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theorem proved term proof

path_weight_max_at_eq

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formal statement (Lean)

  43theorem path_weight_max_at_eq (hbar : ℝ) (h : 0 < hbar) :
  44    ∀ r : ℝ, path_weight r hbar ≤ path_weight 1 hbar := by

proof body

Term-mode proof.

  45  intro r
  46  unfold path_weight
  47  apply Real.exp_le_exp.mpr
  48  apply neg_le_neg
  49  apply div_le_div_of_nonneg_right _ h
  50  exact Jcost_nonneg (by positivity)
  51
  52/-- Gaussian approximation near r = 1: weight ≈ 1 - ε²/(2ℏ). -/

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