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theorem proved term proof

J_log_nonneg

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formal statement (Lean)

  53theorem J_log_nonneg (t : ℝ) : J_log t ≥ 0 := by

proof body

Term-mode proof.

  54  simp only [J_log]
  55  have h : Real.cosh t ≥ 1 := Real.one_le_cosh t
  56  linarith
  57
  58/-- J_log is zero iff t = 0.
  59    Proof: cosh t = 1 iff t = 0 (by AM-GM on e^t + e^{-t}). -/

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