In the private key CPA game, the attacker has access to an encryption oracle anytime during the attack.
However, I have seen this statement in lecture notes I downloaded "You can prove that for every polynomial time attacker that uses the encryption oracle after receiving the challenge cyphertext, you can construct another polynomial attacker that also breaks the encryption scheme only querying the oracle before receiving the challenge cyphertext."
I have tried to do reductions but I don't see how I could use the first type of attacker to build the second type, since the first requires oracle queries after knowing the challenge cyphertext.
I have also tried to search this but was unable to find.