By the way, I like the space-time variant of the standard proof that van Emde Boas gives in https://people.irisa.fr/Francois.Schwarzentruber/sif2_thx/articles/tiling.pdf. "Basing the proof on the space-time diagram, uniqueness of the head position is a direct consequence of local consistency throughout the diagram and does not have to be enforced explicitly."
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