For those I may have confused with poor wording:
* the timeline (defeated) plays out prior to OoT. How it play out is speculative, though I'd imagine anything we deem 'paradox' starts here.
* Link is defeated on this timeline, in a battle against Ganon (as stated in Hyrule Historia). This would mean Ganon is able to get his hands on all the Triforce, as we know he winds up with in LttP.
* How the timeline reverts to this point, again, would be speculative, though I'd suspect it's a result of Zelda attempting to return and prevent this tragedy from occurring at all. The bad dreams Link is getting, are flashes from the 'rewound' timeline.
* you play the other 2 timelines out from there, paradox and 'Hero of Time should SPECIFICALLY BE __' included.
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Locke: You assume Link would have survived on the DT. No matter how you look at it, my way or the generally accepted way, Link's survival is seriously up for debate. In both manners he would lose the Triforce, which already doesn't look good for him. We already know from OoT that however that battle plays out, Link fights to the end. So if he falls... he's not going to be alive to give existing memories to his younger self. So in this case it wouldn't be rewriting any rules; Link isn't specifically being sent back, so his past self is like anyone else when you go back in time -- he knows as much as anyone. But is sensitive to the darkness, ergo, dreams.
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Regarding Rauru, it all depends again on speculative points on how the defeated timeline would have played out. As I've said previously, Ganon and Zelda both appear to rush through the start, racing against one another to cause or prevent the catastrophe the other timeline will have showed them. Rauru, being an ancient sage, has every chance of also being sensitive of what's to come (allowing himself to barricade an area of the Sacred Realm that we know had become a stronghold in LttP. So whether he had an actual part in the defeated timeline, whether his part was the same, or whether he found himself unexpectedly overcome, I couldn't say. But he did know a lot about how the Hero of time should be, given that there hadn't actually been one yet.