How can anyone prove forgiveness?

It can be a bit tricky. The court would have to look at the acts and actions of the parties in order to ascertain whether there has been adequate forgiveness. If the couple resumes marital relations, then there could be said to be forgiveness. Some states require the resumption of marital relations, while others say a mere statement of forgiveness is adequate.
Forgiveness also must be genuine and not be because of fear or duress.