What is the ruling regarding someone who believed he had ablution (wudu'), then remembered during the establishment of prayer (iqamat as-salat) that he did not have ablution, so he continued to perform the actions of prayer without the intention of prayer, and then he performed ablution and prayed afterwards?

Whoever begins prayer and then something that invalidates ablution occurs to him, or he remembers it during the prayer, must stop his prayer because it becomes invalid, and he should resume it after purifying himself again; this is based on the Prophet's (peace be upon him) saying: "The prayer of one who has invalidated his ablution is not accepted until he performs it again."