Concept of "guessed ID" in Authenticated Identity-Based Encryption In Authenticated Identity-Based Encryption by Ben Lynn, in Proof of Integrity (section 4.3) and Proof of Security (section 4.4), I cannot grab the concept of "guessed ID" . Because encryption differs according to "guessed ID", I am unable to know how it works.

Is there anyone who can help explain this term and how it affects the proof?
"Guessed ID" means ID that the oracle guesses the attacker algorithm $A$ will attack.