Is it permissible to say "may Allah have mercy on him" (yarhamuhu Allah) for the Prophet (peace be upon him)?

Scholars have differed on the permissibility of supplicating for mercy upon the Prophet, peace and blessings be upon him. Some have deemed it permissible, while others have prohibited it. The argument of those who prohibit it is that the Prophet, peace and blessings be upon him, taught us to invoke blessings upon him without mentioning mercy, and that the word "mercy" implies the existence of sin. The correct view is the permissibility of supplicating for mercy and forgiveness for him, as evidenced by the statement of the Bedouin in the presence of the Prophet, peace and blessings be upon him: "O Allah, have mercy on me and Muhammad, and do not have mercy on anyone else with us." The Prophet, peace and blessings be upon him, did not rebuke him.