DO MECHITZOS CAUSE STRINGENCIES?
Answer #2 (Rava): We find that Mechitzos cause stringencies!
It was taught that if one put Sechach on top of an Achsadra with [two walls on adjacent (Tosfos; Rashi - opposite) sides, beams on top from corner to corner, and] pillars [a Tefach wide, in two corners], it is Kosher. (See note 29 in Appendix);
If one extended (Tosfos R. Peretz; Rashi - built a wall next to) each pillar [parallel to and as long as the wall next to the pillar - see Perush Chai diagram, Perek 9 number 56, in the English Charts section], it is Pasul. (It has only two walls.)
Rejection #1 (Abaye): I hold that extending the walls would not disqualify it. In any case there are four walls due to Pi Tikra Yored v'Sosem (from the beams)!
Rejection #2 (Abaye): Even if you do not say Pi Tikra Yored v'Sosem, the extensions disqualify only because they remove Mechitzos!
Answer #3 (Rabah bar Rav Chanan): We find that Mechitzos cause stringencies!
(Beraisa): If half of a house has a roof, one may plant vines on one side and anything else on the other side. (It is as if there is a Mechitzah between them, due to Pi Tikra Yored v'Sosem);
If he completed the roof, it is forbidden!
Rejection (Abaye): It forbids because it removes the Mechitzah.
Answer #4 (Rava): We find that Mechitzos cause stringencies!
(Beraisa): Walls in a vineyard can cause leniencies and stringencies:
A leniency is that if a vineyard extends until a wall, one may plant [anything else] on the other side of the wall. If not for the wall, one would have to distance four Amos.
A stringency is that if a vineyard is 11 Amos from a wall, one may not plant anything else there. If not for the Mechitzah, one could distance four Amos and plant!
Objection (Abaye): Why didn't you challenge me from a Mishnah? (It is more authoritative than a Beraisa!)
(Mishnah - Beis Shamai): Karachas ha'Kerem (an empty area in the middle of a vineyard) must be 24 Amos [wide from one end of the vineyard to the other to permit planting something else in the middle];
Beis Hillel say, it must be 16 Amos. If it is less, one may not plant [another crop] there.
If it is [at least] 16, one may plant there, as long as he leaves Kedai Avodaso (the distance around from the vines needed to tend them, i.e. four Amos) from the vines on each side.
Beis Shamai say, Mechul ha'Kerem (an empty area between a vineyard and a fence) must be 16 Amos;
Beis Hillel say, it is 12 Amos. If it is less, one may not plant there.
If it is 12, one may plant there, as long as he leaves Kedai Avodaso from the vines.
Summation of objection: (You did not ask from the Mishnah because a Halachic Mechitzah does not cause the stringency, rather, the physical wall does.) After leaving four Amos for Avodas ha'Kerem, and four Amos next to the wall, which people do not plant [lest it ruin the wall], if four Amos remain, the area is important. If less than four Amos remain it is Batel to the vineyard. (The same applies to the Beraisa!)
THE WIDE RESHUS DOMINATES THE NARROW ONE
(Rav Yehudah): If there are three Karfifos in a row (encampments surrounded by Mechitzos of horizontal ropes or vertical stakes within three Tefachim of each other), and the middle one is narrower than the others (they have Gefufim, like the upper left diagram in Rashi), and there is one person in each,[the outer dwellers are considered to dwell in the narrow Reshus. When three people camp together,] the law of a caravan applies (Rashi - to the middle Karfef; Rambam - to all of them), so they may enclose as large an area as they need [and carry in it on Shabbos. Individuals may enclose only Beis Se'atayim per person];
Surely, if the middle one is wider than the others (it has Gefufim, like the bottom diagram in Rashi), and there is one person in each, they get only six Beis Sa'im. (No matter which way the middle person will go (we consider him to be in that Karfef), there are not three in any Karfef.)
Question #1: [When the middle one is wider,] if there is one person in each side Karfef and two in the middle Karfef, what is the law?
Whichever way the middle people will go, there will be three people (they are like a caravan);
Or, perhaps the middle people will go in different directions, and there will not be three in any Karfef!
Question #2: If you will say that the middle people will go in different directions, if there are two people in each side Karfef and one in the middle, what is the law?
Whichever way the middle person will go, there will be three;
Or, [they are not like three because] we do not know in which direction he will go!
Answer to both questions: We are lenient [to consider them like a caravan].
DOES A GIDUD JOIN WITH A WALL?
(Rav Chisda): If there are five Tefachim of Gidud (a vertical ascent from a lower surface to an upper surface, e.g. the ground of a Chatzer is five Tefachim above the ground of the neighboring Chatzer) and there is a wall five Tefachim [tall on top of the Gidud], they do not join to be considered a Mechitzah. (See Perush Chai diagram, Perek 9 number 64, in the English Charts section);
A Mechitzah must be 10 Tefachim of Gidud (a vertical ascent from a lower surface to a higher surface) or 10 Tefachim of a standard wall (it is 10 above the ground on both sides).
Question (Beraisa): If the ground of a Chatzer is 10 Tefachim above the ground of the neighboring Chatzer, or if there are five Tefachim of Gidud and five Tefachim of wall between them, they may be Me'arev separately, but not together. (Gidud and wall join to make a Mechitzah!)
If it is less than this, they may be Me'arev together, but not separately.
Answer (Rava): Rav Chisda agrees that Gidud and wall join to make a Mechitzah with respect to the lower Chatzer, for the lower Chatzer faces a wall of 10. (The top is 10 above their ground.)
Question: If so, we should say that the lower Chatzer may be Me'arev separately but not together, and the upper Chatzer may not be Me'arev separately [because it lacks a Mechitzah] nor together [because the lower Chatzer has a Mechitzah]!
Answer (Rabah bar Ula): The case is, the upper Chatzer has Gefufim (a proper 10 Tefachim wall on the side that borders the other Chatzer, and) up to 10 Amos is semi-breached (it is only five Tefachim tall. It is like an opening in their wall, therefore they may be Me'arev separately.)
Question (Seifa): If it (the wall) is less than this (five Tefachim), they may be Me'arev together, but not separately.
They should be able to be Me'arev together or separately! (Each has a wall with an opening.)
Answer #1 (Rabah brei d'Rava): The case is, the lower Chatzer is totally breached to the upper Chatzer.
Question: If so, the lower Chatzer should be able to be Me'arev together but not separately, and the upper Chatzer should be able to be Me'arev together or separately!
Answer: Indeed, this is true! The Seifa discusses the lower Chatzer. It may be Me'arev together, but not separately.
(Mereimar): Five Tefachim of Gidud and five Tefachim of wall join.
Ravina (to Rav Acha brei d'Rava): Did you learn anything (e.g. a Beraisa) about Mechitzos?
Rav Acha: No.
The Halachah follows Mereimar.
A WALL THAT FELL ON SHABBOS
Question (R. Hoshaya): Do dwellers who come on Shabbos (i.e. the wall that separated from them fell) forbid?
Answer (Rav Chisda - Mishnah): If a wide Chatzer was breached to a narrow Chatzer (some texts say vice-versa), the wide Chatzer is permitted, and the narrow Chatzer is forbidden, for it is like an opening of the wide one.
Rejection (Rabah): Perhaps the wall fell before Shabbos.
Abaye (to Rabah): Why do you say perhaps? You must say that it fell before Shabbos [for you accepted the following answer of Rav Huna]!
Question (Rabah): If one was Me'arev through an opening or window and it became sealed [on Shabbos], what is the law?
Answer (Rav Huna): Once Shabbos was permitted, the Heter stands.