Convicted of Sin

This is "study" is in response to someone who has said that it is the Holy Spirit that convicts us of sin but I have searched and searched and I cannot find a scripture reference where it says that "the Holy Spirit convicts one of sin"

I did find where it says the Spirit will REPROVE the world of sin because they did not believe on Christ:

(John 16:7-11 KJV) Nevertheless I tell you the truth; It is expedient for you that I go away: for if I go not away, the Comforter will not come unto you; but if I depart, I will send him unto you. {8} And when he is come, he will reprove the world of sin, and of righteousness, and of judgment: {9} Of sin, because they believe not on me; {10} Of righteousness, because I go to my Father, and ye see me no more; {11} Of judgment, because the prince of this world is judged.

In Webster’s 1828 dictionary on the definitions of convict is to convince of sin; to prove to be guilty, as by conscience. To which there is a passage which supports this idea that it is the conscience that convicts one of sin.

(John 8:6-9 KJV) This they said, tempting him, that they might have to accuse him. But Jesus stooped down, and with his finger wrote on the ground, as though he heard them not. {7} So when they continued asking him, he lifted up himself, and said unto them, He that is without sin among you, let him first cast a stone at her. {8} And again he stooped down, and wrote on the ground. {9} And they which heard it, being convicted by their own conscience, went out one by one, beginning at the eldest, even unto the last and Jesus was left alone, and the woman standing in the midst.

Paul tells us that the conscience bears witness of the work of the law:

(Romans 2:15 KJV) Which show the work of the law written in their hearts, their conscience also bearing witness, and their thoughts the mean while accusing or else excusing one another;

What is the work of the law?
The law tells us that we are guilty before God and by the law is the knowledge of sin:

(Romans 3:19-20 KJV) Now we know that what things soever the law saith, it saith to them who are under the law: that every mouth may be stopped, and all the world may become guilty before God. {20} Therefore by the deeds of the law there shall no flesh be justified in his sight: for by the law is the knowledge of sin.

I also find it interesting that the only verse that says ones were convicted of the sin is John 8:9 and that the modern versions: RSV, NEB, JB, NAS, NIV all omit "being convicted by their conscience"

Since the definition of convict is: "to find or prove guilty" and "to convince of error or sinfulness" then can we not conclude that it is by the law that we are found guilty of sin and our conscience is what convicts us?