Question: What is the source for this minimum?

The Answer was given by Rav, R. Chanina, R. Yochanan and R. Chaviva.

There is a tendency, throughout Moed, to substitute R. Yonasan for R. Yochanan when he is paired with R. Chaviva.

This is due to the fact that R. Yonasan was the Ben Zug to R. Chaviva.

They answered that the Aron was nine Tefachim (1.5 Amah), and its Kapores was an additional Tefach, and from above the Kapores Hash-m spoke with Moshe.

We were taught (R. Yosi) that the Shechinah does not enter the domain given over to Man, nor does Man (even Eliyahu and Moshe Rabeinu) enter the domain Above.

It then follows that a division between two things below (e.g. The Sukah and that which is beyond it) is created with a 10-Tefach divider.

Question: But we find that the Shechinah did come down (on Har Sinai)?

Answer: The Shechinah hovered above 10 Tefachim.

Question: But in Zechariah we read that the Shechinah will rest (lit. place its feet) on Har ha'Zeisim!?

Answer: Again, that will be above 10 Tefachim.

Question: But at Har Sinai we read that Moshe did go up to the place of the Shechinah!?

Answer: Beneath 10.

Question: But what of Eliyahu's stormy ascent to Shamayim!?

Answer: Again, beneath 10.

Question: But the Pasuk in Iyov (26:9) is understood to mean that Hash-m protected Moshe from the Malachim, surely taking place in Shamayim!?

Answer: That, too, was below 10.

Question: But that Pasuk makes reference to Moshe grabbing the Kisei ha'Kavod!?

Answer: The Kisei ha'Kavod came down within 10 for Moshe to grab.

Question: While height of the Aron is clear from the Pasuk, whence that the Kapores was a Tefach?

Answer: R. Chanina infers from the Misgeres that it was a Tefach.

The height, width and length of all the Kelim in the Mishkan are stated excepting the height of the Kapores, which must be inferred.

We deduce this from the minimum height recorded for any of the Kelim, the rim (Misgeres) around the Shulchan, which is a Tefach.

Question: Learn from Kelim themselves (all of which were taller than a Tefach) rather than from a part of a Kli?

Answer: Always adopt the minimum Chidush (Tafasta Merubah).

Question: Then learn from the Tzitz, which was only two Etzbaos tall (the details of the Tzitz are described and debated in the cited Beraisa)?

Answer: We derive the dimensions of a Kli from another (the rim), not a Kli from an adornment (the Tzitz).

Question: Learn from the crown-edge (Zer) of the Aron, Mizbe'ach and on the Misgeres of the Shulchan (which was a Mashehu)?

Answer: We derive the dimensions of a functional Kli from another Kli and not from a "touch" (Hechsher) of the Kli.

Question: But the Misgeres was also a Hechsher!?

Answer: The Misgeres was integral in that it ran from leg to leg under the tabletop of the Shulchan.

Question: But what of the opinion that the Misgeres was above the tabletop (it would seem to be a Hechsher)?

Answer: Rather, we learn from the Misgeres (and not from the Tzitz or the Zer) because we derive the measurement of the Kapores whose (other) measurements are stated, from that whose measurements are stated (ie. the Misgeres, and not from that which has no stated measure [the Tzitz and Zer).

Answer (R. Huna): We know that the Kapores was a Tefach because the Torah refers to it as having a Panim (a face is never less a Tefach).

Question: Then why not use the measure of a huge beast (with a larger face)?

Answer: Tafasta Merubah Lo Tafasta...(minimum Chidush).

Question: Then use the measure of a small-faced creature?

Answer: We link this Panim to the Panim of a person (Yitzchak Avinu) which is never less than a Tefach.

Question: Why not link it to the limitless Panim of P'nei Elokim!?

Answer: Tafasta...

Question: Learn from the Keruvim (which were on the Kapores and whose faces were less than a Tefach).

Answer: We have a tradition that the faces of the Keruvim were at least a Tefach.

R. Huna also derived his measurement based on this tradition.

Indeed, its name, Keruv, derives from the word (in Babylonian) for baby (Ravia) indicating that the face was like that of a baby.

Question: But the Pasuk in Yechezkel (10:14) differentiates between the face of a person and the face of a Keruv!?

Answer: One is the child and one is the adult.

Question: If we derive the height of the Sukah from the Aron and Kapores, perhaps that includes the Sechach, as well (how do we know that the interior height must be 10 Tefachim)?

Answer: Rather, we learn the height of the Sukah from the Beis ha'Mikdash.

In both the Mikdash and Mishkan the Keruvim stood one- third the height of the building itself.

In the case of the Mishkan, this would make the Keruvim 10 Tefachim (they reached 20 Tefachim, a third of the 60 Tefach height of the Mishkan, less the 10 Tefach height of the Aron and Kapores, as above).

The Keruvim are called "Sochechim," a reference to Sechach (assuming that the wings of the Keruvim are 10 Tefachim above the Kapores).

Question: How do we know that their wings rose above the heads; perhaps the wings were level with the heads, and there was not the 10 Tefach open space beneath the Keruvim to derive a 10 Tefach interior Sukah height?

Answer (R. Acha b. Yakov): The Pasuk says "above," implying above the heads.

Question: Perhaps they were further above the heads!?

Answer: The Pasuk says l'Ma'alah, not more than that.

Question: This all works using the opinion of R. Meir (that the Amos of the Kelim of Mishkan were of six Tefachim as were the parts of the building), but what of R. Yehudah who holds that the Kelim (unlike the building) were made of five-Tefach Amos.

The Aron and Kapores then work out to 8.5 Tefachim, leaving the distance from the Kapores to the Keruvim of 11.5 Tefachim (still working with a third of the total 60-Tefach height of the Mishkan).

We would then have to make the minimum height of a Sukah 11.5 Tefachim!?

Answer: According to R. Yehudah the source for a 10-Tefach minimum Sukah derives from Halachah l'Moshe mi'Sinai (as R. Chiya taught).