If semen is discharged from the vagina during the day after intercourse at night, does that invalidate the fast, and is ghusl (ritual bathing) required to perform the prayer?

Fasting is not invalidated by the emission of semen during the day after nocturnal intercourse, because intercourse is permissible on the night of fasting until the dawn breaks. The semen is a result of a permissible act of intimacy. It is not obligatory to repeat the ritual bath (ghusl (definition)) if semen is discharged after having already performed ghusl, because the cause is the same. However, ghusl becomes obligatory if semen is discharged due to a new urge.