Is it a condition for the validity of worship to believe in its validity before performing it, and is worship invalidated if performed while doubting its validity?

A person who prays while doubting the entry of the prayer time has an invalid prayer, even if it later becomes clear that it occurred within the time. This is because he proceeded with it believing in its invalidity. Similar to this is doubting the complete washing of a limb with water during ablution (wudu'); one must be certain or predominantly assume the complete washing. Therefore, a Muslim should not perform an act of worship while believing in its invalidity, or doubting the fulfillment of its conditions for validity.