Alive in Him, my living Head, And clothed in righteousness divine, Bold I approach the eternal throne, And claim the crown, through Christ my own.
It is this principle of righteousness imparted to men in regeneration which is ever in conflict with the old Adamic nature.
The judge decides the outcome of the dispute between the parties, declaring one to be correct and the other incorrect.
Paul was positing that the people of such faith are vindicated when Messiah returns, being declared "righteous" (or in other words, vindicated for their stance), which is exactly the meaning of the Biblical term "justified" in N. T. Wright's view.
(ESV), which has traditionally been interpreted to mean that the Christian has, in some way, become righteous (by infusion or imputation), in exchange for Jesus' sinlessness.
In fact, N. T. Wright says, Paul is speaking here of the apostles, and pointing out that in their role as apostles, their activity is effectively God's righteousness (covenant faithfulness) in action ("we are ambassadors for Christ, God making his appeal through us.