No, it's quite simple. You assumed that the 4th Empire was NOT Greece to argue that the little horns were different people. I did NOT assume that the 4h Empire was Greece at all, that was the conclusion I came to AFTER identifying the two little horns as the same individual.
No, I did not. That would be circular logic. Here's my approach:
1) I conclude that the "little horns" in ch 7 and 8 are different based on their descriptions (e.g. one comes after 10 horns, the other comes from 4 horns).
2) The little horn of ch 8 comes from Greece, according to the text.
3) I conclude that the second empire matches best with the Medo-Persian ram, and the third with the Greek goat, based on their descriptions.
(Sorry for compressing/concatenating this in my first message and confusing you as to the approach.)
Here's your approach, as I see it:
1) You assume that the two "little horns" are the same.
2) This forces your conclusion that the 4th empire is Greece.