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theorem proved tactic proof

b1_pos_lowNf

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formal statement (Lean)

  54theorem b1_pos_lowNf (N_f : ℕ) (hNf : N_f ≤ 8) : 0 < b1 N_f := by

proof body

Tactic-mode proof.

  55  unfold b1
  56  apply div_pos _ (by positivity : (0 : ℝ) < 8 * Real.pi ^ 2)
  57  have hNf_real : (N_f : ℝ) ≤ 8 := by exact_mod_cast hNf
  58  linarith
  59
  60/-- At N_f = 5 (canonical between bottom and top thresholds): b1 > 0. -/

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