Try to picture this. A fixed strap runs from the bottom of the hinged wall, through a slot at the bottom of the pop-up top, to the top of the wall. As you lift the top, the strap slides through the slot, lifting the wall. Except for the weight, would this work?
Hummm... I’m not sure of your scheme, so let me restate what I think the arrangement is:
The strap (cord) is anchored at the hinge and the top of the hinged wall but through an eyelet on the inside of the elevating top. In the down position the eyelet is at the hinge. In the raised position, the eyelet meets the top of the rotating wall.
This will not work because the cord will be too short while the top is being raised. Here is an example: Say the rotating wall is 30 inches high (i.e. the top elevates 30 inches). Now consider the triangle formed by the hinge, eyelet and anchor point on the top of the rotating wall when the top is half way up. The side of the triangle from the hinge to the eyelet is 15 inches (vertical). This leaves 15 inches of cord between the eyelet and the rotating top wall. Since the wall is 30 inches, the triangle has sides of 15, 15, and 30. The only triangle with these sides degenerates to a straight line, which is not possible for this configuration