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theorem proved term proof

self_ref_query_impossible

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formal statement (Lean)

  86theorem self_ref_query_impossible : ¬∃ q : SelfRefQuery, True := by

proof body

Term-mode proof.

  87  intro ⟨q, _⟩
  88  -- q.self_ref says: (defect config = 0) ↔ ¬(defect config = 0)
  89  -- This is impossible: P ↔ ¬P has no model
  90  have h := q.self_ref
  91  -- Assume defect config = 0
  92  by_cases hd : defect q.config = 0
  93  · -- If defect = 0, then by self_ref, ¬(defect = 0)
  94    have : ¬(defect q.config = 0) := h.mp hd
  95    contradiction
  96  · -- If defect ≠ 0, then by self_ref.symm, defect = 0
  97    have : defect q.config = 0 := h.mpr hd
  98    contradiction
  99
 100/-- **COROLLARY**: No consistent configuration can be a self-referential
 101    stabilization query. Such "configurations" are syntactically expressible
 102    but ontologically empty. -/

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