Where We Stand as of Wednesday

Last night, we spent time reviewing the first suggestion of the Gemara - to view the Machloket between R. Elazar and Chachaim as a machloket on יש/אין דיחוי - and we proceeded to the Gemara's rejection of this proposal. The Gemara begins its rejection by saying that both RE and Chachamim hold אין דיחוי...

We pointed out at the time that this is fine for Chachamim, who hold that the de-berried hadas is kosher, but for R. Elazar, on what basis would the hadas be pasul if RE holds אין דיחוי?

The Gemara now proposes that the two sides are divided on the question as to whether or not we learn Lulav from Succah.

We noted that this must mean that the Gemara is re-visiting the possibility that Lulav needs an אגד. Learning Lulav from Succah means that we are considering a psul of תעשה ולא מן העשוי, since our last mention of Succah was in the framework of a mitzvah that had a component of עשיה, from the pasuk of חג הסוכות תעשה לך....Rashi, reading this between the lines, has this to say: (see italics)

Rashi:
לא דכולי עלמא לא אמרינן יש דחוי במצוה - וטעמא דמאן דפסל משום תעשה ולא מן העשוי הוא, דקסבר: לולב צריך למיגד, ושייך ביה עשיה, והכא במילף לולב מסוכה פליגי.

But now that we say this, ie that RE's psul is based on Lulav needing an egged and ta'aseh --- what is the machloket between RE and Chachamim?

Frank suggested that it is whether or not Lulav needs an egged. RE says yes, therefore a psul of ta'aseh, and Chachamim say no, therefore no such psul. But we ended the shiur by showing that if that is what the Gemara was saying, it certainly didn't say it! Rather, the Gemara says that the machloket is on whether or not we learn lulav from Succah. What does this mean?

The key for tonight is the next Rashi:

ילפינן - בבנין אב, הואיל וזה בעשיה וזה בעשיה, מה זה ולא מן העשוי - אף זה ולא מן העשוי.

What is a "binyan av" and how is it applicable to this answer?