Eruvin, Chapter 6, Mishnah 8. This mishnah discusses the relationship between eruvei chatzeros (courtyard eruvin) and shitufei mevo'os (alleyway partnerships) operating side by side: when one is effective in place of the other, and when it is not.
They made an eruv in the courtyards but did not make a partnership in the alleyway:
"Chamesh chatzeros pesuchos zu la'zu u'fesuchos la'mavoi" - five courtyards that have openings from one to another, and all of them also open into the alleyway. Each courtyard made an eruv on its own, so that it would be permitted to carry within it from the various houses into the courtyard, and the courtyards are joined to one another by virtue of the openings between them. However, they did not make a separate partnership in the alleyway itself, since their intention was only to carry among themselves, without passing through the alleyway.
"Mutarin ba'chatzeros va'asurin ba'mavoi" - they are permitted in the courtyards, for that is precisely what the courtyard eruv accomplished; but they may not carry in the alleyway. This is the opinion of Rabbi Meir, who holds that both an eruv of courtyards and a partnership of alleyways are required, so that future generations will not forget that there is a need for eruvei chatzeros and a need for shitufei mevo'os - and particularly in a case where the two are separate from each other. And where no eruv was made between the courtyards, a partnership of the alleyway is certainly required.
They made a partnership in the alleyway:
"Ve'im nishtatfu ba'mavoi - mutarin kan ve'kan" - once they also made a partnership of the alleyway, they are permitted in both: in the alleyway and in the courtyards. The commentators explain that even if no eruv was made between the courtyards, the partnership of the alleyway is effective to allow carrying from one courtyard to another. It does not take the place of the eruv made within each individual courtyard - that must be done separately - but it does cover the ability to carry from one courtyard to its neighbor.
One of the residents of the courtyard forgot:
"Eirvu ba'chatzeros ve'nishtatfu ba'mavoi, ve'shachach echad mi'bnei chatzer ve'lo eirev - mutarin kan ve'kan" - both were made, an eruv of the courtyards and a partnership of the alleyway, except that one of the residents of a courtyard did not join the courtyard eruv of his courtyard, and the halachah is that they are permitted in both places.
The reason for this: we said that the partnership of the alleyway is not effective and does not take the place of the courtyard eruv, and that a courtyard eruv must be made separately, because of the concern that the next generation will forget that a courtyard eruv must be made in its own right - a courtyard eruv is indispensable in a situation calling for a courtyard eruv, and a partnership of the alleyway is required where there is a partnership of the alleyway, and we are concerned that they will think they have no need for a courtyard eruv at all. But in this case, where everyone made the eruv and only a single individual forgot, there is no room for the concern that they will think the partnership of the alleyway is all that is needed and that a courtyard eruv is unnecessary: after all, before their very eyes both were made, and only one person forgot. Therefore the partnership of the alleyway does cover the courtyard eruv here, even though one person was left out of it.
One of the residents of the alleyway forgot:
"Echad mi'bnei mavoi ve'lo nishtatef - mutarin ba'chatzeros va'asurin ba'mavoi" - one of the courtyards in the alleyway forgot and did not join the partnership of the alleyway. They are permitted in the courtyards, since they made a courtyard eruv; but they are forbidden in the alleyway, since the partnership of the alleyway was not made properly, and a complete partnership of the alleyway is required.
"She'ha'mavoi la'chatzeros ke'chatzer la'batim" - just as with a courtyard eruv alone, if one person remained outside the eruv and there is no partnership of the alleyway, they may not carry in the courtyards, so too here: if one courtyard remained outside the partnership of the alleyway, they may not carry in the alleyway. The courtyard eruv cannot help the partnership of the alleyway, even though a courtyard eruv was made here - and even though the reverse relationship does exist, that the partnership of the alleyway is sometimes effective for the courtyard eruv in a case where one person forgot.
In summary: in this mishnah we learned the relationship between eruvei chatzeros and shitufei mevo'os. If they made an eruv in the courtyards but no partnership in the alleyway - they are permitted in the courtyards and forbidden in the alleyway, according to Rabbi Meir, who requires both so that the need for each one will not be forgotten. If they made a partnership in the alleyway - they are permitted in both, and the partnership of the alleyway is effective even for carrying from courtyard to courtyard, but not for the eruv within each individual courtyard. If one of the residents of the courtyard forgot - they are permitted in both, since there is no concern that the need for a courtyard eruv will be forgotten. If one of the residents of the alleyway forgot - they are permitted in the courtyards and forbidden in the alleyway, for the alleyway is to the courtyards as the courtyard is to the houses, and the courtyard eruv is not effective for the partnership of the alleyway.