The difference between interlaced and progressive scan is nothing to do with resolution, it is only a different refresh system.

so 1080i is NOT lower res than 720P.

Interlaced scan refreshes every other line @25Hz (30Hz in usa)

Progressive scan refreshes every line @50Hz (60Hz in usa)

So progressive scan gives a sharper, clearer, less flickery picture, but it does not increase resolution at all.

1080i is higher res than 720P

720P is exactly the same res as 720i

1080p is exactly the same res as 1080i, clearer, maybe but the same resolution.