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In the definition of $F_{NIZK}$ in [GOS06b], on receiving prove from a party, the functionality forwards the statement to the ideal world adversary $S$.

This ideal world adversary then creates a proof $\pi$ and replies to the ideal functionality, who forwards $\pi$ to the party.

Can someone give me an intuition why $S$ decides the proof for a given statement? Why can't the ideal functionality itself compute a proof and reply to the querying party?

Is it because you need it in the proof of security of the protocol?

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