<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def derived_from_all(self, identities: List[QualName]) -> MutableSet[QualName]: """Return list of identities transitively derived from all `identity`."""

        if not identities:
            return set()
        res = self.derived_from(identities[0])
        for id in identities[1:]:
            res &= self.derived_from(id)
        return res