Is it permissible for one who has eaten on the Day of Ashura to complete the remainder of the day fasting, based on the transmitted hadiths?

It is permissible for one who intends to observe a voluntary fast to make the intention during the day, provided that they have not committed any acts that break the fast before making the intention. As for an obligatory fast, the intention for it must be made from the night before. The hadiths that mention the Prophet, peace and blessings be upon him, commanding those who had eaten or not eaten to complete the fast of Ashura were because the fast of Ashura was obligatory at that time. And whoever becomes aware of the obligation to fast during the day must refrain from eating and drinking from the moment they learn of it. However, after Ramadan was enjoined and the fast of Ashura became merely recommended, its ruling became the same as other supererogatory fasts, and it is not valid for one who has consumed a fast-breaking item at the beginning of the day to refrain from eating for the rest of the day.