For our proof we develop techniques for flip sequences of triangulations whose counterparts were introduced for the study of flip sequences of non-crossing spanning trees by Bjerkevik, Kleist, Ueckerdt, and Vogtenhuber~[SODA25] and Bjerkevik, Dorfer, Kleist, Ueckerdt, and Vogtenhuber~[SoCG26].
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Forgetting releaseLock() permanently breaks the stream. The locked property tells you that a stream is locked, but not why, by whom, or whether the lock is even still usable. Piping internally acquires locks, making streams unusable during pipe operations in ways that aren't obvious.