Commentary for Sukkah 7:10

A house where we reduce - ...its roof. Their roofs were made of separate components. They were of equal height, not beveled. And the middle section of the roof is removed.

Sekhakh is placed - ...with valid sekhakh, on the opening, and we find valid sekhakh that is far away from the walls on every side.

Less than four amah is valid - Since the walls of the house are made into valid walls [of the sukkah]. And the ceiling which is invalid [for sekhakh], between [the walls and the sekhakh], is considered to be part of the wall, and the wall into [the sekhakh]. [The ceiling] is not invalid sekhakh; rather, it is a wall that connects to valid sekhakh.