I believe the concept here is that a doubling of f stop values from F11 to F22, halves the resolution of the lens, provided the lens is completely diffraction limited at both of those f stops.
Conversely, quadrupling the pixel count from 4mp to 16mp doubles the (potential) resolution of the sensor.
Therefore, doubling the resolution in the sensor, coupled with a halving of resolution from the lens, is equivalent to doubling the resolution from the lens coupled with halving the resolution in the sensor.
In practice, I suspect this is only a rough approximation.
The print size possible without interpolation depends only on the number of pixels, not the sharpness of the pixels.
A 4mp 35mm image taken at F11, interpolated to 16mp, should have roughly the same resolution on print as the uninterpolated 16mp 35mm shot taken at F22, but my guess is the interpolated 4mp image would have slightly less resolution in practice.