Is the rule "whoever's prayer is valid for himself, it is valid for others (his imamate)" absolute, given that there are categories whose imamate is not valid except for those like them or those inferior to them, such as the illiterate, and one who abandons a pillar like the mute, and women?

There are cases where the rule "whoever's prayer is valid for himself, it is valid for others" does not apply. These include: the imamate of a mute person, someone unable to perform a pillar like bowing or prostration, someone who makes a grammatical error in Al-Fatiha and is unable to correct it, and a woman leading other women in prayer.