit to where the walls of this sukkah are situated. According to Tosfos and the Chacham Tzvi, how can we apply lavud there, when there is the ground (ledge) between the pit and the wall?

The Avnei Neizer O"C 309b resolves this question by explaining the concept of lavud. Lavud can function by creating something from nothing or it can make nothing from something. When there is open space less than three tefachim, the gap gets filled up and closed by its surroundings. This is evident from Rashi in Eruvin 9a that translates lavud as an extender. Likewise, when there is something separating a pit from the wall, lavud can extend the pit and transpose the ground to be considered open space.

The explanation in our Tosfos is that when there is ineligible s'chach less than three tefachim surrounded by valid s'chach, we cannot transpose the ineligible s'chach to nothing because there is valid s'chach surrounding it. We cannot consider this space as valid s'chach either because there is ineligible s'chach there presently.