What is entailed for one who led the people in prayer after wiping over his leather socks, believing he had put them on while in a state of purity, then it became clear to him that he had put them on without having performed ablution?

Among the conditions for wiping over the khuffayn (leather socks) is wearing them while in a state of ritual purity (tahara). Therefore, if someone wipes over them, having forgotten that he put them on while not in a state of purity, his ablution (wudu’) and prayer are invalid. If the worshipper remembers this while praying alone, he should exit the prayer, perform ablution, and repeat the prayer. If he remembers after the prayer, he should repeat the ablution and the prayer. However, if he was leading the prayer as an Imam and remembered after the prayer, their (the congregants') prayer is valid. Similarly, if he remembered during the prayer, he should exit and appoint someone else to lead, and their prayer is valid.