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theorem proved tactic proof

row_fermi_pred_upper

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formal statement (Lean)

  80theorem row_fermi_pred_upper :
  81    row_fermi_pred < (1.17e-5 : ℝ) := by

proof body

Tactic-mode proof.

  82  unfold row_fermi_pred
  83  rw [div_lt_iff₀ fermi_den_pos]
  84  have hs : (1.4142 : ℝ) < Real.sqrt 2 := sqrt2_gt_14142
  85  have hden :
  86      (1.4142 : ℝ) * (246 : ℝ) ^ 2 < Real.sqrt 2 * vev_canonical ^ 2 := by
  87    have hv : vev_canonical = (246 : ℝ) := rfl
  88    rw [hv]
  89    nlinarith
  90  have hnum : 1 < (1.17e-5 : ℝ) * ((1.4142 : ℝ) * (246 : ℝ) ^ 2) := by
  91    norm_num
  92  nlinarith
  93

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