What is the grammatical role of "did" in the following excerpt of a passage?:
The smoke just went out the same hatchway that people used for going in and out themselves. So there would have been an open fire inside the house with only one hole in the roof to let the smoke out. You and I would have found it a bit too smoky in there. You can see on the walls, which they plastered and decorated with paintings. They ended up with a layer of black soot on them, and so did people’s lungs.