Pictured in this order:

1. Ghost of previous goalpost
2. Current goalpost

1.          2.
!           |
!           |
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You don’t need to declare independence to be independent. Only if you were dependent in the first place you claim independence.

ROC was never dependent on PRC. They just both claim the same territory. They are 2 independent countries that claim the same territory, just like both Israel and Palestine are 2 independent countries that claim the same territory.