Amud 28a

תוס' ד"ה ואם

And if he was a Kohain, she should not live in the same street with him - ואם היה כהן לא תדור עמו במבוי

Summary:
A ישראל may live in the same שכונה as his former unmarried wife. If she remarried they may live in the same מבוי but not in the same שכונה, this applies to an אשת כהן as well. However by a כהן if she is still single he may not live even in the same מבוי as his former unmarried wife.

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תוס' ד"ה כפר

A small village is treated as a Shchuna - כפר קטן נידון כשכונה

Summary:
A small village is like a (מבוי (שכונה (the lack of people make it easier for him to be with her), but an average village is like a city.

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תוס' ד"ה רב הונא

רב הונא said, we surely smite them - רב הונא אמר נגודי מנגדינן להו

Summary:
ר"ה requires מלקות besides the שמתא. A שמתא is more severe than מלקות.

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תוס' ד"ה אלו

These are believed to testify as adults what they saw in their childhood - אלו נאמנין להעיד בגודלן מה שראו בקוטנן

Summary:
בדיקת חמץ is somewhat בידו, therefore נשים עבדים וקטנים are believed only because it is a דרבנן; by a complete בידו like ניקור וחלה, a woman is believed even by a דאורייתא; where it is not בידו at all, only גדולים can testify what they saw בקוטנן (and only by a דרבנן).

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תוס' ד"ה והוא

Provided that there is an adult with him - והוא שיש גדול עמו

Summary:
By תרומה, one person is sufficient to testify what he saw בקטנותו.

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תוס' ד"ה קיום

Verification of notes is a Derabonon - קיום שטרות דרבנן

Summary:
It is understandable that קיום is מדרבנן in the case of מודה בשטר שכתבו or if it was an inferior קיום, but not that קיום in general is מדרבנן.

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תוס' ד"ה ודלמא

But perhaps he is the slave of a Kohain - ודלמא עבד כהן הוא

Summary:
We are not concerned that an עבד שנשתחרר will request תרומה.

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