How to know if iphone 4s in FULLY unlocked?

I recently bought an Iphone from ebay (Haven't yet received it). The seller says that the phone was locked to O2, but it was properly unlocked by O2. As soon as i receive the phone i want to make sure that it is unlocked.

I have my sim from Cyprus. If i test the sim in the phone and it works fine then it means that it is unlocked?

Or i have to actually go to cyprus and see if the phone has signal from Cypriot carrier?

Thank you in advance!

Added (1). Something else, if the phone is properly unlocked by O2 and i update it to future iOS version, will it be relocked again?

Yes put any unlocked sim in iPhone to test it.

Put a sim into it.