Yup
I was actually a bit wrong on that, if you meant true, born as baby, children. If he hasn't got children who haven't come of age yet coded for him in descr_strat, and faction expands so game starts wanting to give it more generals, he's likely to end up with adopted generals filling the slots, especially if its an AI controlled faction.
the other thing to look at would be to use an ancillary derived from the inherited traits, which is passed to real son and heirs.... you can quite easily code monitors to use
checking for faction not having a trait is messier as there isn't a FactionwideTraitExists command, though you could probably get round it with countersand not FactionwideAncillaryExists Im_a_heir_anc true
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