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Amud 7b

תוס' ד"ה ואם

And if one carves out in it an area of four טפחים by four טפחים, etc. - ואם חקק בו דע"ד

Summary:
Regarding a סוכה if the distance from the חקק to the outer wall is less than three טפחים, then by utilizing לבוד, the outer wall is joined to the גידוד החקק and forms one straight מחיצה which is סמוך לסכך כשר שע"ג החקק. If however the distance is three טפחים or more, it is a סוכה פסולה. By שבת on the other hand, the area of the חקק is bounded by מחיצות עשרה, through combining the heights of the two מחיצות. We utilize the concept of דופן עקומה only when there is a valid independent מחיצה. if the wall is not גבוה by itself, we cannot accord it the status of a דופן עקומה.

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תוס' ד"ה התם

There its use in not convenient - התם לא ניחא תשמישתיה

Summary:
There are different levels of ניחא תשמישתיה. The least ניחא תשמישתיה is a קרן זוית, the most is חורי רה"ר , and צדי רה"ר is somewhere in between (according to the רבנן it is ככרמלית and according to ר"א it is כרה"ר). In order for an area to be recognized as an extension of the רה"ר it must have the convenience of at least חורי רה"ר, anything less, even if it has the convenience of צדי רה"ר is not sufficient to render it a רה"ר (according to the רבנן).

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תוס' ד"ה והלכה

And it traveled and landed in a miniscule crevice, this depends on the argument between רבי מאיר and the רבנן, etc. - והלכה ונחה בחור כל שהוא באנו למחלוקת רבי מאיר ורבנן

Summary:
תוספות will be discussing how can we compare חוקקין להשלים by מזוזה to חוקקין להשלים by a חור כ"ש. Consequently that will compel תוספות to reinterpret the question וכ"ת דלית בי' דע"ד and the s'גמרא apparent acceptance that we follow the ruling of ר"מ against the majority opinion of the רבנן.

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