This is just an inconsistency/annoyance.
The PS of ETN makes reference to the Eastern Imperial Temple of Haelyn. Furthermore, until the ousting of House Aeren, this temple existed in Aerenwe (1495 or so).
The IHH makes no reference to the eastern imperial temple of Haelyn, but has been in existence since after the split of the Imperial Temple.
So confused, is the IHH the eastern imperial temple of Haelyn? Or is there some other temple that was in existence and is now a goner?