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necessary_is_one

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formal statement (Lean)

  81theorem necessary_is_one (x : ℝ) : RSNecessary x ↔ x = 1 := by

proof body

Term-mode proof.

  82  constructor
  83  · intro ⟨hpos, hzero⟩; exact (defect_zero_iff_one hpos).mp hzero
  84  · intro h; rw [h]; exact ⟨by norm_num, defect_at_one⟩
  85
  86/-! ## II. Possibility = Positive Ratio -/
  87
  88/-- **Theorem (Possibility is Positive Ratio)**:
  89    Anything with positive ratio is possible in RS.
  90    J-cost is finite for all x > 0, so all positive configurations can exist. -/

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