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Although this photo shows the front wheel in the lid of the case, the wheel is actually placed on top of the other items then the compression members are installed before closing the case. The next photo shows the wheel and compression members in place.
From this photo, it looks like the lid won't close over the wheel and tire but that is due to the perspective of the photo. In the previous photo, it's easy to see that the wheel fits into the case. To close the lid, it is necessary to deflate the tire and gently push the tire into the lid while closing it.
Photos provided by Lennard Zinn