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theorem proved tactic proof

lambda_one_is_unique_fixpoint

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formal statement (Lean)

  32theorem lambda_one_is_unique_fixpoint :
  33    ∀ lam : ℝ, 0 < lam → lam = lam⁻¹ → lam = 1 := by

proof body

Tactic-mode proof.

  34  intro lam hlam_pos hlam_eq
  35  have h1 : lam * lam = 1 := by
  36    have : lam * lam⁻¹ = 1 := mul_inv_cancel₀ (ne_of_gt hlam_pos)
  37    rw [← hlam_eq] at this; exact this
  38  nlinarith [sq_nonneg (lam - 1)]
  39
  40/-- **Theorem**: Among the Aczél family cosh(λt), λ = 1 is the unique
  41positive real that equals its own reciprocal. Since the zero-parameter
  42posture requires all structural constants to have O(1) Kolmogorov
  43complexity, and λ = 1 is the unique positive fixpoint of the inversion
  44map, calibration is forced. -/

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