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rational_distance_problem

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Does there exist a point in the plane at rational distance from all four vertices of the unit square?

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Lean 4 Statement 
theorem rational_distance_problem :
    answer(sorry) ↔ ∃ P : ℝ² , ∀ i, ¬ Irrational (dist P (UnitSquareCorners i))
ID: Wikipedia__RationalDistanceProblem__rational_distance_problem
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