The Commander of the Faithful (PBUH) judged in the case of a man against whom two witnesses testified that he…

The Commander of the Faithful (PBUH) judged in the case of a man against whom two witnesses testified that he had stolen, so his hand was cut off. Later, the two witnesses brought another man and said: “This is the thief, not the one whose hand was cut off; we only mistook him for this man.” So he (PBUH) ruled that the two witnesses must pay half the blood money, and he did not accept their testimony against the other man. Does this mean that the hand of an innocent man was cut off?