Is it obligatory to perform the Witr prayer before sleeping if one intends to wake up for Qiyam al-Layl and the Fajr prayer?

The best time for a Muslim to pray Witr is at the end of the night, if he is confident he will wake up, based on the Prophet's (peace be upon him) saying: "Make the last of your prayers at night Witr." However, if he is not confident he will wake up, he should pray Witr before sleeping, based on the saying of Abu Hurairah (may Allah be pleased with him): "My beloved (peace be upon him) advised me with three things: fasting three days of every month, two rak'ahs of Duha (forenoon) prayer, and to pray Witr before I sleep." If he prays Witr before sleeping and then wakes up at the end of the night, he may pray whatever he wishes but should not pray Witr a second time, based on the Prophet's (peace be upon him) saying: "There are not two Witr prayers in one night."