As God said to Cain, "Where is... thy brother?" so He asks the world, "What have you done to My Son?" and the w o r l d answers, "Crucified Him." That is man.
The Holy Ghost convinces or demonstrates to the world its sin, as above (John 16:88And when he is come, he will reprove the world of sin, and of righteousness, and of judgment: (John 16:8)). Next, He demonstrates righteousness. Man's? No, God's righteousness. We have just to believe what it says. God is always righteous. How is it demonstrated? "Because I go to the Father." Christ glorified God on the cross (John 13), and God glorifies Him at His right hand. That is the demonstration of God's righteousness. You might have had
God's righteousness, man set aside, and no love, or you might have had man's idea of love forgiving sins, but where would righteousness be? But in the cross you have both.
What have we got then? When He glorified God on the cross, He was made sin for us. Then the Redeemer when glorified wants His redeemed. Thus I am made the righteousness of God in Christ.
Last, there is demonstration of judgment. The proof that Satan is the prince of this world, is the cross, and as such he is judged-judgment not executed yet, but he is judged.