That was also taught in a baraita: If they placed their eiruv in the outer courtyard, and one person forgot to contribute to the eiruv, whether he is a resident of the outer courtyard or of the inner one, they are both prohibited. If they put their eiruv in the inner courtyard, and one resident of the inner courtyard forgot to contribute to the eiruv, they are both prohibited. Similarly, if one of the residents of the outer courtyard did not contribute to the eiruv, they are both prohibited. This is the statement of Rabbi Akiva. And the Rabbis disagree and say: In this case, where the eiruv was deposited in the inner courtyard and the person who forgot to contribute to the eiruv was a resident of the outer one, the inner courtyard is permitted and the outer one is prohibited.

Rabba bar Ḥanan said to Abaye: What is different according to the Rabbis, who say that the inner courtyard is permitted? It is because the residents of the inner courtyard can shut the door of their courtyard to the members of the outer one and use the inner courtyard on their own. But if so, according to Rabbi Akiva as well, let the residents of the inner courtyard shut the door of their courtyard to the members of the outer one and use their courtyard on their own. Abaye said to him: If the eiruv of the outer courtyard was not placed in the inner courtyard, your argument would be valid. But the fact that the eiruv is deposited in the inner courtyard accustoms the residents of the outer courtyard to enter it.

The Gemara asks: If so, according to the Rabbis as well we should say that the placement of the eiruv in the inner courtyard accustoms the residents of the outer courtyard to enter it. The Gemara answers: The reasoning of the Rabbis is that the members of the inner courtyard can say to the members of the outer one: We joined with you in a single eiruv to our benefit, and not to our detriment. Since one of your residents forgot to contribute to the eiruv, we no longer acquiesce to this partnership.

The Gemara asks: According to Rabbi Akiva as well, let the residents of the inner courtyard say to the residents of the outer courtyard: We joined with you to our benefit and not to our detriment. The Gemara answers that according to Rabbi Akiva, the case is that the residents of the outer courtyard said to the residents of the inner courtyard: We renounce our rights in your favor, in which case the inhabitants of the inner courtyard are permitted to carry in their own courtyard. Consequently, his ruling that the inner courtyard is also prohibited applies only before the residents of the outer courtyard renounce their rights. And the Rabbis hold that there is no renunciation of rights from courtyard to courtyard.

The Gemara asks: Let us say that Shmuel and Rabbi Yoḥanan, who disagree about whether there is renunciation of rights from one courtyard to another, disagree about the same point that was the subject of a disagreement between the Rabbis and Rabbi Akiva. As Shmuel said that there is no renunciation of rights from one courtyard to another, in accordance with the opinion of the Rabbis, and Rabbi Yoḥanan said that such renunciation is valid, in accordance with the opinion of Rabbi Akiva.

The Gemara responds: Shmuel could have said to you: What I said is even in accordance with the opinion of Rabbi Akiva. Rabbi Akiva stated his opinion that there is renunciation of rights from one courtyard to another only here, with regard to two courtyards, one within the other, which render each other prohibited. However, there, where they disagree about two adjacent courtyards, do the courtyards render each other prohibited? Consequently, even Rabbi Akiva would agree that there is no renunciation of rights from one courtyard to another.

And Rabbi Yoḥanan could have said: What I said is even in accordance with the opinion of the Rabbis. The Rabbis stated their opinion that there is no renunciation of rights from one courtyard to another only in the case here, as the residents of the inner courtyard said to the residents of the outer courtyard: Until you renounce your rights in our favor, you render it prohibited for us to carry, and therefore, we will have no connection with you and forgo both the renunciation and the prohibition. But there, does one courtyard prohibit the other? Since it does not, even the Rabbis would agree that there is renunciation from one courtyard to another.

We learned in the mishna: And if the courtyards belonged to individuals, i.e., if only one person lived in each courtyard, they are not required to establish an eiruv. Rav Yosef said: Rabbi Yehuda HaNasi teaches that if there were three people living in the two courtyards, whether two people lived in the outer courtyard and one person in the inner one, or two people lived in the inner courtyard and one person lived in the outer one, they are prohibited from carrying without an eiruv.

Rav Beivai said to the Sages: Do not listen to him, as he is mistaken. I told it to him, and I told it to him in the name of Rav Adda bar Ahava, not Rabbi Yehuda HaNasi, but due to his illness Rav Yosef forgot this detail. And the reason that the residents of both courtyards are prohibited from carrying if two people are living in the outer courtyard is that since I call them many in the outer courtyard, the Sages issued a decree prohibiting carrying, due to a case in which there are two people living in the inner courtyard. When he heard this, Rav Yosef said in astonishment: Master of Abraham! I mistook the word Rabbi for the word many [rabbim]. He now realized that he had mistakenly understood this ruling as attributed to Rabbi Yehuda HaNasi rather than a halakha regarding many, an error that led to his inaccurate version of the teaching.

And Shmuel said: Actually, they are permitted, unless there are two people living in the inner courtyard and one in the outer one.

Rabbi Elazar said: And a gentile is considered like many, i.e., if a gentile lives in the inner courtyard, the gentile’s right of way in the outer courtyard renders it prohibited to carry there. The Gemara asks: What is different about an individual Jew living in the inner courtyard, that he does not prohibit the resident of the outer courtyard? Because one who knows that only one person lives there knows this fact, and one who does not know this thinks that an eiruv has been established. If so, in the case of a gentile also, we should say that one who knows that only one person lives there knows, and one who does not know this thinks that the Jew must have rented the domain from the gentile.

The Gemara answers: This is not so, as a typical gentile, if he had rented out his domain, he would chatter about it, and everyone would know. If he has not talked about it, everyone will assume that he did not rent out his domain.

Rav Yehuda said that Shmuel said: If there are ten houses, one within the other, so that the person living in the innermost house must pass through all the rest in order to reach the courtyard, the innermost one alone contributes to the eiruv for the courtyard, and it is enough. The residents of the other houses are considered as living in the gatehouse and corridor of the innermost one, and therefore they do not have to contribute to the eiruv.

And Rabbi Yoḥanan said: Even the outer one must contribute to the eiruv. The Gemara asks: The outer residence is a gatehouse in relation to the inner ones, so why should it have to contribute to the eiruv? The Gemara answers that Rabbi Yoḥanan was referring to the outer house of the innermost one. In other words, even the second-to-last house, the outer one only in relation to the innermost house, must contribute to the eiruv, as it is not viewed as a gatehouse.

The Gemara explains: With regard to what principle do they disagree? One Sage, Shmuel, holds that the gatehouse of an individual is considered a gatehouse, and therefore the ninth house, i.e., the second innermost is also a gatehouse, as it serves as a passageway for the individual living in the innermost house, and one Sage, Rabbi Yoḥanan, holds that the gatehouse of an individual is not considered a gatehouse, and therefore the ninth house must also contribute to the eiruv.

Rav Naḥman said that Rabba bar Avuh said that Rav said: With regard to two courtyards that have three houses between them, and a resident of this courtyard comes through this house that opens to his courtyard and places his eiruv in that middle house, and a resident of this other courtyard comes through this house that opens to his courtyard and places his eiruv in that middle house,