Socrates's Intuition Pump

Socrates never says, ok, how will we make the citizens r laws just? Or what's the next step to improve the justice of this constitution? He appeals instead to other ideals. And then once they're done building it and they say, gee whiz, here's what justice is. They act like they'r discovering an objective fact when they've been building their preconceptions about justice into the analogy from the beginning. So isn't that reasoning circular? I guess the two best defences i've heard against that objection are, number one, socrates and co don't actually rely on the concept of justice during the city building exercise. But even if they are, there still