'Proof' in the Bible

since they exhibit proof that a knowledge of the conduct which the Law requires is engraven on their hearts, while their consciences also bear witness to the Law, and their thoughts, as if in mutual discussion, accuse them or perhaps maintain their innocence--

But God gives proof of His love to us in Christ's dying for us while we were still sinners.

This is a proof that wherever He chooses He shows mercy, and wherever he chooses He hardens the heart.