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I really don't want to get into this, but since you asked. You are correct in your example. But the reason you are correct has nothing to do with the sensor.Why?
The DOF of a shot on a full-frame camera at 160mm/16 will be the same as the DOF of a shot on a crop camera at 100mm/10.
It has to do with the distance to subject and focal length of the lens. Using your example. If you shoot the same subject at 160mm/f16 standing from the exact same spot using a crop sensor camera and a full frame camera and then examine the same areas in both the crop and full frame image, they will show identical depth of field. In fact, you could take the crop image and overlay it onto the full frame image in Photoshop and they would be identical in depth of field in the cropped portion of the full frame image.
Depth of field is not sensor dependent. It only appears to be so, because you must change either your shooting position or, in the example you are using, the focal length of the lens, in order to get the same cropping in the final image.
Depth of field resides solely within the lens and distance to subject. Since depth of field is sensor independent, I don't like to use the term equivalence for depth of field, because people think it has something to do with the sensor, which it does not.
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