What alternative criteria determine the validity of a minor's divorce?

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Sa'id ibn al-Musayyib stated that a minor's divorce is valid if he has attained the ability to perform prayer regularly and has completed fasting the month of Ramadan. 'Ata stipulated validity when the minor reaches the age capable of sexual intercourse (i.e., maturity in that respect). Al-Hasan linked validity to comprehension, consistent performance of prayer, and fasting Ramadan. Ishaq ibn Rahwayh held that the divorce is valid if the boy has exceeded twelve years of age.