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Washing the feet and the heels
This has been confirmed in mutawatir (continuous) reports from the Prophet, upon whom be peace, concerning his actions and statements. Ibn 'Umar said, "The Prophet lagged behind us in one of our travels. He caught up with us after we had delayed the afternoon prayer. We started to make ablution and were wiping over our feet, when the Prophet said, 'Woe to the heels, save them from the Hell-fire,' repeating it two or three times." (Related by al-Bukhari and Muslim.) Needless to say, the preceding obligations are the ones that Allah has mentioned in (al-Ma'idah 6).
Following the prescribed sequence
Allah mentioned the obligations in a specific order. He also differentiated the legs from the hands--though both of them have to be washed--from the head, which only needs to be wiped. The polytheists of Arabia would not differentiate items unless there was some benefit in doing so. The way Allah structured the ablution made it easier for them to comprehend it. Al-Ma'idah 6 explains what is obligatory and it falls under the generality of the Prophet's statement, "Begin with what Allah began with." The Prophet used to follow that sequence as one of ablution's principles. There is no such report that the Prophet, upon whom be peace, ever departed from that sequence. Ablution is part of worship, and in matters of worship there is no room for anything except doing what has been commanded.
"When a person dies, his works end, except for three: ongoing charity, knowledge that is benefited from, and a righteous child who prays for him."
Prophet Mohammed (PBUH)
"The best of what a man leaves behind are three: a righteous child who supplicates for him, ongoing charity the reward of which reaches him, and knowledge that is acted upon after him."
Sunan Ibn Mājah
"Every day two angels come down from Heaven and one of them says, 'O Allah! Compensate every person who spends in Your Cause,' and the other (angel) says, 'O Allah! Destroy every miser.'"
Sahih Bukhari