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theorem proved tactic proof

Jcost_nonneg

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formal statement (Lean)

  33theorem Jcost_nonneg (x : ℝ) (hx : 0 < x) : 0 ≤ Jcost x := by

proof body

Tactic-mode proof.

  34  unfold Jcost
  35  have : (x - 1)^2 / (2 * x) ≥ 0 := div_nonneg (sq_nonneg _) (by linarith)
  36  have : (x + x⁻¹) / 2 - 1 = (x - 1)^2 / (2 * x) := by field_simp; ring
  37  linarith
  38
  39/-! ## Residual Rate Action -/
  40
  41/-- The residual rate action A for a two-branch geodesic rotation
  42    with separation angle θ_s. A = -ln(sin θ_s) for 0 < θ_s < π/2. -/

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