Talmud for Eruvin 1:2

הֶכְשֵׁר מָבוֹי, בֵּית שַׁמַּאי אוֹמְרִים, לֶחִי וְקוֹרָה, וּבֵית הִלֵּל אוֹמְרִים, לֶחִי אוֹ קוֹרָה. רַבִּי אֱלִיעֶזֶר אוֹמֵר, לְחָיַיִן. מִשּׁוּם רַבִּי יִשְׁמָעֵאל אָמַר תַּלְמִיד אֶחָד לִפְנֵי רַבִּי עֲקִיבָא, לֹא נֶחְלְקוּ בֵּית שַׁמַּאי וּבֵית הִלֵּל עַל מָבוֹי שֶׁהוּא פָחוֹת מֵאַרְבַּע אַמּוֹת, שֶׁהוּא אוֹ בְלֶחִי אוֹ בְקוֹרָה. עַל מַה נֶּחְלְקוּ, עַל רָחָב מֵאַרְבַּע אַמּוֹת וְעַד עֶשֶׂר, שֶׁבֵּית שַׁמַּאי אוֹמְרִים, לֶחִי וְקוֹרָה, וּבֵית הִלֵּל אוֹמְרִים, אוֹ לֶחִי אוֹ קוֹרָה. אָמַר רַבִּי עֲקִיבָא, עַל זֶה וְעַל זֶה נֶחֱלָקוּ:

What is required for a mavui [so that it be permitted to carry therein through shituf (partnership)] — Beth Shammai say: Lechi and korah. [Both are required, Beth Hillel holding that by Torah law four complete partitions are required, and halachah leMosheh miSinai ("a law unto Moses upon Sinai") permits lechi and korah as the fourth.] And Beth Hillel say: Either lechi or korah, [Torah law requiring three complete partitions and no more, and the halachah leMosheh miSinai adding the fourth through a lechi of any size or through a korah as sign of partition. "Mavui" here is a mavui closed on three sides and open to the public domain on the fourth, with its length greater than its width. For if length and width were equal, it would be like a breached chatzer (courtyard) opening into the public domain, requiring a board (pas) somewhat longer than four cubits, or two boards of any size. Likewise, a chatzer breached into the public domain is regarded as a mavui and is permitted with a lechi or a korah. And a mavui permitted through a lechi differs from one permitted through a korah. For a mavui permitted through a lechi is regarded as having four partitions and one who throws something into it from the public domain is liable, whereas a mavui permitted through a korah, even though it is permitted to carry therein through shituf, is not an absolute private domain, and one who throws something into it from the public domain is not liable, it being ruled that a korah serves as a sign (distinguishing the mavui from the public domain), and a lechi, as a partition.] R. Eliezer says: Two lechis. [He holds with Beth Shammai and requires a lechi on either side. The halachah is not in accordance with R. Eliezer.] It was said in the name of R. Yishmael that a certain disciple [R. Meir] said in the presence of R. Akiva: Beth Shammai and Beth Hillel do not differ in respect to a mavui [the width of] which is less than four cubits, [both agreeing] that either a lechi or a korah [suffices]. Where do they differ? Where it is from four to ten cubits, Beth Shammai requiring lechi and korah, and Beth Hillel, either lechi or korah. R. Akiva said: They differ in respect to both. [And the first tanna also holds that no distinction is made between wide and narrow. The Talmud explains that they (the first tanna and R. Akiva) differ in respect to a mavui less than four tefachim in width, one holding that neither lechi nor korah is required, and the other, that either lechi or korah is required. And it is not clear from their statements who requires it and who does not.]

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