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A Link Between Worlds was originally intended to be a remake of A Link to the Past, rather than a distant sequel.In fact we visit both Lorule and Hyrule's Sacred Realms in this game. Lorule drinks heavily from A Link to the Past's version of the Dark World, but it's more like a paralel universe, akin to Termina (while the Dark World is more deeply connected to Hyrule itself, being a corrupted version of its closest analogue to a heaven, the Sacred Realm). Just like we have two mirrors with dark tribes sealed within, a bunch of swords that look and act like the Master Sword, a lot of sacred powers passed down the royal family bloodline, etc. Nintendo just likes reusing themes without actually connecting them.The differences are a little bigger than the single event that differs between the AT and the DT, but it's still closer to them than, say, Termina is. It has its own Sacred Realm, for instance. Lorule actually seems to be more of an Alternate Universe rather than just a world in the same multiverse.Presumably it exists in the other timelines, but we've just never seen it before. Lorule isn't so much an alternate universe so much as it and Hyrule are part of the same multiverse.
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There are the Adult Link and Child Link timelines, then there is the timeline where the Hero of Time loses, which is where this game takes place. Post Ocarina of Time, there are 3 main time lines. and this makes how many Alternate Universes? It's effectively a what-if universe where the Triforce was destroyed instead of sealed in the Sacred Realm. It's a thematically similar, but distinct, alternate world.
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It'a also possible that, at some point in the distant past, there was some contact between Hyrule and Lorule, possibly between their dignitaries, and the shield was passed from Zelda's ancestors to Hilda's as a gift and subsequently hidden as one of the treasures inside Turtle Rock.Alternatively, it was placed there by the powers that be, in order to help Link.
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As for the shield itself, with its Hyrulean elements (the Triforce pointing up), the above is probably right. So it's possible that the pointy-eared inhabitants of Lorule are also called Hylian. Hylian is the race (revealed to be named after the goddess Hylia in Skyward Sword), Hyrulean is the nationality of people born in Hyrule. It's worth mentioning that "Hylian" has no real connection to "Hyrule".Maybe someone stole it (is "Lolian" even used in the game?) from Hyrule and left it there.What is the Hylian Shield doing in Lorule? It's the equivalent of finding a Lolian Shield complete with inverted Triforce in Hyrule.
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