What is the ruling on the fasting and prayer of one who performed ghusl at the beginning of the night, believing themselves to be pure, then became certain of impurity before Fajr and did not repeat the ghusl?

A woman knows her purity from menstruation by two signs: the emission of a white discharge (al-Qassah al-Bayda') or complete dryness. She should not hasten to perform ghusl until she is certain of her purity. If she ascertains purity before Fajr, fasting becomes obligatory upon her. If she does not ascertain it, her fast is not valid. If she performs ghusl without being certain of her purity, then ascertains it before Fajr, her fast is valid, but her prayer is not valid until she performs ghusl again. This is because fasting requires the cessation of menstruation, while prayer necessitates ghusl.